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Research Article Design of a Reliable Hybrid (PV/Diesel) Power System with Energy Storage in Batteries for Remote Residential Home Vincent Anayochukwu Ani Department of Electronic Engineering, University of Nigeria, Nsukka 410001, Nigeria Correspondence should be addressed to Vincent Anayochukwu Ani; vincent [email protected] Received 17 March 2016; Accepted 26 May 2016 Academic Editor: Mohamed Benghanem Copyright © 2016 Vincent Anayochukwu Ani. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is paper reports the experience acquired with a photovoltaic (PV) hybrid system simulated as an alternative to diesel system for a residential home located in Southern Nigeria. e hybrid system was designed to overcome the problem of climate change, to ensure a reliable supply without interruption, and to improve the overall system efficiency (by the integration of the battery bank). e system design philosophy was to maximize simplicity; hence, the system was sized using conventional simulation tool and representative insolation data. e system includes a 15 kW PV array, 21.6 kWh (3600 Ah) worth of battery storage, and a 5.4 kW (6.8kVA) generator. e paper features a detailed analysis of the energy flows through the system and quantifies all losses caused by PV charge controller, battery storage round-trip, rectifier, and inverter conversions. In addition, simulation was run to compare PV/diesel/battery with diesel/battery and the results show that the capital cost of a PV/diesel hybrid solution with batteries is nearly three times higher than that of a generator and battery combination, but the net present cost, representing cost over the lifetime of the system, is less than one-half of the generator and battery combination. 1. Introduction Energy is essential to economic and social development and improves quality of life. It is very important for the developing society [1]. In Nigeria, most residential homes are connected to the electric grid. However, there still exist several “off-grid” or remote locations, which, for financial and/or environmental reasons related to their distance from an existing power line, are not connected to the utility grid. Most of these residences derive their electricity from gasoline or diesel powered generators, which can be noisy and have the disadvantage of increasing the greenhouse gas emission which has a negative impact on the environment. Amid the environmental problems of using petrol and diesel generators, the cost of running them is quite high. Due to the high cost of running petrol/diesel generators, many Nigerians are willing to shiſt from using these traditional generators to the use of renewable energy technologies. Renewable energy technologies (such as solar-photo- voltaic systems) can be localized and decentralized unlike the national electricity grid. is allows end-users to generate their own electricity wherever they are located. Also, the technologies do not require any running cost, unlike the traditional petrol/diesel generators. e installation of a solar power system to replace or offset a portion of the diesel electricity generation is an option to consider for remote residential homes. A complete replace- ment of diesel generation with solar power is usually not feasi- ble, due to low solar input during the rainy season. However, a solar/diesel combination system known as hybrid system can prove to be very reliable and cost effective given the right con- ditions (such as optimal sizing). Hybrid energy applications are of increasing interest, and a well-managed hybrid solar- diesel system can achieve lifetime fuel savings, while ensuring reliable electricity supply. Insofar as diesel fuel is reduced, and such systems reduce CO 2 as well as particulate emissions that are harmful to health. ey are an economical option in areas isolated from the grid. is paper describes the way to design the aspects of a hybrid power system, a photovoltaic (PV) generator with energy storage for a residential use. e decision to select a PV generator hybrid system rather than a pure PV system for Hindawi Publishing Corporation Journal of Energy Volume 2016, Article ID 6278138, 16 pages http://dx.doi.org/10.1155/2016/6278138
Transcript
Page 1: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

Research ArticleDesign of a Reliable Hybrid (PVDiesel) Power System withEnergy Storage in Batteries for Remote Residential Home

Vincent Anayochukwu Ani

Department of Electronic Engineering University of Nigeria Nsukka 410001 Nigeria

Correspondence should be addressed to Vincent Anayochukwu Ani vincent aniyahoocom

Received 17 March 2016 Accepted 26 May 2016

Academic Editor Mohamed Benghanem

Copyright copy 2016 Vincent Anayochukwu Ani This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper reports the experience acquired with a photovoltaic (PV) hybrid system simulated as an alternative to diesel system fora residential home located in Southern Nigeria The hybrid system was designed to overcome the problem of climate change toensure a reliable supply without interruption and to improve the overall system efficiency (by the integration of the battery bank)The system design philosophy was to maximize simplicity hence the system was sized using conventional simulation tool andrepresentative insolation data The system includes a 15 kW PV array 216 kWh (3600Ah) worth of battery storage and a 54 kW(68 kVA) generator The paper features a detailed analysis of the energy flows through the system and quantifies all losses causedby PV charge controller battery storage round-trip rectifier and inverter conversions In addition simulation was run to comparePVdieselbattery with dieselbattery and the results show that the capital cost of a PVdiesel hybrid solution with batteries is nearlythree times higher than that of a generator and battery combination but the net present cost representing cost over the lifetime ofthe system is less than one-half of the generator and battery combination

1 Introduction

Energy is essential to economic and social developmentand improves quality of life It is very important for thedeveloping society [1] In Nigeria most residential homesare connected to the electric grid However there still existseveral ldquooff-gridrdquo or remote locations which for financialandor environmental reasons related to their distance froman existing power line are not connected to the utilitygrid Most of these residences derive their electricity fromgasoline or diesel powered generators which can be noisyand have the disadvantage of increasing the greenhouse gasemission which has a negative impact on the environmentAmid the environmental problems of using petrol and dieselgenerators the cost of running them is quite high Due to thehigh cost of running petroldiesel generatorsmanyNigeriansare willing to shift from using these traditional generators tothe use of renewable energy technologies

Renewable energy technologies (such as solar-photo-voltaic systems) can be localized and decentralized unlike thenational electricity grid This allows end-users to generate

their own electricity wherever they are located Also thetechnologies do not require any running cost unlike thetraditional petroldiesel generators

The installation of a solar power system to replace or offseta portion of the diesel electricity generation is an option toconsider for remote residential homes A complete replace-ment of diesel generationwith solar power is usually not feasi-ble due to low solar input during the rainy seasonHowever asolardiesel combination system known as hybrid system canprove to be very reliable and cost effective given the right con-ditions (such as optimal sizing) Hybrid energy applicationsare of increasing interest and a well-managed hybrid solar-diesel system can achieve lifetime fuel savings while ensuringreliable electricity supply Insofar as diesel fuel is reduced andsuch systems reduce CO

2as well as particulate emissions that

are harmful to healthThey are an economical option in areasisolated from the grid

This paper describes the way to design the aspects ofa hybrid power system a photovoltaic (PV) generator withenergy storage for a residential use The decision to select aPV generator hybrid system rather than a pure PV system for

Hindawi Publishing CorporationJournal of EnergyVolume 2016 Article ID 6278138 16 pageshttpdxdoiorg10115520166278138

2 Journal of Energy

Table 1 Energy needed for the household use

Description of item Itemabbreviation

Power rating(watts) Qty Total load

(watts) Daily hour of actual utilization (hr per day)

Medium size deep-freezer DF 130 1 130 24 h (0000 hndash2400 h)Water pumping machine PM 1000 1 1000 1 h (1300 h-1400 h)Washing machine WM 280 1 280 1 h (0900 h-1000 h)Electric stove ES 1000 1 1000 2 h (1700 hndash1900 h)Microwave oven MO 1000 1 1000 2 h (0600 h-0700 h 1100 h-1200 h)Electric pressing iron PI 1000 1 1000 1 h (1200 h-1300 h)Air-conditioner AC 1170 1 1170 9 h (0800 hndash1700 h)Refrigerator RF 500 1 500 9 h (0800 hndash1700 h)Water bath WB 1000 1 1000 2 h (0300 h-0400 h 1800 h-1900 h)Ceiling fan CF 100 14 1400 14 h (0800 hndash2200 h)Energy efficient lighting EL 6 23 138 8 h (0400 hndash0800 h 1800 hndash2200 h)Lighting-outdoor (security) LO 9 4 36 13 h (1800 hndash0700 h)2110158401015840 TV with decoder 2110158401015840 TV-D 150 1 150 9 h (0800 hndash1700 h)2110158401015840 television 2110158401015840 TV 100 1 100 11 h (1800 hndash0500 h)1410158401015840 television 1410158401015840 TV 80 8 640 22 h (0600 hndash1700 h 1800 hndash0500 h)Sony music system SM 100 1 100 1 h (0400 h-0500 h)DSTV receiver D-R 50 1 50 22 h (0600 hndash1700 h 1800 hndash0500 h)DVD player D-P 50 1 50 2 h (1900 hndash2100 h)Computer printer CP 100 1 100 1 h (1500 h-1600 h)Computer PC PC 115 1 115 9 h (0800 hndash1700 h)Computer laptop CL 35 1 35 9 h (0800 hndash1700 h)Miscellaneous M 100 1 100 24 h (0000 hndash2400 h)

the considered location is consistent with its solar irradiationThis system will replace an existing diesel powered electricgenerator and was sized to meet the residencersquos knownlighting and plug loads refrigeration cooking and heatingneeds The residence is located about a km from the utilitygrid and the location is characterized by a yearly globalirradiation of about 2150 kWhm2 Also this study is toproduce a detailed experimental accounting of energy flowsthrough the hybrid system and quantify all system losses Inaddition the hybrid system designed will be compared withthe dieselbattery system in terms of costs and environmentalimpacts

(1) Description of the Residential Home The residence is aduplex building and has six rooms a kitchen and a sittingroom at the ground floor while it has three mastersrsquo roomsa library and a small sitting room upstairs The building isfurnished with electric power consumptions such as washingmachine electric stove electric pressing iron DVD stereocassette television decodercable water pumping machinefans electric bulbs water bath deep-freezer and microwaveEach room has fan electric bulb and television The sittingroom at the upstairs uses air-condition while the one at theground floor uses four fans The residence is not connectedto the grid and currently utilizes a diesel power generatingsystem to meet its energy needs

In this research load assessment and the pattern of usingelectricity power within the house were carried out basedon data provided by the occupant of the house and a sitevisit to evaluate the characteristics of the power systempower requirements and power system management andoperationThe daily power demands for the residential homeare tabulated in Tables 1 and 2 and shown in Figure 1 Thesetables show the estimation of each appliancersquos rated power itsquantity and the hours of use by the residence in a single dayThe miscellaneous load is for unknown loads in the house

(2) Overview of the Study Area This research focuses onthe design of a hybrid power system with energy storagein batteries for a residential home The residential homewhere the study was done is located in a remote setting ofNdiagu-Akpugo Ogologo-Eji Ndiagu-Akpugo is in Nkanu-West LGA of Enugu State in South-Eastern Nigeria onlatitude 6∘351015840N and longitude 7∘511015840E The data for solarresource (used in generating Figure 2) were obtained fromthe National Aeronautics and Space Administration (NASA)Surface Meteorology and Solar Energy web site [2] Afterscaling on this data the scaled annual average resource of47 kWhm2d was obtained for the site As can be seen inFigure 2months below45 kWhm2d are themonths of JuneJuly August and September which are the months of rainingseason in Nigeria and there are likely to be more cloudy dayson these months

Journal of Energy 3

Table2Th

eelectric

alload

(dailyload

demands)d

atafor

theh

ouseho

ld

Time

Thea

ppliancea

bbreviations

areg

iven

inTable1

Total(WH

r)DF

PMWM

ESMO

PIAC

RFWB

CFEL

LO2110158401015840TV

-D2110158401015840TV

1410158401015840TV

SMD-R

D-P

CPPC

CLM

000-100

130

36100

640

50100

1056

100-200

130

36100

640

50100

1056

200-300

130

36100

640

50100

1056

300-400

130

1000

36100

640

50100

2056

400-500

130

138

36100

640

100

50100

1294

500-600

130

138

36100

404

600-700

130

1000

138

3664

050

100

2094

700-800

130

138

640

50100

1058

800-900

130

1170

500

1400

150

640

50115

35100

4290

900-1000

130

280

1170

500

1400

150

640

50115

35100

4570

1000-1100

130

1170

500

1400

150

640

50115

35100

4290

1100-1200

130

1000

1170

500

1400

150

640

50115

35100

5290

1200-1300

130

1000

1170

500

1400

150

640

50115

35100

5290

1300-1400

130

1000

1170

500

1400

150

640

50115

35100

5290

1400-1500

130

1170

500

1400

150

640

50115

35100

4290

1500-1600

130

1170

500

1400

150

640

50100

115

35100

4390

1600-1700

130

1170

500

1400

150

640

50115

35100

4290

1700-1800

130

1000

1400

100

2630

1800-1900

130

1000

1000

1400

138

36100

640

50100

4594

1900-2000

130

1400

138

36100

640

5050

100

2644

2000-2100

130

1400

138

36100

640

5050

100

2644

2100-2200

130

1400

138

36100

640

50100

2594

2200-2300

130

36100

640

50100

1056

2300-2400

130

36100

640

50100

1056

Total

3120

1000

280

2000

2000

1000

10530

4500

2000

1960

0110

446

81350

1100

14080

100

1100

100

100

1035

315

2400

69282

4 Journal of Energy

0

1000

2000

3000

4000

5000

6000

Hou

rly d

eman

d (W

)

Medium size deep-freezer Water pumping machine Washing machine Electric stoveMicrowave oven Electric pressing iron Air-conditioner RefrigeratorWater bath Ceiling fan Energy efficient lighting Lighting-outdoor (security)

Sony music systemDSTV receiver DVD player Computer printer Computer PCComputer laptop Miscellaneous

10

0-2

00

00

0-1

00

20

0-3

00

30

0-4

00

40

0-5

00

50

0-6

00

60

0-7

00

70

0-8

00

80

0-9

00

90

0-1

00

0

100

0-1

10

0

110

0-1

20

0

120

0-1

30

0

130

0-1

40

0

140

0-1

50

0

150

0-1

60

0

160

0-1

70

0

170

0-1

80

0

180

0-1

90

0

190

0-2

00

0

200

0-2

10

0

210

0-2

20

0

220

0-2

30

0

230

0-2

40

0

14998400998400 television21

998400998400 television21998400998400 TV with decoder

Figure 1 Hourly power demand profile of the household

Jan

Feb

Mar

Apr

May Jun Jul

Aug

Sep

Oct

Nov Dec

Daily radiationClearness index

Clea

rnes

s ind

ex

6

5

4

3

2

1

0

Dai

ly ra

diat

ion

(kW

hm

2d

) 10

08

06

04

02

00

Global horizontal radiation

Figure 2 Solar daily radiation profile forNdiagu-Akpugo inNkanu-West (Enugu State) [2]

2 Energy Models

Energy model depends mainly on the economic feasibil-ity and the proper sizing of the components in order toavoid outages as well as ensuring quality and reliability ofsupply Energy design system looks into its sizing and theprocess of selecting the best components to provide cheapefficient reliable environmentally friendly and cost effectivepower supply [3] The technoeconomic analysis looks at

both environmental cost and the cheapest cost of energyproduced by the system components Designing a hybridsystem would require correct components selection andsizing with appropriate operation strategy [4 5]

In energy systems the sizing of the individual systemscan be made in a variety of ways depending upon the choiceof parameters of interest Energy models are employed asa supporting tool to develop energy strategies as well asoutlining the likely future structure of the system underparticular conditions This helps to provide insights intothe technological paths structural evolution and policiesthat should be followed [3] A lot of research has beenconducted on the performance of hybrid power systems andexperimental results have been published in many articles[6ndash13] The energy output of a hybrid system can be enoughfor the demands of a house placed in regions where theextension of the already available electricity grid would befinancially unadvisable [9] A method of sizing hybrid PVsystems regarding the reliability to satisfy the load demandeconomy of components and discharge depth exploited bythe batteries is therefore required

Several models have been developed simulating andsizing PV systems using different operation strategies Theestimation of performance of PV systems based on the Lossof Load Probability (LLP) technique is developed by [14ndash17] These analytical methods are simple to apply but theyare not general On the other hand the numerical methods

Journal of Energy 5

presented by [18ndash24] present a good solution but these needa long period solar radiation data record Other methodsestimate the excess of energy provided by PV generators andthe storage capacity of the batteries using the utilizabilitymethod [25]

The conventional methodology (empiric analytic andnumeric) for sizing PV systems has been used for a locationwhere the required weather data (irradiation temperaturehumidity clearness index etc) and the information concern-ing the site where we want to implement the PV system areavailable In this case these methods present a good solutionfor sizing PV systems However these techniques could notbe used for sizing PV systems in remote areas in the casewhere the required data are not available Moreover themajority of the above methods need the long term meteoro-logical data such as total solar irradiation and air temperaturefor their operation So when the relevantmeteorological dataare not available these methods cannot be used especiallyin the isolated areas In this context a model was developedand the methodology aims at finding the configurationamong a set of systems components which meets the desiredsystem reliability requirements with the lowest value oflevelised cost of energy (LCE) This methodology can beused for determining the optimum number of solar panelsand batteries configurations (the storage capacity of thebatteries necessary to satisfy a given consumption) Since theinvestigation of this paper is based on a detailed study of ananalysis of the energy flows the analysis reveals the energylosses (charge controller rectifier battery and inverter) in thesystem and the storage requirement In addition the modeldeveloped was used to select the optimal sizing parameters ofPV system in which the results obtained have been comparedand tested with HOMER software

21 Development of a Model for Energy System ComponentsModelisation is an essential step before any phase of com-ponent sizing Various modeling techniques are developedto model hybrid PVdiesel system components in previousstudies For a hybrid PVdiesel system with storage batterythree principal subsystems are included the PVgenerator thediesel generator and the battery storage A methodology formodeling hybrid PVdiesel system components is describedbelowThe theoretical aspects are given below (Sections 211212 213 214 and 215) and are based on the works of Ani[3] Gupta et al [26] and Ashok [27]

211 Modeling of Solar-Photovoltaic Generator Using thesolar radiation available the hourly energy output of the PVgenerator (119864PVG) can be calculated according to the followingequation [3 27ndash29]

119864PVG = 119866 (119905) times 119860 times 119875 times 120578PVG (1)

212 Modeling of Diesel Generator Hourly energy generatedby diesel generator (119864DEG) with rated power output (119875DEG) isdefined by the following expression [3 27 28]

119864DEG (119905) = 119875DEG (119905) times 120578DEG (2)

213 Modeling of Converter In the proposed scheme aconverter contains both rectifier and inverter PV energygenerator and battery subsystems are connected with DC buswhile diesel generating unit subsystem is connected with ACbusThe electric loads connected in this scheme are AC loads

The rectifier is used to transform the surplus AC powerfrom the diesel electric generator to charge the battery Thediesel electric generator will be powering the load and at thesame time charging the battery The rectifier model is givenbelow

119864REC-OUT (119905) = 119864REC-IN (119905) times 120578REC

119864REC-IN (119905) = 119864SUR-AC (119905) (3)

At any time 119905

119864SUR-AC (119905) = 119864DEG (119905) minus 119864Load (119905) (4)

The inverter model for photovoltaic generator and batterybank are given below

119864PVG-IN (119905) = 119864PVG (119905) times 120578INV

119864BAT-INV (119905) = [(119864BAT (119905 minus 1) minus 119864LOAD (119905))

(120578INV times 120578DCHG)]

(5)

214Modeling of Charge Controller To prevent overchargingof a battery a charge controller is used to sense when thebatteries are fully charged and to stop or reduce the amountof energy flowing from the energy source to the batteriesThemodel of the charge controller is presented below

119864CC-OUT (119905) = 119864CC-IN (119905) times 120578CC

119864CC-IN (119905) = 119864REC-OUT (119905) + 119864SUR-DC (119905) (6)

215 Modeling of Battery Bank The battery state of charge(SOC) is the cumulative sum of the daily chargedischargetransfers The battery serves as an energy source entity whendischarging and a loadwhen charging At any time 119905 the stateof battery is related to the previous state of charge and to theenergy production and consumption situation of the systemduring the time from 119905 minus 1 to 119905

During the charging process when the total output ofall generators exceeds the load demand the available batterybank capacity at time 119905 can be described by [3 29 30]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864CC-OUT (119905) times 120578CHG (7)

On the other hand when the load demand is greater than theavailable energy generated the battery bank is in dischargingstate Therefore the available battery bank capacity at time 119905can be expressed as [3 29]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864Needed (119905) (8)

Let 119889 be the ratio of minimum allowable SOC voltage limit tothemaximum SOC voltage across the battery terminals whenit is fully charged So the depth of discharge (DOD) is

DOD = (1 minus 119889) times 100 (9)

6 Journal of Energy

DOD is a measure of how much energy has been withdrawnfrom a storage device expressed as a percentage of fullcapacity The maximum value of SOC is 1 and the minimumSOC is determined by maximum depth of discharge (DOD)

SOCMin = 1 minusDOD100

(10)

22 Mathematical Cost Model (Economic and EnvironmentalCosts) of Energy Systems This work developed a mathemati-cal model of a system that could represent the integral (totalsum) of the minimum economic and environmental (healthand safety) costs of the considered options

221 The Annualized Cost of a Component The annualizedcost of a component includes annualized capital cost annu-alized replacement cost annual OampM cost emissions costand annual fuel cost (generator) Operation cost is calculatedhourly on daily basis [3 27 29 31]

222 Annualized Capital Cost The annualized capital costof a system component is equal to the total initial capital costmultiplied by the capital recovery factor Annualized capitalcost is calculated using [3 27 29 31]

119862acap = 119862cap sdot CRF (119894 119877proj) (11)

223 Annualized Replacement Cost The annualized replace-ment cost of a system component is the annualized value ofall the replacement costs occurring throughout the lifetimeof the project minus the salvage value at the end of theproject lifetime Annualized replacement cost is calculatedusing [3 27 29 31]

119862arep = 119862rep sdot 119891rep sdot SFF (119894 119877comp) minus 119878 sdot SFF (119894 119877proj) (12)

119891rep a factor arising because the component lifetime can bedifferent from the project lifetime is given by

119891rep =

CRF (119894 119877proj)

CRF (119894 119877rep) 119877rep gt 0

0 119877rep = 0

(13)

119877rep the replacement cost duration is given by

119877rep = 119877comp sdot INT(119877proj

119877comp) (14)

SFF( ) the sinking fund factor which is a ratio used tocalculate the future value of a series of equal annual cashflows is given by

SFF (119894 119873) = 119894

(1 + 119894)119873minus 1 (15)

The salvaged value of the component at the end of the projectlifetime is proportional to its remaining life Therefore thesalvage value 119878 is given by

119878 = 119862rep sdot119877rem119877comp

(16)

119877rem the remaining life of the component at the end of theproject lifetime is given by

119877rem = 119877comp minus (119877proj minus 119877rep) (17)

224 Annualized Operating Cost The operating cost is theannualized value of all costs and revenues other than initialcapital costs and is calculated using [3 27 29 31]

119862aop =365

sum119905=1

24

sum119905=1

[119862oc (119905)] (18)

225 Cost of Emissions The following equation is used tocalculate the cost of emissions [3 27 29 31]

119862emissions =119888CO2

119872CO2

+ 119888CO119872CO + 119888UHC119872UHC + 119888PM119872PM + 119888SO2

119872SO2

+ 119888NO119909

119872NO119909

1000 (19)

Total cost of a component = economic cost + environmentalcost where economic cost = capital cost + replacement cost +operation and maintenance cost + fuel cost (generator) Alsoenvironmental cost = emissions cost

Annualized Cost of a Component Is Calculated Using [327 29 31]

119862ann = 119862acap + 119862arep + 119862aop + 119862emissions (20)

Annualized Total Cost of a Component Is CalculatedUsing [29 31]

119862anntot119888 =

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888 + 119862emissions) (21)

From (21) the economic and environmental cost modelthrough annualized total cost of different configurations of

Journal of Energy 7

power system results in the hybridizing of the renewableenergy generator (PV) with existing energy (diesel) is givenbelow

Economic and environmental costmodel of running solar+ diesel generator + batteries + converter is calculated as

119862anntot119904+119892+119887+119888 =

119873119904

sum119904=1

(119862acap119904 + 119862arep119904 + 119862aop119904

+ 119862emissions) +

119873119892

sum119892=1

(119862acap119892 + 119862arep119892 + 119862aop119892

+ 119862emissions + 119862af 119892) +

119873119887

sum119887=1

(119862acap119887 + 119862arep119887 + 119862aop119887

+ 119862emissions) +

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888)

(22)

23 Description of the Computer Simulation A computerprogram was developed and used to build the hybrid(PVdiesel) system model Data inputs to the programare hourly load demand data latitude and longitude ofthe site and reference component cost The designed soft-ware determines as its output the size of system com-ponents (sizing parameters) and the performance of thesystem over the course of the year (see the supple-mentary data in Supplementary Material available onlineat httpdxdoiorg10115520166278138) by showing thepower supplied by each of the energy systems over theyear given the load conditions and taking into account thetechnical factors The designed software can be used to studyhow the hybrid (PVdiesel) system is being supplied

24 Validation of the Model The designed software resultswere carried out followed with HOMER data to validate theanalysis The comparison shows a close agreement betweenresults obtained from the designed software module andresults obtained from HOMER setup In addition beforeusing the measured data gotten from NASA datasets insimulating the individual components of a PVdiesel hybridsystem the developed program accuracy was established thesimulated data predicted by the software program fall withinthe bounds of the measured data The algorithm that thedeveloped program uses to synthesize solar data is based onthe work of Graham andHollands [32]The realistic nature ofsynthetic data created by this algorithm is demonstrated andthe test shows that synthetic solar data (simulated) producevirtually the same simulation results as real data (measured)as shown in Figure 3

3 System Description

The designed system considered in this paper is a hybridsystem which consists of a renewable (photovoltaic) energysystem integrated in a conventional (diesel) power generationsystem energy storage in battery a DCAC converter (aninverter for the conversion of generated DC power into

0

1

2

3

4

5

6

7

Month of the yearMeasuredSimulated

Jan

Feb

Mar

ch

April

May

June July

Aug

Sept Oct

Nov Dec

Dai

ly ra

diat

ion

(kW

hm

2d

)

Figure 3 Calibrated solar radiation

required AC power) and an ACDC converter (a rectifierfor the conversion of generated AC power in order to chargethe battery) as shown in Figure 4 The inverter used is bidi-rectional also known as power converter which maintainsenergy flow between AC and DC components since the flowcomes in two different directions (from AC to DC and fromDC to AC)

The flow from the solar array passes through the chargecontroller to charge the battery and at the same time supplyelectricity to the load through the inverter The actual ACpower obtained after the conversion from a solar array can beseen in Table 3 The charge controller monitors and controlsthe charging and discharging of the battery in order not toallow the battery to be damaged (due to overcharging oroverdischarging)

Another flow comes from diesel generator when the PVand the battery could no longer serve the load the generatorsupplies electricity direct to serve the load and at the sametime charge the battery through the rectifier That is how thedesigned hybrid system is expected to work

The system design was to be representative of the typeof residential systems that were likely to be installed inthe foreseeable future Hence the system was sized usingconventional simulation tool and representative insolationdata

31 Cost of Key Components (including Installation andLabour) and Interest Rate for Capital Investments

311 PV System Cost (US$ 2Wp) The cost of PV panelson the Nigerian market was estimated as US$ 0600Wpbased on prices cited by Nigerian suppliers (based on thecost of a module of 1210 times 808 times 35mm size generating 130watts of peak power (Wp DC) in controlled conditions) [34]This was adjusted upward to US$ 2Wp to account for othersupport components that are required also known as balanceof system (BOS) parts such as cables charge controller withmaximum power point tracker lightening protection anddeliverylabour and installation costs

8 Journal of Energy

Table3Re

sults

oftheh

ybrid

electric

ityprod

uctio

nbatte

rychargesup

plyexcesslossesandconsum

ption(kW)

Mon

th

Hybrid

PVdieselelectric

itygeneratio

nRe

ctifier

Batte

ryInverter

ACload

Electricity

generatedandsupp

liedcharging

the

batte

ryand

excessele

ctric

ityby

theh

ybrid

syste

m(kW)

Energy

received

byther

ectifi

erto

charge

theb

attery

(kW)

Energy

received

bytheb

attery

andsupp

liedto

theA

Cload

viainverter(kW

)

Energy

received

bythe

inverter

andsupp

liedto

the

ACload

(kW)

ACload

served

(kW)

Electricity

generatedlowastSupp

liedto

theload

lowastCh

arging

theb

attery

Losses

Excess

electricity

generated

Energy

inEn

ergy

out

Losses

Charge

Disc

harge

Losses

Energy

inEn

ergy

out

Losses

Janu

ary

271539

91862277

538799

0159

314164

2995

1725464

644

871

493928minus427515

66413

141514

31273589

1415

542148238

February

2527428

1695987

4897

000154

3415

872899

82246547

43435

446265minus379553

66712

135152

3121632

7135196

1940

344

March

2802411

1887039

533918

0154

3813

003014

72256311

4516

1488757minus411872

76885

1506288

1355615

150673

2148238

April

2629097

1827413

5093

320146

292206

2897

05246309

4339

6465936minus395701

70235

144131

1129713

7144174

2078940

May

2631846

187612

3535826

0179

2197

18314101

2670

4847053

488773minus419038

69735

1468844

1321921

146923

2148238

June

2522854

1804

867

528865

0177

188945

313288

266355

46933

4819

32minus408659

73273

1345553

1210967

134586

2078940

July

2544

529

1860281

5410

310167

143050

31466

6267531

4713

5493896minus420576

7332

01325833

1193214

132619

2148238

August

2565565

1849784

551749

0164

163868

324882

276211

48671

503078minus425589

77489

1270987

1143852

127135

2148238

Septem

ber

256819

51799896

5298

540171

238274

312814

265950

46864

482990minus409230

7376

01301553

11713

67130186

2078940

Octob

er2681092

1873098

5412

030184

266607

324375

275785

48590

492613minus422554

70059

1473828

1326414

1474

142148238

Novem

ber

2649461

181232

15297

430158

3072

39305717

2599

1945798

483945minus409988

73957

143333

71289968

143369

2078940

Decem

ber

266810

71868682

5414

490185

2577

91314356

2672

6847088

494361minus423486

70875

1438938

1295008

143930

2148238

Total

31505984

220177

686371469

1998

311474

93704875

3149880

554995

5816474minus495376

1862713

16773138

15095379

1677759

25293770

lowastIn

term

sofelectric

itysupp

lyandbatte

rychargethe

PVsupp

liese

lectric

ityto

theA

Cload

viathe

inverter

andchargesthe

batte

rydirectly

whereas

thed

ieselgenerator

supp

liese

lectric

ityto

theA

Cload

directly

andchargesthe

batte

rythroug

hther

ectifi

erassho

wnin

Table4

Also

the

batte

rysupp

liese

lectric

ityto

theA

Cload

throug

htheinverteras

show

nin

thistable

Journal of Energy 9

Multiple solar panelsmaking up a solar array Charge

controller

Control unit coordinates the power system and displays

the energy flow through the system

Converter contains both rectifier and inverter

Generator toconverter

disconnectswitch

Converter bypassswitch (selects

output aseither converteror generator)

Service box(main breaker

panel)

To loadsappliances

AC lightning arresters

Generator

Wires for automatic generator starterstoppersystem to start generator automaticallywhen the batteries are low and stop the

generator automatically when the batteries are fully charged

Multiple batteriesmaking up a battery

bank

Batteriesto converterdisconnect

switchCharge controller

to batteriesdisconnect

switch

DC lightningarrester

Solar tocharge

controllerdisconnect

switchCombiner box (combines multiplewires from solar array to just a few and

may contain breakers or fuses)

Figure 4 Photovoltaic hybrid power system structure [33]

Table 4 Results of each of the energy components of the hybrid system (PV and diesel) for electricity production supply and battery charging(kW)

Month

Electricity generated and supplied and batterycharge by the PV in hybrid system (kW)

Electricity generated and supplied and batterycharge by the diesel in hybrid system (kW)

Electricitygenerated

Supplied to the loadvia inverter

Charging thebattery directly

Electricitygenerated

Supplied to theload directly

Charging thebattery via rectifier

January 1538295 987628 239282 1177104 874649 299517February 1510492 971970 199718 1016936 724017 289982March 1705644 1094416 232446 1096767 792623 301472April 1554395 1045610 219627 1074702 781803 289705May 1488347 1049806 221725 1143499 826317 314101June 1333962 936894 215577 1188892 867973 313288July 1271351 905257 226365 1273178 955024 314666August 1230539 845398 226867 1335026 1004386 324882September 1343075 892323 217040 1225120 907573 312814October 1534355 1051274 216828 1146737 821824 324375November 1552498 1023349 224026 1096963 788972 305717December 1499299 1015452 227093 1168808 853230 314356Total 17562252 11819377 2666594 13943732 10198391 3704875

312 Converter Cost (US$ 0320Wp) The cost of a con-verter based on prices cited by Nigerian suppliers was US$0320Wp [35]

313 Battery Cost (US$ 180kWh) The cost of a 6V225Ahlead acid battery on the Nigerian market was found to be inthe range of US$ 172 [35] Including balance of system (BOS)components and labourinstallation costs the capital cost for

the battery arrays was adjusted upward to US$ 180kWhTheprecise number of batteries required for each option is thendetermined by the simulation

314 Generator Cost (US$ 1000kW) The capital cost ofthe genset includes the generator itself (usually diesel orgasoline) as well as BOS costs and labourinstallation costsOn the Nigerian local market a generator of smaller range

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

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Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 2: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

2 Journal of Energy

Table 1 Energy needed for the household use

Description of item Itemabbreviation

Power rating(watts) Qty Total load

(watts) Daily hour of actual utilization (hr per day)

Medium size deep-freezer DF 130 1 130 24 h (0000 hndash2400 h)Water pumping machine PM 1000 1 1000 1 h (1300 h-1400 h)Washing machine WM 280 1 280 1 h (0900 h-1000 h)Electric stove ES 1000 1 1000 2 h (1700 hndash1900 h)Microwave oven MO 1000 1 1000 2 h (0600 h-0700 h 1100 h-1200 h)Electric pressing iron PI 1000 1 1000 1 h (1200 h-1300 h)Air-conditioner AC 1170 1 1170 9 h (0800 hndash1700 h)Refrigerator RF 500 1 500 9 h (0800 hndash1700 h)Water bath WB 1000 1 1000 2 h (0300 h-0400 h 1800 h-1900 h)Ceiling fan CF 100 14 1400 14 h (0800 hndash2200 h)Energy efficient lighting EL 6 23 138 8 h (0400 hndash0800 h 1800 hndash2200 h)Lighting-outdoor (security) LO 9 4 36 13 h (1800 hndash0700 h)2110158401015840 TV with decoder 2110158401015840 TV-D 150 1 150 9 h (0800 hndash1700 h)2110158401015840 television 2110158401015840 TV 100 1 100 11 h (1800 hndash0500 h)1410158401015840 television 1410158401015840 TV 80 8 640 22 h (0600 hndash1700 h 1800 hndash0500 h)Sony music system SM 100 1 100 1 h (0400 h-0500 h)DSTV receiver D-R 50 1 50 22 h (0600 hndash1700 h 1800 hndash0500 h)DVD player D-P 50 1 50 2 h (1900 hndash2100 h)Computer printer CP 100 1 100 1 h (1500 h-1600 h)Computer PC PC 115 1 115 9 h (0800 hndash1700 h)Computer laptop CL 35 1 35 9 h (0800 hndash1700 h)Miscellaneous M 100 1 100 24 h (0000 hndash2400 h)

the considered location is consistent with its solar irradiationThis system will replace an existing diesel powered electricgenerator and was sized to meet the residencersquos knownlighting and plug loads refrigeration cooking and heatingneeds The residence is located about a km from the utilitygrid and the location is characterized by a yearly globalirradiation of about 2150 kWhm2 Also this study is toproduce a detailed experimental accounting of energy flowsthrough the hybrid system and quantify all system losses Inaddition the hybrid system designed will be compared withthe dieselbattery system in terms of costs and environmentalimpacts

(1) Description of the Residential Home The residence is aduplex building and has six rooms a kitchen and a sittingroom at the ground floor while it has three mastersrsquo roomsa library and a small sitting room upstairs The building isfurnished with electric power consumptions such as washingmachine electric stove electric pressing iron DVD stereocassette television decodercable water pumping machinefans electric bulbs water bath deep-freezer and microwaveEach room has fan electric bulb and television The sittingroom at the upstairs uses air-condition while the one at theground floor uses four fans The residence is not connectedto the grid and currently utilizes a diesel power generatingsystem to meet its energy needs

In this research load assessment and the pattern of usingelectricity power within the house were carried out basedon data provided by the occupant of the house and a sitevisit to evaluate the characteristics of the power systempower requirements and power system management andoperationThe daily power demands for the residential homeare tabulated in Tables 1 and 2 and shown in Figure 1 Thesetables show the estimation of each appliancersquos rated power itsquantity and the hours of use by the residence in a single dayThe miscellaneous load is for unknown loads in the house

(2) Overview of the Study Area This research focuses onthe design of a hybrid power system with energy storagein batteries for a residential home The residential homewhere the study was done is located in a remote setting ofNdiagu-Akpugo Ogologo-Eji Ndiagu-Akpugo is in Nkanu-West LGA of Enugu State in South-Eastern Nigeria onlatitude 6∘351015840N and longitude 7∘511015840E The data for solarresource (used in generating Figure 2) were obtained fromthe National Aeronautics and Space Administration (NASA)Surface Meteorology and Solar Energy web site [2] Afterscaling on this data the scaled annual average resource of47 kWhm2d was obtained for the site As can be seen inFigure 2months below45 kWhm2d are themonths of JuneJuly August and September which are the months of rainingseason in Nigeria and there are likely to be more cloudy dayson these months

Journal of Energy 3

Table2Th

eelectric

alload

(dailyload

demands)d

atafor

theh

ouseho

ld

Time

Thea

ppliancea

bbreviations

areg

iven

inTable1

Total(WH

r)DF

PMWM

ESMO

PIAC

RFWB

CFEL

LO2110158401015840TV

-D2110158401015840TV

1410158401015840TV

SMD-R

D-P

CPPC

CLM

000-100

130

36100

640

50100

1056

100-200

130

36100

640

50100

1056

200-300

130

36100

640

50100

1056

300-400

130

1000

36100

640

50100

2056

400-500

130

138

36100

640

100

50100

1294

500-600

130

138

36100

404

600-700

130

1000

138

3664

050

100

2094

700-800

130

138

640

50100

1058

800-900

130

1170

500

1400

150

640

50115

35100

4290

900-1000

130

280

1170

500

1400

150

640

50115

35100

4570

1000-1100

130

1170

500

1400

150

640

50115

35100

4290

1100-1200

130

1000

1170

500

1400

150

640

50115

35100

5290

1200-1300

130

1000

1170

500

1400

150

640

50115

35100

5290

1300-1400

130

1000

1170

500

1400

150

640

50115

35100

5290

1400-1500

130

1170

500

1400

150

640

50115

35100

4290

1500-1600

130

1170

500

1400

150

640

50100

115

35100

4390

1600-1700

130

1170

500

1400

150

640

50115

35100

4290

1700-1800

130

1000

1400

100

2630

1800-1900

130

1000

1000

1400

138

36100

640

50100

4594

1900-2000

130

1400

138

36100

640

5050

100

2644

2000-2100

130

1400

138

36100

640

5050

100

2644

2100-2200

130

1400

138

36100

640

50100

2594

2200-2300

130

36100

640

50100

1056

2300-2400

130

36100

640

50100

1056

Total

3120

1000

280

2000

2000

1000

10530

4500

2000

1960

0110

446

81350

1100

14080

100

1100

100

100

1035

315

2400

69282

4 Journal of Energy

0

1000

2000

3000

4000

5000

6000

Hou

rly d

eman

d (W

)

Medium size deep-freezer Water pumping machine Washing machine Electric stoveMicrowave oven Electric pressing iron Air-conditioner RefrigeratorWater bath Ceiling fan Energy efficient lighting Lighting-outdoor (security)

Sony music systemDSTV receiver DVD player Computer printer Computer PCComputer laptop Miscellaneous

10

0-2

00

00

0-1

00

20

0-3

00

30

0-4

00

40

0-5

00

50

0-6

00

60

0-7

00

70

0-8

00

80

0-9

00

90

0-1

00

0

100

0-1

10

0

110

0-1

20

0

120

0-1

30

0

130

0-1

40

0

140

0-1

50

0

150

0-1

60

0

160

0-1

70

0

170

0-1

80

0

180

0-1

90

0

190

0-2

00

0

200

0-2

10

0

210

0-2

20

0

220

0-2

30

0

230

0-2

40

0

14998400998400 television21

998400998400 television21998400998400 TV with decoder

Figure 1 Hourly power demand profile of the household

Jan

Feb

Mar

Apr

May Jun Jul

Aug

Sep

Oct

Nov Dec

Daily radiationClearness index

Clea

rnes

s ind

ex

6

5

4

3

2

1

0

Dai

ly ra

diat

ion

(kW

hm

2d

) 10

08

06

04

02

00

Global horizontal radiation

Figure 2 Solar daily radiation profile forNdiagu-Akpugo inNkanu-West (Enugu State) [2]

2 Energy Models

Energy model depends mainly on the economic feasibil-ity and the proper sizing of the components in order toavoid outages as well as ensuring quality and reliability ofsupply Energy design system looks into its sizing and theprocess of selecting the best components to provide cheapefficient reliable environmentally friendly and cost effectivepower supply [3] The technoeconomic analysis looks at

both environmental cost and the cheapest cost of energyproduced by the system components Designing a hybridsystem would require correct components selection andsizing with appropriate operation strategy [4 5]

In energy systems the sizing of the individual systemscan be made in a variety of ways depending upon the choiceof parameters of interest Energy models are employed asa supporting tool to develop energy strategies as well asoutlining the likely future structure of the system underparticular conditions This helps to provide insights intothe technological paths structural evolution and policiesthat should be followed [3] A lot of research has beenconducted on the performance of hybrid power systems andexperimental results have been published in many articles[6ndash13] The energy output of a hybrid system can be enoughfor the demands of a house placed in regions where theextension of the already available electricity grid would befinancially unadvisable [9] A method of sizing hybrid PVsystems regarding the reliability to satisfy the load demandeconomy of components and discharge depth exploited bythe batteries is therefore required

Several models have been developed simulating andsizing PV systems using different operation strategies Theestimation of performance of PV systems based on the Lossof Load Probability (LLP) technique is developed by [14ndash17] These analytical methods are simple to apply but theyare not general On the other hand the numerical methods

Journal of Energy 5

presented by [18ndash24] present a good solution but these needa long period solar radiation data record Other methodsestimate the excess of energy provided by PV generators andthe storage capacity of the batteries using the utilizabilitymethod [25]

The conventional methodology (empiric analytic andnumeric) for sizing PV systems has been used for a locationwhere the required weather data (irradiation temperaturehumidity clearness index etc) and the information concern-ing the site where we want to implement the PV system areavailable In this case these methods present a good solutionfor sizing PV systems However these techniques could notbe used for sizing PV systems in remote areas in the casewhere the required data are not available Moreover themajority of the above methods need the long term meteoro-logical data such as total solar irradiation and air temperaturefor their operation So when the relevantmeteorological dataare not available these methods cannot be used especiallyin the isolated areas In this context a model was developedand the methodology aims at finding the configurationamong a set of systems components which meets the desiredsystem reliability requirements with the lowest value oflevelised cost of energy (LCE) This methodology can beused for determining the optimum number of solar panelsand batteries configurations (the storage capacity of thebatteries necessary to satisfy a given consumption) Since theinvestigation of this paper is based on a detailed study of ananalysis of the energy flows the analysis reveals the energylosses (charge controller rectifier battery and inverter) in thesystem and the storage requirement In addition the modeldeveloped was used to select the optimal sizing parameters ofPV system in which the results obtained have been comparedand tested with HOMER software

21 Development of a Model for Energy System ComponentsModelisation is an essential step before any phase of com-ponent sizing Various modeling techniques are developedto model hybrid PVdiesel system components in previousstudies For a hybrid PVdiesel system with storage batterythree principal subsystems are included the PVgenerator thediesel generator and the battery storage A methodology formodeling hybrid PVdiesel system components is describedbelowThe theoretical aspects are given below (Sections 211212 213 214 and 215) and are based on the works of Ani[3] Gupta et al [26] and Ashok [27]

211 Modeling of Solar-Photovoltaic Generator Using thesolar radiation available the hourly energy output of the PVgenerator (119864PVG) can be calculated according to the followingequation [3 27ndash29]

119864PVG = 119866 (119905) times 119860 times 119875 times 120578PVG (1)

212 Modeling of Diesel Generator Hourly energy generatedby diesel generator (119864DEG) with rated power output (119875DEG) isdefined by the following expression [3 27 28]

119864DEG (119905) = 119875DEG (119905) times 120578DEG (2)

213 Modeling of Converter In the proposed scheme aconverter contains both rectifier and inverter PV energygenerator and battery subsystems are connected with DC buswhile diesel generating unit subsystem is connected with ACbusThe electric loads connected in this scheme are AC loads

The rectifier is used to transform the surplus AC powerfrom the diesel electric generator to charge the battery Thediesel electric generator will be powering the load and at thesame time charging the battery The rectifier model is givenbelow

119864REC-OUT (119905) = 119864REC-IN (119905) times 120578REC

119864REC-IN (119905) = 119864SUR-AC (119905) (3)

At any time 119905

119864SUR-AC (119905) = 119864DEG (119905) minus 119864Load (119905) (4)

The inverter model for photovoltaic generator and batterybank are given below

119864PVG-IN (119905) = 119864PVG (119905) times 120578INV

119864BAT-INV (119905) = [(119864BAT (119905 minus 1) minus 119864LOAD (119905))

(120578INV times 120578DCHG)]

(5)

214Modeling of Charge Controller To prevent overchargingof a battery a charge controller is used to sense when thebatteries are fully charged and to stop or reduce the amountof energy flowing from the energy source to the batteriesThemodel of the charge controller is presented below

119864CC-OUT (119905) = 119864CC-IN (119905) times 120578CC

119864CC-IN (119905) = 119864REC-OUT (119905) + 119864SUR-DC (119905) (6)

215 Modeling of Battery Bank The battery state of charge(SOC) is the cumulative sum of the daily chargedischargetransfers The battery serves as an energy source entity whendischarging and a loadwhen charging At any time 119905 the stateof battery is related to the previous state of charge and to theenergy production and consumption situation of the systemduring the time from 119905 minus 1 to 119905

During the charging process when the total output ofall generators exceeds the load demand the available batterybank capacity at time 119905 can be described by [3 29 30]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864CC-OUT (119905) times 120578CHG (7)

On the other hand when the load demand is greater than theavailable energy generated the battery bank is in dischargingstate Therefore the available battery bank capacity at time 119905can be expressed as [3 29]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864Needed (119905) (8)

Let 119889 be the ratio of minimum allowable SOC voltage limit tothemaximum SOC voltage across the battery terminals whenit is fully charged So the depth of discharge (DOD) is

DOD = (1 minus 119889) times 100 (9)

6 Journal of Energy

DOD is a measure of how much energy has been withdrawnfrom a storage device expressed as a percentage of fullcapacity The maximum value of SOC is 1 and the minimumSOC is determined by maximum depth of discharge (DOD)

SOCMin = 1 minusDOD100

(10)

22 Mathematical Cost Model (Economic and EnvironmentalCosts) of Energy Systems This work developed a mathemati-cal model of a system that could represent the integral (totalsum) of the minimum economic and environmental (healthand safety) costs of the considered options

221 The Annualized Cost of a Component The annualizedcost of a component includes annualized capital cost annu-alized replacement cost annual OampM cost emissions costand annual fuel cost (generator) Operation cost is calculatedhourly on daily basis [3 27 29 31]

222 Annualized Capital Cost The annualized capital costof a system component is equal to the total initial capital costmultiplied by the capital recovery factor Annualized capitalcost is calculated using [3 27 29 31]

119862acap = 119862cap sdot CRF (119894 119877proj) (11)

223 Annualized Replacement Cost The annualized replace-ment cost of a system component is the annualized value ofall the replacement costs occurring throughout the lifetimeof the project minus the salvage value at the end of theproject lifetime Annualized replacement cost is calculatedusing [3 27 29 31]

119862arep = 119862rep sdot 119891rep sdot SFF (119894 119877comp) minus 119878 sdot SFF (119894 119877proj) (12)

119891rep a factor arising because the component lifetime can bedifferent from the project lifetime is given by

119891rep =

CRF (119894 119877proj)

CRF (119894 119877rep) 119877rep gt 0

0 119877rep = 0

(13)

119877rep the replacement cost duration is given by

119877rep = 119877comp sdot INT(119877proj

119877comp) (14)

SFF( ) the sinking fund factor which is a ratio used tocalculate the future value of a series of equal annual cashflows is given by

SFF (119894 119873) = 119894

(1 + 119894)119873minus 1 (15)

The salvaged value of the component at the end of the projectlifetime is proportional to its remaining life Therefore thesalvage value 119878 is given by

119878 = 119862rep sdot119877rem119877comp

(16)

119877rem the remaining life of the component at the end of theproject lifetime is given by

119877rem = 119877comp minus (119877proj minus 119877rep) (17)

224 Annualized Operating Cost The operating cost is theannualized value of all costs and revenues other than initialcapital costs and is calculated using [3 27 29 31]

119862aop =365

sum119905=1

24

sum119905=1

[119862oc (119905)] (18)

225 Cost of Emissions The following equation is used tocalculate the cost of emissions [3 27 29 31]

119862emissions =119888CO2

119872CO2

+ 119888CO119872CO + 119888UHC119872UHC + 119888PM119872PM + 119888SO2

119872SO2

+ 119888NO119909

119872NO119909

1000 (19)

Total cost of a component = economic cost + environmentalcost where economic cost = capital cost + replacement cost +operation and maintenance cost + fuel cost (generator) Alsoenvironmental cost = emissions cost

Annualized Cost of a Component Is Calculated Using [327 29 31]

119862ann = 119862acap + 119862arep + 119862aop + 119862emissions (20)

Annualized Total Cost of a Component Is CalculatedUsing [29 31]

119862anntot119888 =

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888 + 119862emissions) (21)

From (21) the economic and environmental cost modelthrough annualized total cost of different configurations of

Journal of Energy 7

power system results in the hybridizing of the renewableenergy generator (PV) with existing energy (diesel) is givenbelow

Economic and environmental costmodel of running solar+ diesel generator + batteries + converter is calculated as

119862anntot119904+119892+119887+119888 =

119873119904

sum119904=1

(119862acap119904 + 119862arep119904 + 119862aop119904

+ 119862emissions) +

119873119892

sum119892=1

(119862acap119892 + 119862arep119892 + 119862aop119892

+ 119862emissions + 119862af 119892) +

119873119887

sum119887=1

(119862acap119887 + 119862arep119887 + 119862aop119887

+ 119862emissions) +

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888)

(22)

23 Description of the Computer Simulation A computerprogram was developed and used to build the hybrid(PVdiesel) system model Data inputs to the programare hourly load demand data latitude and longitude ofthe site and reference component cost The designed soft-ware determines as its output the size of system com-ponents (sizing parameters) and the performance of thesystem over the course of the year (see the supple-mentary data in Supplementary Material available onlineat httpdxdoiorg10115520166278138) by showing thepower supplied by each of the energy systems over theyear given the load conditions and taking into account thetechnical factors The designed software can be used to studyhow the hybrid (PVdiesel) system is being supplied

24 Validation of the Model The designed software resultswere carried out followed with HOMER data to validate theanalysis The comparison shows a close agreement betweenresults obtained from the designed software module andresults obtained from HOMER setup In addition beforeusing the measured data gotten from NASA datasets insimulating the individual components of a PVdiesel hybridsystem the developed program accuracy was established thesimulated data predicted by the software program fall withinthe bounds of the measured data The algorithm that thedeveloped program uses to synthesize solar data is based onthe work of Graham andHollands [32]The realistic nature ofsynthetic data created by this algorithm is demonstrated andthe test shows that synthetic solar data (simulated) producevirtually the same simulation results as real data (measured)as shown in Figure 3

3 System Description

The designed system considered in this paper is a hybridsystem which consists of a renewable (photovoltaic) energysystem integrated in a conventional (diesel) power generationsystem energy storage in battery a DCAC converter (aninverter for the conversion of generated DC power into

0

1

2

3

4

5

6

7

Month of the yearMeasuredSimulated

Jan

Feb

Mar

ch

April

May

June July

Aug

Sept Oct

Nov Dec

Dai

ly ra

diat

ion

(kW

hm

2d

)

Figure 3 Calibrated solar radiation

required AC power) and an ACDC converter (a rectifierfor the conversion of generated AC power in order to chargethe battery) as shown in Figure 4 The inverter used is bidi-rectional also known as power converter which maintainsenergy flow between AC and DC components since the flowcomes in two different directions (from AC to DC and fromDC to AC)

The flow from the solar array passes through the chargecontroller to charge the battery and at the same time supplyelectricity to the load through the inverter The actual ACpower obtained after the conversion from a solar array can beseen in Table 3 The charge controller monitors and controlsthe charging and discharging of the battery in order not toallow the battery to be damaged (due to overcharging oroverdischarging)

Another flow comes from diesel generator when the PVand the battery could no longer serve the load the generatorsupplies electricity direct to serve the load and at the sametime charge the battery through the rectifier That is how thedesigned hybrid system is expected to work

The system design was to be representative of the typeof residential systems that were likely to be installed inthe foreseeable future Hence the system was sized usingconventional simulation tool and representative insolationdata

31 Cost of Key Components (including Installation andLabour) and Interest Rate for Capital Investments

311 PV System Cost (US$ 2Wp) The cost of PV panelson the Nigerian market was estimated as US$ 0600Wpbased on prices cited by Nigerian suppliers (based on thecost of a module of 1210 times 808 times 35mm size generating 130watts of peak power (Wp DC) in controlled conditions) [34]This was adjusted upward to US$ 2Wp to account for othersupport components that are required also known as balanceof system (BOS) parts such as cables charge controller withmaximum power point tracker lightening protection anddeliverylabour and installation costs

8 Journal of Energy

Table3Re

sults

oftheh

ybrid

electric

ityprod

uctio

nbatte

rychargesup

plyexcesslossesandconsum

ption(kW)

Mon

th

Hybrid

PVdieselelectric

itygeneratio

nRe

ctifier

Batte

ryInverter

ACload

Electricity

generatedandsupp

liedcharging

the

batte

ryand

excessele

ctric

ityby

theh

ybrid

syste

m(kW)

Energy

received

byther

ectifi

erto

charge

theb

attery

(kW)

Energy

received

bytheb

attery

andsupp

liedto

theA

Cload

viainverter(kW

)

Energy

received

bythe

inverter

andsupp

liedto

the

ACload

(kW)

ACload

served

(kW)

Electricity

generatedlowastSupp

liedto

theload

lowastCh

arging

theb

attery

Losses

Excess

electricity

generated

Energy

inEn

ergy

out

Losses

Charge

Disc

harge

Losses

Energy

inEn

ergy

out

Losses

Janu

ary

271539

91862277

538799

0159

314164

2995

1725464

644

871

493928minus427515

66413

141514

31273589

1415

542148238

February

2527428

1695987

4897

000154

3415

872899

82246547

43435

446265minus379553

66712

135152

3121632

7135196

1940

344

March

2802411

1887039

533918

0154

3813

003014

72256311

4516

1488757minus411872

76885

1506288

1355615

150673

2148238

April

2629097

1827413

5093

320146

292206

2897

05246309

4339

6465936minus395701

70235

144131

1129713

7144174

2078940

May

2631846

187612

3535826

0179

2197

18314101

2670

4847053

488773minus419038

69735

1468844

1321921

146923

2148238

June

2522854

1804

867

528865

0177

188945

313288

266355

46933

4819

32minus408659

73273

1345553

1210967

134586

2078940

July

2544

529

1860281

5410

310167

143050

31466

6267531

4713

5493896minus420576

7332

01325833

1193214

132619

2148238

August

2565565

1849784

551749

0164

163868

324882

276211

48671

503078minus425589

77489

1270987

1143852

127135

2148238

Septem

ber

256819

51799896

5298

540171

238274

312814

265950

46864

482990minus409230

7376

01301553

11713

67130186

2078940

Octob

er2681092

1873098

5412

030184

266607

324375

275785

48590

492613minus422554

70059

1473828

1326414

1474

142148238

Novem

ber

2649461

181232

15297

430158

3072

39305717

2599

1945798

483945minus409988

73957

143333

71289968

143369

2078940

Decem

ber

266810

71868682

5414

490185

2577

91314356

2672

6847088

494361minus423486

70875

1438938

1295008

143930

2148238

Total

31505984

220177

686371469

1998

311474

93704875

3149880

554995

5816474minus495376

1862713

16773138

15095379

1677759

25293770

lowastIn

term

sofelectric

itysupp

lyandbatte

rychargethe

PVsupp

liese

lectric

ityto

theA

Cload

viathe

inverter

andchargesthe

batte

rydirectly

whereas

thed

ieselgenerator

supp

liese

lectric

ityto

theA

Cload

directly

andchargesthe

batte

rythroug

hther

ectifi

erassho

wnin

Table4

Also

the

batte

rysupp

liese

lectric

ityto

theA

Cload

throug

htheinverteras

show

nin

thistable

Journal of Energy 9

Multiple solar panelsmaking up a solar array Charge

controller

Control unit coordinates the power system and displays

the energy flow through the system

Converter contains both rectifier and inverter

Generator toconverter

disconnectswitch

Converter bypassswitch (selects

output aseither converteror generator)

Service box(main breaker

panel)

To loadsappliances

AC lightning arresters

Generator

Wires for automatic generator starterstoppersystem to start generator automaticallywhen the batteries are low and stop the

generator automatically when the batteries are fully charged

Multiple batteriesmaking up a battery

bank

Batteriesto converterdisconnect

switchCharge controller

to batteriesdisconnect

switch

DC lightningarrester

Solar tocharge

controllerdisconnect

switchCombiner box (combines multiplewires from solar array to just a few and

may contain breakers or fuses)

Figure 4 Photovoltaic hybrid power system structure [33]

Table 4 Results of each of the energy components of the hybrid system (PV and diesel) for electricity production supply and battery charging(kW)

Month

Electricity generated and supplied and batterycharge by the PV in hybrid system (kW)

Electricity generated and supplied and batterycharge by the diesel in hybrid system (kW)

Electricitygenerated

Supplied to the loadvia inverter

Charging thebattery directly

Electricitygenerated

Supplied to theload directly

Charging thebattery via rectifier

January 1538295 987628 239282 1177104 874649 299517February 1510492 971970 199718 1016936 724017 289982March 1705644 1094416 232446 1096767 792623 301472April 1554395 1045610 219627 1074702 781803 289705May 1488347 1049806 221725 1143499 826317 314101June 1333962 936894 215577 1188892 867973 313288July 1271351 905257 226365 1273178 955024 314666August 1230539 845398 226867 1335026 1004386 324882September 1343075 892323 217040 1225120 907573 312814October 1534355 1051274 216828 1146737 821824 324375November 1552498 1023349 224026 1096963 788972 305717December 1499299 1015452 227093 1168808 853230 314356Total 17562252 11819377 2666594 13943732 10198391 3704875

312 Converter Cost (US$ 0320Wp) The cost of a con-verter based on prices cited by Nigerian suppliers was US$0320Wp [35]

313 Battery Cost (US$ 180kWh) The cost of a 6V225Ahlead acid battery on the Nigerian market was found to be inthe range of US$ 172 [35] Including balance of system (BOS)components and labourinstallation costs the capital cost for

the battery arrays was adjusted upward to US$ 180kWhTheprecise number of batteries required for each option is thendetermined by the simulation

314 Generator Cost (US$ 1000kW) The capital cost ofthe genset includes the generator itself (usually diesel orgasoline) as well as BOS costs and labourinstallation costsOn the Nigerian local market a generator of smaller range

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 3: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

Journal of Energy 3

Table2Th

eelectric

alload

(dailyload

demands)d

atafor

theh

ouseho

ld

Time

Thea

ppliancea

bbreviations

areg

iven

inTable1

Total(WH

r)DF

PMWM

ESMO

PIAC

RFWB

CFEL

LO2110158401015840TV

-D2110158401015840TV

1410158401015840TV

SMD-R

D-P

CPPC

CLM

000-100

130

36100

640

50100

1056

100-200

130

36100

640

50100

1056

200-300

130

36100

640

50100

1056

300-400

130

1000

36100

640

50100

2056

400-500

130

138

36100

640

100

50100

1294

500-600

130

138

36100

404

600-700

130

1000

138

3664

050

100

2094

700-800

130

138

640

50100

1058

800-900

130

1170

500

1400

150

640

50115

35100

4290

900-1000

130

280

1170

500

1400

150

640

50115

35100

4570

1000-1100

130

1170

500

1400

150

640

50115

35100

4290

1100-1200

130

1000

1170

500

1400

150

640

50115

35100

5290

1200-1300

130

1000

1170

500

1400

150

640

50115

35100

5290

1300-1400

130

1000

1170

500

1400

150

640

50115

35100

5290

1400-1500

130

1170

500

1400

150

640

50115

35100

4290

1500-1600

130

1170

500

1400

150

640

50100

115

35100

4390

1600-1700

130

1170

500

1400

150

640

50115

35100

4290

1700-1800

130

1000

1400

100

2630

1800-1900

130

1000

1000

1400

138

36100

640

50100

4594

1900-2000

130

1400

138

36100

640

5050

100

2644

2000-2100

130

1400

138

36100

640

5050

100

2644

2100-2200

130

1400

138

36100

640

50100

2594

2200-2300

130

36100

640

50100

1056

2300-2400

130

36100

640

50100

1056

Total

3120

1000

280

2000

2000

1000

10530

4500

2000

1960

0110

446

81350

1100

14080

100

1100

100

100

1035

315

2400

69282

4 Journal of Energy

0

1000

2000

3000

4000

5000

6000

Hou

rly d

eman

d (W

)

Medium size deep-freezer Water pumping machine Washing machine Electric stoveMicrowave oven Electric pressing iron Air-conditioner RefrigeratorWater bath Ceiling fan Energy efficient lighting Lighting-outdoor (security)

Sony music systemDSTV receiver DVD player Computer printer Computer PCComputer laptop Miscellaneous

10

0-2

00

00

0-1

00

20

0-3

00

30

0-4

00

40

0-5

00

50

0-6

00

60

0-7

00

70

0-8

00

80

0-9

00

90

0-1

00

0

100

0-1

10

0

110

0-1

20

0

120

0-1

30

0

130

0-1

40

0

140

0-1

50

0

150

0-1

60

0

160

0-1

70

0

170

0-1

80

0

180

0-1

90

0

190

0-2

00

0

200

0-2

10

0

210

0-2

20

0

220

0-2

30

0

230

0-2

40

0

14998400998400 television21

998400998400 television21998400998400 TV with decoder

Figure 1 Hourly power demand profile of the household

Jan

Feb

Mar

Apr

May Jun Jul

Aug

Sep

Oct

Nov Dec

Daily radiationClearness index

Clea

rnes

s ind

ex

6

5

4

3

2

1

0

Dai

ly ra

diat

ion

(kW

hm

2d

) 10

08

06

04

02

00

Global horizontal radiation

Figure 2 Solar daily radiation profile forNdiagu-Akpugo inNkanu-West (Enugu State) [2]

2 Energy Models

Energy model depends mainly on the economic feasibil-ity and the proper sizing of the components in order toavoid outages as well as ensuring quality and reliability ofsupply Energy design system looks into its sizing and theprocess of selecting the best components to provide cheapefficient reliable environmentally friendly and cost effectivepower supply [3] The technoeconomic analysis looks at

both environmental cost and the cheapest cost of energyproduced by the system components Designing a hybridsystem would require correct components selection andsizing with appropriate operation strategy [4 5]

In energy systems the sizing of the individual systemscan be made in a variety of ways depending upon the choiceof parameters of interest Energy models are employed asa supporting tool to develop energy strategies as well asoutlining the likely future structure of the system underparticular conditions This helps to provide insights intothe technological paths structural evolution and policiesthat should be followed [3] A lot of research has beenconducted on the performance of hybrid power systems andexperimental results have been published in many articles[6ndash13] The energy output of a hybrid system can be enoughfor the demands of a house placed in regions where theextension of the already available electricity grid would befinancially unadvisable [9] A method of sizing hybrid PVsystems regarding the reliability to satisfy the load demandeconomy of components and discharge depth exploited bythe batteries is therefore required

Several models have been developed simulating andsizing PV systems using different operation strategies Theestimation of performance of PV systems based on the Lossof Load Probability (LLP) technique is developed by [14ndash17] These analytical methods are simple to apply but theyare not general On the other hand the numerical methods

Journal of Energy 5

presented by [18ndash24] present a good solution but these needa long period solar radiation data record Other methodsestimate the excess of energy provided by PV generators andthe storage capacity of the batteries using the utilizabilitymethod [25]

The conventional methodology (empiric analytic andnumeric) for sizing PV systems has been used for a locationwhere the required weather data (irradiation temperaturehumidity clearness index etc) and the information concern-ing the site where we want to implement the PV system areavailable In this case these methods present a good solutionfor sizing PV systems However these techniques could notbe used for sizing PV systems in remote areas in the casewhere the required data are not available Moreover themajority of the above methods need the long term meteoro-logical data such as total solar irradiation and air temperaturefor their operation So when the relevantmeteorological dataare not available these methods cannot be used especiallyin the isolated areas In this context a model was developedand the methodology aims at finding the configurationamong a set of systems components which meets the desiredsystem reliability requirements with the lowest value oflevelised cost of energy (LCE) This methodology can beused for determining the optimum number of solar panelsand batteries configurations (the storage capacity of thebatteries necessary to satisfy a given consumption) Since theinvestigation of this paper is based on a detailed study of ananalysis of the energy flows the analysis reveals the energylosses (charge controller rectifier battery and inverter) in thesystem and the storage requirement In addition the modeldeveloped was used to select the optimal sizing parameters ofPV system in which the results obtained have been comparedand tested with HOMER software

21 Development of a Model for Energy System ComponentsModelisation is an essential step before any phase of com-ponent sizing Various modeling techniques are developedto model hybrid PVdiesel system components in previousstudies For a hybrid PVdiesel system with storage batterythree principal subsystems are included the PVgenerator thediesel generator and the battery storage A methodology formodeling hybrid PVdiesel system components is describedbelowThe theoretical aspects are given below (Sections 211212 213 214 and 215) and are based on the works of Ani[3] Gupta et al [26] and Ashok [27]

211 Modeling of Solar-Photovoltaic Generator Using thesolar radiation available the hourly energy output of the PVgenerator (119864PVG) can be calculated according to the followingequation [3 27ndash29]

119864PVG = 119866 (119905) times 119860 times 119875 times 120578PVG (1)

212 Modeling of Diesel Generator Hourly energy generatedby diesel generator (119864DEG) with rated power output (119875DEG) isdefined by the following expression [3 27 28]

119864DEG (119905) = 119875DEG (119905) times 120578DEG (2)

213 Modeling of Converter In the proposed scheme aconverter contains both rectifier and inverter PV energygenerator and battery subsystems are connected with DC buswhile diesel generating unit subsystem is connected with ACbusThe electric loads connected in this scheme are AC loads

The rectifier is used to transform the surplus AC powerfrom the diesel electric generator to charge the battery Thediesel electric generator will be powering the load and at thesame time charging the battery The rectifier model is givenbelow

119864REC-OUT (119905) = 119864REC-IN (119905) times 120578REC

119864REC-IN (119905) = 119864SUR-AC (119905) (3)

At any time 119905

119864SUR-AC (119905) = 119864DEG (119905) minus 119864Load (119905) (4)

The inverter model for photovoltaic generator and batterybank are given below

119864PVG-IN (119905) = 119864PVG (119905) times 120578INV

119864BAT-INV (119905) = [(119864BAT (119905 minus 1) minus 119864LOAD (119905))

(120578INV times 120578DCHG)]

(5)

214Modeling of Charge Controller To prevent overchargingof a battery a charge controller is used to sense when thebatteries are fully charged and to stop or reduce the amountof energy flowing from the energy source to the batteriesThemodel of the charge controller is presented below

119864CC-OUT (119905) = 119864CC-IN (119905) times 120578CC

119864CC-IN (119905) = 119864REC-OUT (119905) + 119864SUR-DC (119905) (6)

215 Modeling of Battery Bank The battery state of charge(SOC) is the cumulative sum of the daily chargedischargetransfers The battery serves as an energy source entity whendischarging and a loadwhen charging At any time 119905 the stateof battery is related to the previous state of charge and to theenergy production and consumption situation of the systemduring the time from 119905 minus 1 to 119905

During the charging process when the total output ofall generators exceeds the load demand the available batterybank capacity at time 119905 can be described by [3 29 30]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864CC-OUT (119905) times 120578CHG (7)

On the other hand when the load demand is greater than theavailable energy generated the battery bank is in dischargingstate Therefore the available battery bank capacity at time 119905can be expressed as [3 29]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864Needed (119905) (8)

Let 119889 be the ratio of minimum allowable SOC voltage limit tothemaximum SOC voltage across the battery terminals whenit is fully charged So the depth of discharge (DOD) is

DOD = (1 minus 119889) times 100 (9)

6 Journal of Energy

DOD is a measure of how much energy has been withdrawnfrom a storage device expressed as a percentage of fullcapacity The maximum value of SOC is 1 and the minimumSOC is determined by maximum depth of discharge (DOD)

SOCMin = 1 minusDOD100

(10)

22 Mathematical Cost Model (Economic and EnvironmentalCosts) of Energy Systems This work developed a mathemati-cal model of a system that could represent the integral (totalsum) of the minimum economic and environmental (healthand safety) costs of the considered options

221 The Annualized Cost of a Component The annualizedcost of a component includes annualized capital cost annu-alized replacement cost annual OampM cost emissions costand annual fuel cost (generator) Operation cost is calculatedhourly on daily basis [3 27 29 31]

222 Annualized Capital Cost The annualized capital costof a system component is equal to the total initial capital costmultiplied by the capital recovery factor Annualized capitalcost is calculated using [3 27 29 31]

119862acap = 119862cap sdot CRF (119894 119877proj) (11)

223 Annualized Replacement Cost The annualized replace-ment cost of a system component is the annualized value ofall the replacement costs occurring throughout the lifetimeof the project minus the salvage value at the end of theproject lifetime Annualized replacement cost is calculatedusing [3 27 29 31]

119862arep = 119862rep sdot 119891rep sdot SFF (119894 119877comp) minus 119878 sdot SFF (119894 119877proj) (12)

119891rep a factor arising because the component lifetime can bedifferent from the project lifetime is given by

119891rep =

CRF (119894 119877proj)

CRF (119894 119877rep) 119877rep gt 0

0 119877rep = 0

(13)

119877rep the replacement cost duration is given by

119877rep = 119877comp sdot INT(119877proj

119877comp) (14)

SFF( ) the sinking fund factor which is a ratio used tocalculate the future value of a series of equal annual cashflows is given by

SFF (119894 119873) = 119894

(1 + 119894)119873minus 1 (15)

The salvaged value of the component at the end of the projectlifetime is proportional to its remaining life Therefore thesalvage value 119878 is given by

119878 = 119862rep sdot119877rem119877comp

(16)

119877rem the remaining life of the component at the end of theproject lifetime is given by

119877rem = 119877comp minus (119877proj minus 119877rep) (17)

224 Annualized Operating Cost The operating cost is theannualized value of all costs and revenues other than initialcapital costs and is calculated using [3 27 29 31]

119862aop =365

sum119905=1

24

sum119905=1

[119862oc (119905)] (18)

225 Cost of Emissions The following equation is used tocalculate the cost of emissions [3 27 29 31]

119862emissions =119888CO2

119872CO2

+ 119888CO119872CO + 119888UHC119872UHC + 119888PM119872PM + 119888SO2

119872SO2

+ 119888NO119909

119872NO119909

1000 (19)

Total cost of a component = economic cost + environmentalcost where economic cost = capital cost + replacement cost +operation and maintenance cost + fuel cost (generator) Alsoenvironmental cost = emissions cost

Annualized Cost of a Component Is Calculated Using [327 29 31]

119862ann = 119862acap + 119862arep + 119862aop + 119862emissions (20)

Annualized Total Cost of a Component Is CalculatedUsing [29 31]

119862anntot119888 =

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888 + 119862emissions) (21)

From (21) the economic and environmental cost modelthrough annualized total cost of different configurations of

Journal of Energy 7

power system results in the hybridizing of the renewableenergy generator (PV) with existing energy (diesel) is givenbelow

Economic and environmental costmodel of running solar+ diesel generator + batteries + converter is calculated as

119862anntot119904+119892+119887+119888 =

119873119904

sum119904=1

(119862acap119904 + 119862arep119904 + 119862aop119904

+ 119862emissions) +

119873119892

sum119892=1

(119862acap119892 + 119862arep119892 + 119862aop119892

+ 119862emissions + 119862af 119892) +

119873119887

sum119887=1

(119862acap119887 + 119862arep119887 + 119862aop119887

+ 119862emissions) +

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888)

(22)

23 Description of the Computer Simulation A computerprogram was developed and used to build the hybrid(PVdiesel) system model Data inputs to the programare hourly load demand data latitude and longitude ofthe site and reference component cost The designed soft-ware determines as its output the size of system com-ponents (sizing parameters) and the performance of thesystem over the course of the year (see the supple-mentary data in Supplementary Material available onlineat httpdxdoiorg10115520166278138) by showing thepower supplied by each of the energy systems over theyear given the load conditions and taking into account thetechnical factors The designed software can be used to studyhow the hybrid (PVdiesel) system is being supplied

24 Validation of the Model The designed software resultswere carried out followed with HOMER data to validate theanalysis The comparison shows a close agreement betweenresults obtained from the designed software module andresults obtained from HOMER setup In addition beforeusing the measured data gotten from NASA datasets insimulating the individual components of a PVdiesel hybridsystem the developed program accuracy was established thesimulated data predicted by the software program fall withinthe bounds of the measured data The algorithm that thedeveloped program uses to synthesize solar data is based onthe work of Graham andHollands [32]The realistic nature ofsynthetic data created by this algorithm is demonstrated andthe test shows that synthetic solar data (simulated) producevirtually the same simulation results as real data (measured)as shown in Figure 3

3 System Description

The designed system considered in this paper is a hybridsystem which consists of a renewable (photovoltaic) energysystem integrated in a conventional (diesel) power generationsystem energy storage in battery a DCAC converter (aninverter for the conversion of generated DC power into

0

1

2

3

4

5

6

7

Month of the yearMeasuredSimulated

Jan

Feb

Mar

ch

April

May

June July

Aug

Sept Oct

Nov Dec

Dai

ly ra

diat

ion

(kW

hm

2d

)

Figure 3 Calibrated solar radiation

required AC power) and an ACDC converter (a rectifierfor the conversion of generated AC power in order to chargethe battery) as shown in Figure 4 The inverter used is bidi-rectional also known as power converter which maintainsenergy flow between AC and DC components since the flowcomes in two different directions (from AC to DC and fromDC to AC)

The flow from the solar array passes through the chargecontroller to charge the battery and at the same time supplyelectricity to the load through the inverter The actual ACpower obtained after the conversion from a solar array can beseen in Table 3 The charge controller monitors and controlsthe charging and discharging of the battery in order not toallow the battery to be damaged (due to overcharging oroverdischarging)

Another flow comes from diesel generator when the PVand the battery could no longer serve the load the generatorsupplies electricity direct to serve the load and at the sametime charge the battery through the rectifier That is how thedesigned hybrid system is expected to work

The system design was to be representative of the typeof residential systems that were likely to be installed inthe foreseeable future Hence the system was sized usingconventional simulation tool and representative insolationdata

31 Cost of Key Components (including Installation andLabour) and Interest Rate for Capital Investments

311 PV System Cost (US$ 2Wp) The cost of PV panelson the Nigerian market was estimated as US$ 0600Wpbased on prices cited by Nigerian suppliers (based on thecost of a module of 1210 times 808 times 35mm size generating 130watts of peak power (Wp DC) in controlled conditions) [34]This was adjusted upward to US$ 2Wp to account for othersupport components that are required also known as balanceof system (BOS) parts such as cables charge controller withmaximum power point tracker lightening protection anddeliverylabour and installation costs

8 Journal of Energy

Table3Re

sults

oftheh

ybrid

electric

ityprod

uctio

nbatte

rychargesup

plyexcesslossesandconsum

ption(kW)

Mon

th

Hybrid

PVdieselelectric

itygeneratio

nRe

ctifier

Batte

ryInverter

ACload

Electricity

generatedandsupp

liedcharging

the

batte

ryand

excessele

ctric

ityby

theh

ybrid

syste

m(kW)

Energy

received

byther

ectifi

erto

charge

theb

attery

(kW)

Energy

received

bytheb

attery

andsupp

liedto

theA

Cload

viainverter(kW

)

Energy

received

bythe

inverter

andsupp

liedto

the

ACload

(kW)

ACload

served

(kW)

Electricity

generatedlowastSupp

liedto

theload

lowastCh

arging

theb

attery

Losses

Excess

electricity

generated

Energy

inEn

ergy

out

Losses

Charge

Disc

harge

Losses

Energy

inEn

ergy

out

Losses

Janu

ary

271539

91862277

538799

0159

314164

2995

1725464

644

871

493928minus427515

66413

141514

31273589

1415

542148238

February

2527428

1695987

4897

000154

3415

872899

82246547

43435

446265minus379553

66712

135152

3121632

7135196

1940

344

March

2802411

1887039

533918

0154

3813

003014

72256311

4516

1488757minus411872

76885

1506288

1355615

150673

2148238

April

2629097

1827413

5093

320146

292206

2897

05246309

4339

6465936minus395701

70235

144131

1129713

7144174

2078940

May

2631846

187612

3535826

0179

2197

18314101

2670

4847053

488773minus419038

69735

1468844

1321921

146923

2148238

June

2522854

1804

867

528865

0177

188945

313288

266355

46933

4819

32minus408659

73273

1345553

1210967

134586

2078940

July

2544

529

1860281

5410

310167

143050

31466

6267531

4713

5493896minus420576

7332

01325833

1193214

132619

2148238

August

2565565

1849784

551749

0164

163868

324882

276211

48671

503078minus425589

77489

1270987

1143852

127135

2148238

Septem

ber

256819

51799896

5298

540171

238274

312814

265950

46864

482990minus409230

7376

01301553

11713

67130186

2078940

Octob

er2681092

1873098

5412

030184

266607

324375

275785

48590

492613minus422554

70059

1473828

1326414

1474

142148238

Novem

ber

2649461

181232

15297

430158

3072

39305717

2599

1945798

483945minus409988

73957

143333

71289968

143369

2078940

Decem

ber

266810

71868682

5414

490185

2577

91314356

2672

6847088

494361minus423486

70875

1438938

1295008

143930

2148238

Total

31505984

220177

686371469

1998

311474

93704875

3149880

554995

5816474minus495376

1862713

16773138

15095379

1677759

25293770

lowastIn

term

sofelectric

itysupp

lyandbatte

rychargethe

PVsupp

liese

lectric

ityto

theA

Cload

viathe

inverter

andchargesthe

batte

rydirectly

whereas

thed

ieselgenerator

supp

liese

lectric

ityto

theA

Cload

directly

andchargesthe

batte

rythroug

hther

ectifi

erassho

wnin

Table4

Also

the

batte

rysupp

liese

lectric

ityto

theA

Cload

throug

htheinverteras

show

nin

thistable

Journal of Energy 9

Multiple solar panelsmaking up a solar array Charge

controller

Control unit coordinates the power system and displays

the energy flow through the system

Converter contains both rectifier and inverter

Generator toconverter

disconnectswitch

Converter bypassswitch (selects

output aseither converteror generator)

Service box(main breaker

panel)

To loadsappliances

AC lightning arresters

Generator

Wires for automatic generator starterstoppersystem to start generator automaticallywhen the batteries are low and stop the

generator automatically when the batteries are fully charged

Multiple batteriesmaking up a battery

bank

Batteriesto converterdisconnect

switchCharge controller

to batteriesdisconnect

switch

DC lightningarrester

Solar tocharge

controllerdisconnect

switchCombiner box (combines multiplewires from solar array to just a few and

may contain breakers or fuses)

Figure 4 Photovoltaic hybrid power system structure [33]

Table 4 Results of each of the energy components of the hybrid system (PV and diesel) for electricity production supply and battery charging(kW)

Month

Electricity generated and supplied and batterycharge by the PV in hybrid system (kW)

Electricity generated and supplied and batterycharge by the diesel in hybrid system (kW)

Electricitygenerated

Supplied to the loadvia inverter

Charging thebattery directly

Electricitygenerated

Supplied to theload directly

Charging thebattery via rectifier

January 1538295 987628 239282 1177104 874649 299517February 1510492 971970 199718 1016936 724017 289982March 1705644 1094416 232446 1096767 792623 301472April 1554395 1045610 219627 1074702 781803 289705May 1488347 1049806 221725 1143499 826317 314101June 1333962 936894 215577 1188892 867973 313288July 1271351 905257 226365 1273178 955024 314666August 1230539 845398 226867 1335026 1004386 324882September 1343075 892323 217040 1225120 907573 312814October 1534355 1051274 216828 1146737 821824 324375November 1552498 1023349 224026 1096963 788972 305717December 1499299 1015452 227093 1168808 853230 314356Total 17562252 11819377 2666594 13943732 10198391 3704875

312 Converter Cost (US$ 0320Wp) The cost of a con-verter based on prices cited by Nigerian suppliers was US$0320Wp [35]

313 Battery Cost (US$ 180kWh) The cost of a 6V225Ahlead acid battery on the Nigerian market was found to be inthe range of US$ 172 [35] Including balance of system (BOS)components and labourinstallation costs the capital cost for

the battery arrays was adjusted upward to US$ 180kWhTheprecise number of batteries required for each option is thendetermined by the simulation

314 Generator Cost (US$ 1000kW) The capital cost ofthe genset includes the generator itself (usually diesel orgasoline) as well as BOS costs and labourinstallation costsOn the Nigerian local market a generator of smaller range

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 4: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

4 Journal of Energy

0

1000

2000

3000

4000

5000

6000

Hou

rly d

eman

d (W

)

Medium size deep-freezer Water pumping machine Washing machine Electric stoveMicrowave oven Electric pressing iron Air-conditioner RefrigeratorWater bath Ceiling fan Energy efficient lighting Lighting-outdoor (security)

Sony music systemDSTV receiver DVD player Computer printer Computer PCComputer laptop Miscellaneous

10

0-2

00

00

0-1

00

20

0-3

00

30

0-4

00

40

0-5

00

50

0-6

00

60

0-7

00

70

0-8

00

80

0-9

00

90

0-1

00

0

100

0-1

10

0

110

0-1

20

0

120

0-1

30

0

130

0-1

40

0

140

0-1

50

0

150

0-1

60

0

160

0-1

70

0

170

0-1

80

0

180

0-1

90

0

190

0-2

00

0

200

0-2

10

0

210

0-2

20

0

220

0-2

30

0

230

0-2

40

0

14998400998400 television21

998400998400 television21998400998400 TV with decoder

Figure 1 Hourly power demand profile of the household

Jan

Feb

Mar

Apr

May Jun Jul

Aug

Sep

Oct

Nov Dec

Daily radiationClearness index

Clea

rnes

s ind

ex

6

5

4

3

2

1

0

Dai

ly ra

diat

ion

(kW

hm

2d

) 10

08

06

04

02

00

Global horizontal radiation

Figure 2 Solar daily radiation profile forNdiagu-Akpugo inNkanu-West (Enugu State) [2]

2 Energy Models

Energy model depends mainly on the economic feasibil-ity and the proper sizing of the components in order toavoid outages as well as ensuring quality and reliability ofsupply Energy design system looks into its sizing and theprocess of selecting the best components to provide cheapefficient reliable environmentally friendly and cost effectivepower supply [3] The technoeconomic analysis looks at

both environmental cost and the cheapest cost of energyproduced by the system components Designing a hybridsystem would require correct components selection andsizing with appropriate operation strategy [4 5]

In energy systems the sizing of the individual systemscan be made in a variety of ways depending upon the choiceof parameters of interest Energy models are employed asa supporting tool to develop energy strategies as well asoutlining the likely future structure of the system underparticular conditions This helps to provide insights intothe technological paths structural evolution and policiesthat should be followed [3] A lot of research has beenconducted on the performance of hybrid power systems andexperimental results have been published in many articles[6ndash13] The energy output of a hybrid system can be enoughfor the demands of a house placed in regions where theextension of the already available electricity grid would befinancially unadvisable [9] A method of sizing hybrid PVsystems regarding the reliability to satisfy the load demandeconomy of components and discharge depth exploited bythe batteries is therefore required

Several models have been developed simulating andsizing PV systems using different operation strategies Theestimation of performance of PV systems based on the Lossof Load Probability (LLP) technique is developed by [14ndash17] These analytical methods are simple to apply but theyare not general On the other hand the numerical methods

Journal of Energy 5

presented by [18ndash24] present a good solution but these needa long period solar radiation data record Other methodsestimate the excess of energy provided by PV generators andthe storage capacity of the batteries using the utilizabilitymethod [25]

The conventional methodology (empiric analytic andnumeric) for sizing PV systems has been used for a locationwhere the required weather data (irradiation temperaturehumidity clearness index etc) and the information concern-ing the site where we want to implement the PV system areavailable In this case these methods present a good solutionfor sizing PV systems However these techniques could notbe used for sizing PV systems in remote areas in the casewhere the required data are not available Moreover themajority of the above methods need the long term meteoro-logical data such as total solar irradiation and air temperaturefor their operation So when the relevantmeteorological dataare not available these methods cannot be used especiallyin the isolated areas In this context a model was developedand the methodology aims at finding the configurationamong a set of systems components which meets the desiredsystem reliability requirements with the lowest value oflevelised cost of energy (LCE) This methodology can beused for determining the optimum number of solar panelsand batteries configurations (the storage capacity of thebatteries necessary to satisfy a given consumption) Since theinvestigation of this paper is based on a detailed study of ananalysis of the energy flows the analysis reveals the energylosses (charge controller rectifier battery and inverter) in thesystem and the storage requirement In addition the modeldeveloped was used to select the optimal sizing parameters ofPV system in which the results obtained have been comparedand tested with HOMER software

21 Development of a Model for Energy System ComponentsModelisation is an essential step before any phase of com-ponent sizing Various modeling techniques are developedto model hybrid PVdiesel system components in previousstudies For a hybrid PVdiesel system with storage batterythree principal subsystems are included the PVgenerator thediesel generator and the battery storage A methodology formodeling hybrid PVdiesel system components is describedbelowThe theoretical aspects are given below (Sections 211212 213 214 and 215) and are based on the works of Ani[3] Gupta et al [26] and Ashok [27]

211 Modeling of Solar-Photovoltaic Generator Using thesolar radiation available the hourly energy output of the PVgenerator (119864PVG) can be calculated according to the followingequation [3 27ndash29]

119864PVG = 119866 (119905) times 119860 times 119875 times 120578PVG (1)

212 Modeling of Diesel Generator Hourly energy generatedby diesel generator (119864DEG) with rated power output (119875DEG) isdefined by the following expression [3 27 28]

119864DEG (119905) = 119875DEG (119905) times 120578DEG (2)

213 Modeling of Converter In the proposed scheme aconverter contains both rectifier and inverter PV energygenerator and battery subsystems are connected with DC buswhile diesel generating unit subsystem is connected with ACbusThe electric loads connected in this scheme are AC loads

The rectifier is used to transform the surplus AC powerfrom the diesel electric generator to charge the battery Thediesel electric generator will be powering the load and at thesame time charging the battery The rectifier model is givenbelow

119864REC-OUT (119905) = 119864REC-IN (119905) times 120578REC

119864REC-IN (119905) = 119864SUR-AC (119905) (3)

At any time 119905

119864SUR-AC (119905) = 119864DEG (119905) minus 119864Load (119905) (4)

The inverter model for photovoltaic generator and batterybank are given below

119864PVG-IN (119905) = 119864PVG (119905) times 120578INV

119864BAT-INV (119905) = [(119864BAT (119905 minus 1) minus 119864LOAD (119905))

(120578INV times 120578DCHG)]

(5)

214Modeling of Charge Controller To prevent overchargingof a battery a charge controller is used to sense when thebatteries are fully charged and to stop or reduce the amountof energy flowing from the energy source to the batteriesThemodel of the charge controller is presented below

119864CC-OUT (119905) = 119864CC-IN (119905) times 120578CC

119864CC-IN (119905) = 119864REC-OUT (119905) + 119864SUR-DC (119905) (6)

215 Modeling of Battery Bank The battery state of charge(SOC) is the cumulative sum of the daily chargedischargetransfers The battery serves as an energy source entity whendischarging and a loadwhen charging At any time 119905 the stateof battery is related to the previous state of charge and to theenergy production and consumption situation of the systemduring the time from 119905 minus 1 to 119905

During the charging process when the total output ofall generators exceeds the load demand the available batterybank capacity at time 119905 can be described by [3 29 30]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864CC-OUT (119905) times 120578CHG (7)

On the other hand when the load demand is greater than theavailable energy generated the battery bank is in dischargingstate Therefore the available battery bank capacity at time 119905can be expressed as [3 29]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864Needed (119905) (8)

Let 119889 be the ratio of minimum allowable SOC voltage limit tothemaximum SOC voltage across the battery terminals whenit is fully charged So the depth of discharge (DOD) is

DOD = (1 minus 119889) times 100 (9)

6 Journal of Energy

DOD is a measure of how much energy has been withdrawnfrom a storage device expressed as a percentage of fullcapacity The maximum value of SOC is 1 and the minimumSOC is determined by maximum depth of discharge (DOD)

SOCMin = 1 minusDOD100

(10)

22 Mathematical Cost Model (Economic and EnvironmentalCosts) of Energy Systems This work developed a mathemati-cal model of a system that could represent the integral (totalsum) of the minimum economic and environmental (healthand safety) costs of the considered options

221 The Annualized Cost of a Component The annualizedcost of a component includes annualized capital cost annu-alized replacement cost annual OampM cost emissions costand annual fuel cost (generator) Operation cost is calculatedhourly on daily basis [3 27 29 31]

222 Annualized Capital Cost The annualized capital costof a system component is equal to the total initial capital costmultiplied by the capital recovery factor Annualized capitalcost is calculated using [3 27 29 31]

119862acap = 119862cap sdot CRF (119894 119877proj) (11)

223 Annualized Replacement Cost The annualized replace-ment cost of a system component is the annualized value ofall the replacement costs occurring throughout the lifetimeof the project minus the salvage value at the end of theproject lifetime Annualized replacement cost is calculatedusing [3 27 29 31]

119862arep = 119862rep sdot 119891rep sdot SFF (119894 119877comp) minus 119878 sdot SFF (119894 119877proj) (12)

119891rep a factor arising because the component lifetime can bedifferent from the project lifetime is given by

119891rep =

CRF (119894 119877proj)

CRF (119894 119877rep) 119877rep gt 0

0 119877rep = 0

(13)

119877rep the replacement cost duration is given by

119877rep = 119877comp sdot INT(119877proj

119877comp) (14)

SFF( ) the sinking fund factor which is a ratio used tocalculate the future value of a series of equal annual cashflows is given by

SFF (119894 119873) = 119894

(1 + 119894)119873minus 1 (15)

The salvaged value of the component at the end of the projectlifetime is proportional to its remaining life Therefore thesalvage value 119878 is given by

119878 = 119862rep sdot119877rem119877comp

(16)

119877rem the remaining life of the component at the end of theproject lifetime is given by

119877rem = 119877comp minus (119877proj minus 119877rep) (17)

224 Annualized Operating Cost The operating cost is theannualized value of all costs and revenues other than initialcapital costs and is calculated using [3 27 29 31]

119862aop =365

sum119905=1

24

sum119905=1

[119862oc (119905)] (18)

225 Cost of Emissions The following equation is used tocalculate the cost of emissions [3 27 29 31]

119862emissions =119888CO2

119872CO2

+ 119888CO119872CO + 119888UHC119872UHC + 119888PM119872PM + 119888SO2

119872SO2

+ 119888NO119909

119872NO119909

1000 (19)

Total cost of a component = economic cost + environmentalcost where economic cost = capital cost + replacement cost +operation and maintenance cost + fuel cost (generator) Alsoenvironmental cost = emissions cost

Annualized Cost of a Component Is Calculated Using [327 29 31]

119862ann = 119862acap + 119862arep + 119862aop + 119862emissions (20)

Annualized Total Cost of a Component Is CalculatedUsing [29 31]

119862anntot119888 =

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888 + 119862emissions) (21)

From (21) the economic and environmental cost modelthrough annualized total cost of different configurations of

Journal of Energy 7

power system results in the hybridizing of the renewableenergy generator (PV) with existing energy (diesel) is givenbelow

Economic and environmental costmodel of running solar+ diesel generator + batteries + converter is calculated as

119862anntot119904+119892+119887+119888 =

119873119904

sum119904=1

(119862acap119904 + 119862arep119904 + 119862aop119904

+ 119862emissions) +

119873119892

sum119892=1

(119862acap119892 + 119862arep119892 + 119862aop119892

+ 119862emissions + 119862af 119892) +

119873119887

sum119887=1

(119862acap119887 + 119862arep119887 + 119862aop119887

+ 119862emissions) +

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888)

(22)

23 Description of the Computer Simulation A computerprogram was developed and used to build the hybrid(PVdiesel) system model Data inputs to the programare hourly load demand data latitude and longitude ofthe site and reference component cost The designed soft-ware determines as its output the size of system com-ponents (sizing parameters) and the performance of thesystem over the course of the year (see the supple-mentary data in Supplementary Material available onlineat httpdxdoiorg10115520166278138) by showing thepower supplied by each of the energy systems over theyear given the load conditions and taking into account thetechnical factors The designed software can be used to studyhow the hybrid (PVdiesel) system is being supplied

24 Validation of the Model The designed software resultswere carried out followed with HOMER data to validate theanalysis The comparison shows a close agreement betweenresults obtained from the designed software module andresults obtained from HOMER setup In addition beforeusing the measured data gotten from NASA datasets insimulating the individual components of a PVdiesel hybridsystem the developed program accuracy was established thesimulated data predicted by the software program fall withinthe bounds of the measured data The algorithm that thedeveloped program uses to synthesize solar data is based onthe work of Graham andHollands [32]The realistic nature ofsynthetic data created by this algorithm is demonstrated andthe test shows that synthetic solar data (simulated) producevirtually the same simulation results as real data (measured)as shown in Figure 3

3 System Description

The designed system considered in this paper is a hybridsystem which consists of a renewable (photovoltaic) energysystem integrated in a conventional (diesel) power generationsystem energy storage in battery a DCAC converter (aninverter for the conversion of generated DC power into

0

1

2

3

4

5

6

7

Month of the yearMeasuredSimulated

Jan

Feb

Mar

ch

April

May

June July

Aug

Sept Oct

Nov Dec

Dai

ly ra

diat

ion

(kW

hm

2d

)

Figure 3 Calibrated solar radiation

required AC power) and an ACDC converter (a rectifierfor the conversion of generated AC power in order to chargethe battery) as shown in Figure 4 The inverter used is bidi-rectional also known as power converter which maintainsenergy flow between AC and DC components since the flowcomes in two different directions (from AC to DC and fromDC to AC)

The flow from the solar array passes through the chargecontroller to charge the battery and at the same time supplyelectricity to the load through the inverter The actual ACpower obtained after the conversion from a solar array can beseen in Table 3 The charge controller monitors and controlsthe charging and discharging of the battery in order not toallow the battery to be damaged (due to overcharging oroverdischarging)

Another flow comes from diesel generator when the PVand the battery could no longer serve the load the generatorsupplies electricity direct to serve the load and at the sametime charge the battery through the rectifier That is how thedesigned hybrid system is expected to work

The system design was to be representative of the typeof residential systems that were likely to be installed inthe foreseeable future Hence the system was sized usingconventional simulation tool and representative insolationdata

31 Cost of Key Components (including Installation andLabour) and Interest Rate for Capital Investments

311 PV System Cost (US$ 2Wp) The cost of PV panelson the Nigerian market was estimated as US$ 0600Wpbased on prices cited by Nigerian suppliers (based on thecost of a module of 1210 times 808 times 35mm size generating 130watts of peak power (Wp DC) in controlled conditions) [34]This was adjusted upward to US$ 2Wp to account for othersupport components that are required also known as balanceof system (BOS) parts such as cables charge controller withmaximum power point tracker lightening protection anddeliverylabour and installation costs

8 Journal of Energy

Table3Re

sults

oftheh

ybrid

electric

ityprod

uctio

nbatte

rychargesup

plyexcesslossesandconsum

ption(kW)

Mon

th

Hybrid

PVdieselelectric

itygeneratio

nRe

ctifier

Batte

ryInverter

ACload

Electricity

generatedandsupp

liedcharging

the

batte

ryand

excessele

ctric

ityby

theh

ybrid

syste

m(kW)

Energy

received

byther

ectifi

erto

charge

theb

attery

(kW)

Energy

received

bytheb

attery

andsupp

liedto

theA

Cload

viainverter(kW

)

Energy

received

bythe

inverter

andsupp

liedto

the

ACload

(kW)

ACload

served

(kW)

Electricity

generatedlowastSupp

liedto

theload

lowastCh

arging

theb

attery

Losses

Excess

electricity

generated

Energy

inEn

ergy

out

Losses

Charge

Disc

harge

Losses

Energy

inEn

ergy

out

Losses

Janu

ary

271539

91862277

538799

0159

314164

2995

1725464

644

871

493928minus427515

66413

141514

31273589

1415

542148238

February

2527428

1695987

4897

000154

3415

872899

82246547

43435

446265minus379553

66712

135152

3121632

7135196

1940

344

March

2802411

1887039

533918

0154

3813

003014

72256311

4516

1488757minus411872

76885

1506288

1355615

150673

2148238

April

2629097

1827413

5093

320146

292206

2897

05246309

4339

6465936minus395701

70235

144131

1129713

7144174

2078940

May

2631846

187612

3535826

0179

2197

18314101

2670

4847053

488773minus419038

69735

1468844

1321921

146923

2148238

June

2522854

1804

867

528865

0177

188945

313288

266355

46933

4819

32minus408659

73273

1345553

1210967

134586

2078940

July

2544

529

1860281

5410

310167

143050

31466

6267531

4713

5493896minus420576

7332

01325833

1193214

132619

2148238

August

2565565

1849784

551749

0164

163868

324882

276211

48671

503078minus425589

77489

1270987

1143852

127135

2148238

Septem

ber

256819

51799896

5298

540171

238274

312814

265950

46864

482990minus409230

7376

01301553

11713

67130186

2078940

Octob

er2681092

1873098

5412

030184

266607

324375

275785

48590

492613minus422554

70059

1473828

1326414

1474

142148238

Novem

ber

2649461

181232

15297

430158

3072

39305717

2599

1945798

483945minus409988

73957

143333

71289968

143369

2078940

Decem

ber

266810

71868682

5414

490185

2577

91314356

2672

6847088

494361minus423486

70875

1438938

1295008

143930

2148238

Total

31505984

220177

686371469

1998

311474

93704875

3149880

554995

5816474minus495376

1862713

16773138

15095379

1677759

25293770

lowastIn

term

sofelectric

itysupp

lyandbatte

rychargethe

PVsupp

liese

lectric

ityto

theA

Cload

viathe

inverter

andchargesthe

batte

rydirectly

whereas

thed

ieselgenerator

supp

liese

lectric

ityto

theA

Cload

directly

andchargesthe

batte

rythroug

hther

ectifi

erassho

wnin

Table4

Also

the

batte

rysupp

liese

lectric

ityto

theA

Cload

throug

htheinverteras

show

nin

thistable

Journal of Energy 9

Multiple solar panelsmaking up a solar array Charge

controller

Control unit coordinates the power system and displays

the energy flow through the system

Converter contains both rectifier and inverter

Generator toconverter

disconnectswitch

Converter bypassswitch (selects

output aseither converteror generator)

Service box(main breaker

panel)

To loadsappliances

AC lightning arresters

Generator

Wires for automatic generator starterstoppersystem to start generator automaticallywhen the batteries are low and stop the

generator automatically when the batteries are fully charged

Multiple batteriesmaking up a battery

bank

Batteriesto converterdisconnect

switchCharge controller

to batteriesdisconnect

switch

DC lightningarrester

Solar tocharge

controllerdisconnect

switchCombiner box (combines multiplewires from solar array to just a few and

may contain breakers or fuses)

Figure 4 Photovoltaic hybrid power system structure [33]

Table 4 Results of each of the energy components of the hybrid system (PV and diesel) for electricity production supply and battery charging(kW)

Month

Electricity generated and supplied and batterycharge by the PV in hybrid system (kW)

Electricity generated and supplied and batterycharge by the diesel in hybrid system (kW)

Electricitygenerated

Supplied to the loadvia inverter

Charging thebattery directly

Electricitygenerated

Supplied to theload directly

Charging thebattery via rectifier

January 1538295 987628 239282 1177104 874649 299517February 1510492 971970 199718 1016936 724017 289982March 1705644 1094416 232446 1096767 792623 301472April 1554395 1045610 219627 1074702 781803 289705May 1488347 1049806 221725 1143499 826317 314101June 1333962 936894 215577 1188892 867973 313288July 1271351 905257 226365 1273178 955024 314666August 1230539 845398 226867 1335026 1004386 324882September 1343075 892323 217040 1225120 907573 312814October 1534355 1051274 216828 1146737 821824 324375November 1552498 1023349 224026 1096963 788972 305717December 1499299 1015452 227093 1168808 853230 314356Total 17562252 11819377 2666594 13943732 10198391 3704875

312 Converter Cost (US$ 0320Wp) The cost of a con-verter based on prices cited by Nigerian suppliers was US$0320Wp [35]

313 Battery Cost (US$ 180kWh) The cost of a 6V225Ahlead acid battery on the Nigerian market was found to be inthe range of US$ 172 [35] Including balance of system (BOS)components and labourinstallation costs the capital cost for

the battery arrays was adjusted upward to US$ 180kWhTheprecise number of batteries required for each option is thendetermined by the simulation

314 Generator Cost (US$ 1000kW) The capital cost ofthe genset includes the generator itself (usually diesel orgasoline) as well as BOS costs and labourinstallation costsOn the Nigerian local market a generator of smaller range

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

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FuelsJournal of

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Renewable Energy

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Page 5: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

Journal of Energy 5

presented by [18ndash24] present a good solution but these needa long period solar radiation data record Other methodsestimate the excess of energy provided by PV generators andthe storage capacity of the batteries using the utilizabilitymethod [25]

The conventional methodology (empiric analytic andnumeric) for sizing PV systems has been used for a locationwhere the required weather data (irradiation temperaturehumidity clearness index etc) and the information concern-ing the site where we want to implement the PV system areavailable In this case these methods present a good solutionfor sizing PV systems However these techniques could notbe used for sizing PV systems in remote areas in the casewhere the required data are not available Moreover themajority of the above methods need the long term meteoro-logical data such as total solar irradiation and air temperaturefor their operation So when the relevantmeteorological dataare not available these methods cannot be used especiallyin the isolated areas In this context a model was developedand the methodology aims at finding the configurationamong a set of systems components which meets the desiredsystem reliability requirements with the lowest value oflevelised cost of energy (LCE) This methodology can beused for determining the optimum number of solar panelsand batteries configurations (the storage capacity of thebatteries necessary to satisfy a given consumption) Since theinvestigation of this paper is based on a detailed study of ananalysis of the energy flows the analysis reveals the energylosses (charge controller rectifier battery and inverter) in thesystem and the storage requirement In addition the modeldeveloped was used to select the optimal sizing parameters ofPV system in which the results obtained have been comparedand tested with HOMER software

21 Development of a Model for Energy System ComponentsModelisation is an essential step before any phase of com-ponent sizing Various modeling techniques are developedto model hybrid PVdiesel system components in previousstudies For a hybrid PVdiesel system with storage batterythree principal subsystems are included the PVgenerator thediesel generator and the battery storage A methodology formodeling hybrid PVdiesel system components is describedbelowThe theoretical aspects are given below (Sections 211212 213 214 and 215) and are based on the works of Ani[3] Gupta et al [26] and Ashok [27]

211 Modeling of Solar-Photovoltaic Generator Using thesolar radiation available the hourly energy output of the PVgenerator (119864PVG) can be calculated according to the followingequation [3 27ndash29]

119864PVG = 119866 (119905) times 119860 times 119875 times 120578PVG (1)

212 Modeling of Diesel Generator Hourly energy generatedby diesel generator (119864DEG) with rated power output (119875DEG) isdefined by the following expression [3 27 28]

119864DEG (119905) = 119875DEG (119905) times 120578DEG (2)

213 Modeling of Converter In the proposed scheme aconverter contains both rectifier and inverter PV energygenerator and battery subsystems are connected with DC buswhile diesel generating unit subsystem is connected with ACbusThe electric loads connected in this scheme are AC loads

The rectifier is used to transform the surplus AC powerfrom the diesel electric generator to charge the battery Thediesel electric generator will be powering the load and at thesame time charging the battery The rectifier model is givenbelow

119864REC-OUT (119905) = 119864REC-IN (119905) times 120578REC

119864REC-IN (119905) = 119864SUR-AC (119905) (3)

At any time 119905

119864SUR-AC (119905) = 119864DEG (119905) minus 119864Load (119905) (4)

The inverter model for photovoltaic generator and batterybank are given below

119864PVG-IN (119905) = 119864PVG (119905) times 120578INV

119864BAT-INV (119905) = [(119864BAT (119905 minus 1) minus 119864LOAD (119905))

(120578INV times 120578DCHG)]

(5)

214Modeling of Charge Controller To prevent overchargingof a battery a charge controller is used to sense when thebatteries are fully charged and to stop or reduce the amountof energy flowing from the energy source to the batteriesThemodel of the charge controller is presented below

119864CC-OUT (119905) = 119864CC-IN (119905) times 120578CC

119864CC-IN (119905) = 119864REC-OUT (119905) + 119864SUR-DC (119905) (6)

215 Modeling of Battery Bank The battery state of charge(SOC) is the cumulative sum of the daily chargedischargetransfers The battery serves as an energy source entity whendischarging and a loadwhen charging At any time 119905 the stateof battery is related to the previous state of charge and to theenergy production and consumption situation of the systemduring the time from 119905 minus 1 to 119905

During the charging process when the total output ofall generators exceeds the load demand the available batterybank capacity at time 119905 can be described by [3 29 30]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864CC-OUT (119905) times 120578CHG (7)

On the other hand when the load demand is greater than theavailable energy generated the battery bank is in dischargingstate Therefore the available battery bank capacity at time 119905can be expressed as [3 29]

119864BAT (119905) = 119864BAT (119905 minus 1) minus 119864Needed (119905) (8)

Let 119889 be the ratio of minimum allowable SOC voltage limit tothemaximum SOC voltage across the battery terminals whenit is fully charged So the depth of discharge (DOD) is

DOD = (1 minus 119889) times 100 (9)

6 Journal of Energy

DOD is a measure of how much energy has been withdrawnfrom a storage device expressed as a percentage of fullcapacity The maximum value of SOC is 1 and the minimumSOC is determined by maximum depth of discharge (DOD)

SOCMin = 1 minusDOD100

(10)

22 Mathematical Cost Model (Economic and EnvironmentalCosts) of Energy Systems This work developed a mathemati-cal model of a system that could represent the integral (totalsum) of the minimum economic and environmental (healthand safety) costs of the considered options

221 The Annualized Cost of a Component The annualizedcost of a component includes annualized capital cost annu-alized replacement cost annual OampM cost emissions costand annual fuel cost (generator) Operation cost is calculatedhourly on daily basis [3 27 29 31]

222 Annualized Capital Cost The annualized capital costof a system component is equal to the total initial capital costmultiplied by the capital recovery factor Annualized capitalcost is calculated using [3 27 29 31]

119862acap = 119862cap sdot CRF (119894 119877proj) (11)

223 Annualized Replacement Cost The annualized replace-ment cost of a system component is the annualized value ofall the replacement costs occurring throughout the lifetimeof the project minus the salvage value at the end of theproject lifetime Annualized replacement cost is calculatedusing [3 27 29 31]

119862arep = 119862rep sdot 119891rep sdot SFF (119894 119877comp) minus 119878 sdot SFF (119894 119877proj) (12)

119891rep a factor arising because the component lifetime can bedifferent from the project lifetime is given by

119891rep =

CRF (119894 119877proj)

CRF (119894 119877rep) 119877rep gt 0

0 119877rep = 0

(13)

119877rep the replacement cost duration is given by

119877rep = 119877comp sdot INT(119877proj

119877comp) (14)

SFF( ) the sinking fund factor which is a ratio used tocalculate the future value of a series of equal annual cashflows is given by

SFF (119894 119873) = 119894

(1 + 119894)119873minus 1 (15)

The salvaged value of the component at the end of the projectlifetime is proportional to its remaining life Therefore thesalvage value 119878 is given by

119878 = 119862rep sdot119877rem119877comp

(16)

119877rem the remaining life of the component at the end of theproject lifetime is given by

119877rem = 119877comp minus (119877proj minus 119877rep) (17)

224 Annualized Operating Cost The operating cost is theannualized value of all costs and revenues other than initialcapital costs and is calculated using [3 27 29 31]

119862aop =365

sum119905=1

24

sum119905=1

[119862oc (119905)] (18)

225 Cost of Emissions The following equation is used tocalculate the cost of emissions [3 27 29 31]

119862emissions =119888CO2

119872CO2

+ 119888CO119872CO + 119888UHC119872UHC + 119888PM119872PM + 119888SO2

119872SO2

+ 119888NO119909

119872NO119909

1000 (19)

Total cost of a component = economic cost + environmentalcost where economic cost = capital cost + replacement cost +operation and maintenance cost + fuel cost (generator) Alsoenvironmental cost = emissions cost

Annualized Cost of a Component Is Calculated Using [327 29 31]

119862ann = 119862acap + 119862arep + 119862aop + 119862emissions (20)

Annualized Total Cost of a Component Is CalculatedUsing [29 31]

119862anntot119888 =

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888 + 119862emissions) (21)

From (21) the economic and environmental cost modelthrough annualized total cost of different configurations of

Journal of Energy 7

power system results in the hybridizing of the renewableenergy generator (PV) with existing energy (diesel) is givenbelow

Economic and environmental costmodel of running solar+ diesel generator + batteries + converter is calculated as

119862anntot119904+119892+119887+119888 =

119873119904

sum119904=1

(119862acap119904 + 119862arep119904 + 119862aop119904

+ 119862emissions) +

119873119892

sum119892=1

(119862acap119892 + 119862arep119892 + 119862aop119892

+ 119862emissions + 119862af 119892) +

119873119887

sum119887=1

(119862acap119887 + 119862arep119887 + 119862aop119887

+ 119862emissions) +

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888)

(22)

23 Description of the Computer Simulation A computerprogram was developed and used to build the hybrid(PVdiesel) system model Data inputs to the programare hourly load demand data latitude and longitude ofthe site and reference component cost The designed soft-ware determines as its output the size of system com-ponents (sizing parameters) and the performance of thesystem over the course of the year (see the supple-mentary data in Supplementary Material available onlineat httpdxdoiorg10115520166278138) by showing thepower supplied by each of the energy systems over theyear given the load conditions and taking into account thetechnical factors The designed software can be used to studyhow the hybrid (PVdiesel) system is being supplied

24 Validation of the Model The designed software resultswere carried out followed with HOMER data to validate theanalysis The comparison shows a close agreement betweenresults obtained from the designed software module andresults obtained from HOMER setup In addition beforeusing the measured data gotten from NASA datasets insimulating the individual components of a PVdiesel hybridsystem the developed program accuracy was established thesimulated data predicted by the software program fall withinthe bounds of the measured data The algorithm that thedeveloped program uses to synthesize solar data is based onthe work of Graham andHollands [32]The realistic nature ofsynthetic data created by this algorithm is demonstrated andthe test shows that synthetic solar data (simulated) producevirtually the same simulation results as real data (measured)as shown in Figure 3

3 System Description

The designed system considered in this paper is a hybridsystem which consists of a renewable (photovoltaic) energysystem integrated in a conventional (diesel) power generationsystem energy storage in battery a DCAC converter (aninverter for the conversion of generated DC power into

0

1

2

3

4

5

6

7

Month of the yearMeasuredSimulated

Jan

Feb

Mar

ch

April

May

June July

Aug

Sept Oct

Nov Dec

Dai

ly ra

diat

ion

(kW

hm

2d

)

Figure 3 Calibrated solar radiation

required AC power) and an ACDC converter (a rectifierfor the conversion of generated AC power in order to chargethe battery) as shown in Figure 4 The inverter used is bidi-rectional also known as power converter which maintainsenergy flow between AC and DC components since the flowcomes in two different directions (from AC to DC and fromDC to AC)

The flow from the solar array passes through the chargecontroller to charge the battery and at the same time supplyelectricity to the load through the inverter The actual ACpower obtained after the conversion from a solar array can beseen in Table 3 The charge controller monitors and controlsthe charging and discharging of the battery in order not toallow the battery to be damaged (due to overcharging oroverdischarging)

Another flow comes from diesel generator when the PVand the battery could no longer serve the load the generatorsupplies electricity direct to serve the load and at the sametime charge the battery through the rectifier That is how thedesigned hybrid system is expected to work

The system design was to be representative of the typeof residential systems that were likely to be installed inthe foreseeable future Hence the system was sized usingconventional simulation tool and representative insolationdata

31 Cost of Key Components (including Installation andLabour) and Interest Rate for Capital Investments

311 PV System Cost (US$ 2Wp) The cost of PV panelson the Nigerian market was estimated as US$ 0600Wpbased on prices cited by Nigerian suppliers (based on thecost of a module of 1210 times 808 times 35mm size generating 130watts of peak power (Wp DC) in controlled conditions) [34]This was adjusted upward to US$ 2Wp to account for othersupport components that are required also known as balanceof system (BOS) parts such as cables charge controller withmaximum power point tracker lightening protection anddeliverylabour and installation costs

8 Journal of Energy

Table3Re

sults

oftheh

ybrid

electric

ityprod

uctio

nbatte

rychargesup

plyexcesslossesandconsum

ption(kW)

Mon

th

Hybrid

PVdieselelectric

itygeneratio

nRe

ctifier

Batte

ryInverter

ACload

Electricity

generatedandsupp

liedcharging

the

batte

ryand

excessele

ctric

ityby

theh

ybrid

syste

m(kW)

Energy

received

byther

ectifi

erto

charge

theb

attery

(kW)

Energy

received

bytheb

attery

andsupp

liedto

theA

Cload

viainverter(kW

)

Energy

received

bythe

inverter

andsupp

liedto

the

ACload

(kW)

ACload

served

(kW)

Electricity

generatedlowastSupp

liedto

theload

lowastCh

arging

theb

attery

Losses

Excess

electricity

generated

Energy

inEn

ergy

out

Losses

Charge

Disc

harge

Losses

Energy

inEn

ergy

out

Losses

Janu

ary

271539

91862277

538799

0159

314164

2995

1725464

644

871

493928minus427515

66413

141514

31273589

1415

542148238

February

2527428

1695987

4897

000154

3415

872899

82246547

43435

446265minus379553

66712

135152

3121632

7135196

1940

344

March

2802411

1887039

533918

0154

3813

003014

72256311

4516

1488757minus411872

76885

1506288

1355615

150673

2148238

April

2629097

1827413

5093

320146

292206

2897

05246309

4339

6465936minus395701

70235

144131

1129713

7144174

2078940

May

2631846

187612

3535826

0179

2197

18314101

2670

4847053

488773minus419038

69735

1468844

1321921

146923

2148238

June

2522854

1804

867

528865

0177

188945

313288

266355

46933

4819

32minus408659

73273

1345553

1210967

134586

2078940

July

2544

529

1860281

5410

310167

143050

31466

6267531

4713

5493896minus420576

7332

01325833

1193214

132619

2148238

August

2565565

1849784

551749

0164

163868

324882

276211

48671

503078minus425589

77489

1270987

1143852

127135

2148238

Septem

ber

256819

51799896

5298

540171

238274

312814

265950

46864

482990minus409230

7376

01301553

11713

67130186

2078940

Octob

er2681092

1873098

5412

030184

266607

324375

275785

48590

492613minus422554

70059

1473828

1326414

1474

142148238

Novem

ber

2649461

181232

15297

430158

3072

39305717

2599

1945798

483945minus409988

73957

143333

71289968

143369

2078940

Decem

ber

266810

71868682

5414

490185

2577

91314356

2672

6847088

494361minus423486

70875

1438938

1295008

143930

2148238

Total

31505984

220177

686371469

1998

311474

93704875

3149880

554995

5816474minus495376

1862713

16773138

15095379

1677759

25293770

lowastIn

term

sofelectric

itysupp

lyandbatte

rychargethe

PVsupp

liese

lectric

ityto

theA

Cload

viathe

inverter

andchargesthe

batte

rydirectly

whereas

thed

ieselgenerator

supp

liese

lectric

ityto

theA

Cload

directly

andchargesthe

batte

rythroug

hther

ectifi

erassho

wnin

Table4

Also

the

batte

rysupp

liese

lectric

ityto

theA

Cload

throug

htheinverteras

show

nin

thistable

Journal of Energy 9

Multiple solar panelsmaking up a solar array Charge

controller

Control unit coordinates the power system and displays

the energy flow through the system

Converter contains both rectifier and inverter

Generator toconverter

disconnectswitch

Converter bypassswitch (selects

output aseither converteror generator)

Service box(main breaker

panel)

To loadsappliances

AC lightning arresters

Generator

Wires for automatic generator starterstoppersystem to start generator automaticallywhen the batteries are low and stop the

generator automatically when the batteries are fully charged

Multiple batteriesmaking up a battery

bank

Batteriesto converterdisconnect

switchCharge controller

to batteriesdisconnect

switch

DC lightningarrester

Solar tocharge

controllerdisconnect

switchCombiner box (combines multiplewires from solar array to just a few and

may contain breakers or fuses)

Figure 4 Photovoltaic hybrid power system structure [33]

Table 4 Results of each of the energy components of the hybrid system (PV and diesel) for electricity production supply and battery charging(kW)

Month

Electricity generated and supplied and batterycharge by the PV in hybrid system (kW)

Electricity generated and supplied and batterycharge by the diesel in hybrid system (kW)

Electricitygenerated

Supplied to the loadvia inverter

Charging thebattery directly

Electricitygenerated

Supplied to theload directly

Charging thebattery via rectifier

January 1538295 987628 239282 1177104 874649 299517February 1510492 971970 199718 1016936 724017 289982March 1705644 1094416 232446 1096767 792623 301472April 1554395 1045610 219627 1074702 781803 289705May 1488347 1049806 221725 1143499 826317 314101June 1333962 936894 215577 1188892 867973 313288July 1271351 905257 226365 1273178 955024 314666August 1230539 845398 226867 1335026 1004386 324882September 1343075 892323 217040 1225120 907573 312814October 1534355 1051274 216828 1146737 821824 324375November 1552498 1023349 224026 1096963 788972 305717December 1499299 1015452 227093 1168808 853230 314356Total 17562252 11819377 2666594 13943732 10198391 3704875

312 Converter Cost (US$ 0320Wp) The cost of a con-verter based on prices cited by Nigerian suppliers was US$0320Wp [35]

313 Battery Cost (US$ 180kWh) The cost of a 6V225Ahlead acid battery on the Nigerian market was found to be inthe range of US$ 172 [35] Including balance of system (BOS)components and labourinstallation costs the capital cost for

the battery arrays was adjusted upward to US$ 180kWhTheprecise number of batteries required for each option is thendetermined by the simulation

314 Generator Cost (US$ 1000kW) The capital cost ofthe genset includes the generator itself (usually diesel orgasoline) as well as BOS costs and labourinstallation costsOn the Nigerian local market a generator of smaller range

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 6: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

6 Journal of Energy

DOD is a measure of how much energy has been withdrawnfrom a storage device expressed as a percentage of fullcapacity The maximum value of SOC is 1 and the minimumSOC is determined by maximum depth of discharge (DOD)

SOCMin = 1 minusDOD100

(10)

22 Mathematical Cost Model (Economic and EnvironmentalCosts) of Energy Systems This work developed a mathemati-cal model of a system that could represent the integral (totalsum) of the minimum economic and environmental (healthand safety) costs of the considered options

221 The Annualized Cost of a Component The annualizedcost of a component includes annualized capital cost annu-alized replacement cost annual OampM cost emissions costand annual fuel cost (generator) Operation cost is calculatedhourly on daily basis [3 27 29 31]

222 Annualized Capital Cost The annualized capital costof a system component is equal to the total initial capital costmultiplied by the capital recovery factor Annualized capitalcost is calculated using [3 27 29 31]

119862acap = 119862cap sdot CRF (119894 119877proj) (11)

223 Annualized Replacement Cost The annualized replace-ment cost of a system component is the annualized value ofall the replacement costs occurring throughout the lifetimeof the project minus the salvage value at the end of theproject lifetime Annualized replacement cost is calculatedusing [3 27 29 31]

119862arep = 119862rep sdot 119891rep sdot SFF (119894 119877comp) minus 119878 sdot SFF (119894 119877proj) (12)

119891rep a factor arising because the component lifetime can bedifferent from the project lifetime is given by

119891rep =

CRF (119894 119877proj)

CRF (119894 119877rep) 119877rep gt 0

0 119877rep = 0

(13)

119877rep the replacement cost duration is given by

119877rep = 119877comp sdot INT(119877proj

119877comp) (14)

SFF( ) the sinking fund factor which is a ratio used tocalculate the future value of a series of equal annual cashflows is given by

SFF (119894 119873) = 119894

(1 + 119894)119873minus 1 (15)

The salvaged value of the component at the end of the projectlifetime is proportional to its remaining life Therefore thesalvage value 119878 is given by

119878 = 119862rep sdot119877rem119877comp

(16)

119877rem the remaining life of the component at the end of theproject lifetime is given by

119877rem = 119877comp minus (119877proj minus 119877rep) (17)

224 Annualized Operating Cost The operating cost is theannualized value of all costs and revenues other than initialcapital costs and is calculated using [3 27 29 31]

119862aop =365

sum119905=1

24

sum119905=1

[119862oc (119905)] (18)

225 Cost of Emissions The following equation is used tocalculate the cost of emissions [3 27 29 31]

119862emissions =119888CO2

119872CO2

+ 119888CO119872CO + 119888UHC119872UHC + 119888PM119872PM + 119888SO2

119872SO2

+ 119888NO119909

119872NO119909

1000 (19)

Total cost of a component = economic cost + environmentalcost where economic cost = capital cost + replacement cost +operation and maintenance cost + fuel cost (generator) Alsoenvironmental cost = emissions cost

Annualized Cost of a Component Is Calculated Using [327 29 31]

119862ann = 119862acap + 119862arep + 119862aop + 119862emissions (20)

Annualized Total Cost of a Component Is CalculatedUsing [29 31]

119862anntot119888 =

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888 + 119862emissions) (21)

From (21) the economic and environmental cost modelthrough annualized total cost of different configurations of

Journal of Energy 7

power system results in the hybridizing of the renewableenergy generator (PV) with existing energy (diesel) is givenbelow

Economic and environmental costmodel of running solar+ diesel generator + batteries + converter is calculated as

119862anntot119904+119892+119887+119888 =

119873119904

sum119904=1

(119862acap119904 + 119862arep119904 + 119862aop119904

+ 119862emissions) +

119873119892

sum119892=1

(119862acap119892 + 119862arep119892 + 119862aop119892

+ 119862emissions + 119862af 119892) +

119873119887

sum119887=1

(119862acap119887 + 119862arep119887 + 119862aop119887

+ 119862emissions) +

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888)

(22)

23 Description of the Computer Simulation A computerprogram was developed and used to build the hybrid(PVdiesel) system model Data inputs to the programare hourly load demand data latitude and longitude ofthe site and reference component cost The designed soft-ware determines as its output the size of system com-ponents (sizing parameters) and the performance of thesystem over the course of the year (see the supple-mentary data in Supplementary Material available onlineat httpdxdoiorg10115520166278138) by showing thepower supplied by each of the energy systems over theyear given the load conditions and taking into account thetechnical factors The designed software can be used to studyhow the hybrid (PVdiesel) system is being supplied

24 Validation of the Model The designed software resultswere carried out followed with HOMER data to validate theanalysis The comparison shows a close agreement betweenresults obtained from the designed software module andresults obtained from HOMER setup In addition beforeusing the measured data gotten from NASA datasets insimulating the individual components of a PVdiesel hybridsystem the developed program accuracy was established thesimulated data predicted by the software program fall withinthe bounds of the measured data The algorithm that thedeveloped program uses to synthesize solar data is based onthe work of Graham andHollands [32]The realistic nature ofsynthetic data created by this algorithm is demonstrated andthe test shows that synthetic solar data (simulated) producevirtually the same simulation results as real data (measured)as shown in Figure 3

3 System Description

The designed system considered in this paper is a hybridsystem which consists of a renewable (photovoltaic) energysystem integrated in a conventional (diesel) power generationsystem energy storage in battery a DCAC converter (aninverter for the conversion of generated DC power into

0

1

2

3

4

5

6

7

Month of the yearMeasuredSimulated

Jan

Feb

Mar

ch

April

May

June July

Aug

Sept Oct

Nov Dec

Dai

ly ra

diat

ion

(kW

hm

2d

)

Figure 3 Calibrated solar radiation

required AC power) and an ACDC converter (a rectifierfor the conversion of generated AC power in order to chargethe battery) as shown in Figure 4 The inverter used is bidi-rectional also known as power converter which maintainsenergy flow between AC and DC components since the flowcomes in two different directions (from AC to DC and fromDC to AC)

The flow from the solar array passes through the chargecontroller to charge the battery and at the same time supplyelectricity to the load through the inverter The actual ACpower obtained after the conversion from a solar array can beseen in Table 3 The charge controller monitors and controlsthe charging and discharging of the battery in order not toallow the battery to be damaged (due to overcharging oroverdischarging)

Another flow comes from diesel generator when the PVand the battery could no longer serve the load the generatorsupplies electricity direct to serve the load and at the sametime charge the battery through the rectifier That is how thedesigned hybrid system is expected to work

The system design was to be representative of the typeof residential systems that were likely to be installed inthe foreseeable future Hence the system was sized usingconventional simulation tool and representative insolationdata

31 Cost of Key Components (including Installation andLabour) and Interest Rate for Capital Investments

311 PV System Cost (US$ 2Wp) The cost of PV panelson the Nigerian market was estimated as US$ 0600Wpbased on prices cited by Nigerian suppliers (based on thecost of a module of 1210 times 808 times 35mm size generating 130watts of peak power (Wp DC) in controlled conditions) [34]This was adjusted upward to US$ 2Wp to account for othersupport components that are required also known as balanceof system (BOS) parts such as cables charge controller withmaximum power point tracker lightening protection anddeliverylabour and installation costs

8 Journal of Energy

Table3Re

sults

oftheh

ybrid

electric

ityprod

uctio

nbatte

rychargesup

plyexcesslossesandconsum

ption(kW)

Mon

th

Hybrid

PVdieselelectric

itygeneratio

nRe

ctifier

Batte

ryInverter

ACload

Electricity

generatedandsupp

liedcharging

the

batte

ryand

excessele

ctric

ityby

theh

ybrid

syste

m(kW)

Energy

received

byther

ectifi

erto

charge

theb

attery

(kW)

Energy

received

bytheb

attery

andsupp

liedto

theA

Cload

viainverter(kW

)

Energy

received

bythe

inverter

andsupp

liedto

the

ACload

(kW)

ACload

served

(kW)

Electricity

generatedlowastSupp

liedto

theload

lowastCh

arging

theb

attery

Losses

Excess

electricity

generated

Energy

inEn

ergy

out

Losses

Charge

Disc

harge

Losses

Energy

inEn

ergy

out

Losses

Janu

ary

271539

91862277

538799

0159

314164

2995

1725464

644

871

493928minus427515

66413

141514

31273589

1415

542148238

February

2527428

1695987

4897

000154

3415

872899

82246547

43435

446265minus379553

66712

135152

3121632

7135196

1940

344

March

2802411

1887039

533918

0154

3813

003014

72256311

4516

1488757minus411872

76885

1506288

1355615

150673

2148238

April

2629097

1827413

5093

320146

292206

2897

05246309

4339

6465936minus395701

70235

144131

1129713

7144174

2078940

May

2631846

187612

3535826

0179

2197

18314101

2670

4847053

488773minus419038

69735

1468844

1321921

146923

2148238

June

2522854

1804

867

528865

0177

188945

313288

266355

46933

4819

32minus408659

73273

1345553

1210967

134586

2078940

July

2544

529

1860281

5410

310167

143050

31466

6267531

4713

5493896minus420576

7332

01325833

1193214

132619

2148238

August

2565565

1849784

551749

0164

163868

324882

276211

48671

503078minus425589

77489

1270987

1143852

127135

2148238

Septem

ber

256819

51799896

5298

540171

238274

312814

265950

46864

482990minus409230

7376

01301553

11713

67130186

2078940

Octob

er2681092

1873098

5412

030184

266607

324375

275785

48590

492613minus422554

70059

1473828

1326414

1474

142148238

Novem

ber

2649461

181232

15297

430158

3072

39305717

2599

1945798

483945minus409988

73957

143333

71289968

143369

2078940

Decem

ber

266810

71868682

5414

490185

2577

91314356

2672

6847088

494361minus423486

70875

1438938

1295008

143930

2148238

Total

31505984

220177

686371469

1998

311474

93704875

3149880

554995

5816474minus495376

1862713

16773138

15095379

1677759

25293770

lowastIn

term

sofelectric

itysupp

lyandbatte

rychargethe

PVsupp

liese

lectric

ityto

theA

Cload

viathe

inverter

andchargesthe

batte

rydirectly

whereas

thed

ieselgenerator

supp

liese

lectric

ityto

theA

Cload

directly

andchargesthe

batte

rythroug

hther

ectifi

erassho

wnin

Table4

Also

the

batte

rysupp

liese

lectric

ityto

theA

Cload

throug

htheinverteras

show

nin

thistable

Journal of Energy 9

Multiple solar panelsmaking up a solar array Charge

controller

Control unit coordinates the power system and displays

the energy flow through the system

Converter contains both rectifier and inverter

Generator toconverter

disconnectswitch

Converter bypassswitch (selects

output aseither converteror generator)

Service box(main breaker

panel)

To loadsappliances

AC lightning arresters

Generator

Wires for automatic generator starterstoppersystem to start generator automaticallywhen the batteries are low and stop the

generator automatically when the batteries are fully charged

Multiple batteriesmaking up a battery

bank

Batteriesto converterdisconnect

switchCharge controller

to batteriesdisconnect

switch

DC lightningarrester

Solar tocharge

controllerdisconnect

switchCombiner box (combines multiplewires from solar array to just a few and

may contain breakers or fuses)

Figure 4 Photovoltaic hybrid power system structure [33]

Table 4 Results of each of the energy components of the hybrid system (PV and diesel) for electricity production supply and battery charging(kW)

Month

Electricity generated and supplied and batterycharge by the PV in hybrid system (kW)

Electricity generated and supplied and batterycharge by the diesel in hybrid system (kW)

Electricitygenerated

Supplied to the loadvia inverter

Charging thebattery directly

Electricitygenerated

Supplied to theload directly

Charging thebattery via rectifier

January 1538295 987628 239282 1177104 874649 299517February 1510492 971970 199718 1016936 724017 289982March 1705644 1094416 232446 1096767 792623 301472April 1554395 1045610 219627 1074702 781803 289705May 1488347 1049806 221725 1143499 826317 314101June 1333962 936894 215577 1188892 867973 313288July 1271351 905257 226365 1273178 955024 314666August 1230539 845398 226867 1335026 1004386 324882September 1343075 892323 217040 1225120 907573 312814October 1534355 1051274 216828 1146737 821824 324375November 1552498 1023349 224026 1096963 788972 305717December 1499299 1015452 227093 1168808 853230 314356Total 17562252 11819377 2666594 13943732 10198391 3704875

312 Converter Cost (US$ 0320Wp) The cost of a con-verter based on prices cited by Nigerian suppliers was US$0320Wp [35]

313 Battery Cost (US$ 180kWh) The cost of a 6V225Ahlead acid battery on the Nigerian market was found to be inthe range of US$ 172 [35] Including balance of system (BOS)components and labourinstallation costs the capital cost for

the battery arrays was adjusted upward to US$ 180kWhTheprecise number of batteries required for each option is thendetermined by the simulation

314 Generator Cost (US$ 1000kW) The capital cost ofthe genset includes the generator itself (usually diesel orgasoline) as well as BOS costs and labourinstallation costsOn the Nigerian local market a generator of smaller range

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 7: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

Journal of Energy 7

power system results in the hybridizing of the renewableenergy generator (PV) with existing energy (diesel) is givenbelow

Economic and environmental costmodel of running solar+ diesel generator + batteries + converter is calculated as

119862anntot119904+119892+119887+119888 =

119873119904

sum119904=1

(119862acap119904 + 119862arep119904 + 119862aop119904

+ 119862emissions) +

119873119892

sum119892=1

(119862acap119892 + 119862arep119892 + 119862aop119892

+ 119862emissions + 119862af 119892) +

119873119887

sum119887=1

(119862acap119887 + 119862arep119887 + 119862aop119887

+ 119862emissions) +

119873119888

sum119888=1

(119862acap119888 + 119862arep119888 + 119862aop119888)

(22)

23 Description of the Computer Simulation A computerprogram was developed and used to build the hybrid(PVdiesel) system model Data inputs to the programare hourly load demand data latitude and longitude ofthe site and reference component cost The designed soft-ware determines as its output the size of system com-ponents (sizing parameters) and the performance of thesystem over the course of the year (see the supple-mentary data in Supplementary Material available onlineat httpdxdoiorg10115520166278138) by showing thepower supplied by each of the energy systems over theyear given the load conditions and taking into account thetechnical factors The designed software can be used to studyhow the hybrid (PVdiesel) system is being supplied

24 Validation of the Model The designed software resultswere carried out followed with HOMER data to validate theanalysis The comparison shows a close agreement betweenresults obtained from the designed software module andresults obtained from HOMER setup In addition beforeusing the measured data gotten from NASA datasets insimulating the individual components of a PVdiesel hybridsystem the developed program accuracy was established thesimulated data predicted by the software program fall withinthe bounds of the measured data The algorithm that thedeveloped program uses to synthesize solar data is based onthe work of Graham andHollands [32]The realistic nature ofsynthetic data created by this algorithm is demonstrated andthe test shows that synthetic solar data (simulated) producevirtually the same simulation results as real data (measured)as shown in Figure 3

3 System Description

The designed system considered in this paper is a hybridsystem which consists of a renewable (photovoltaic) energysystem integrated in a conventional (diesel) power generationsystem energy storage in battery a DCAC converter (aninverter for the conversion of generated DC power into

0

1

2

3

4

5

6

7

Month of the yearMeasuredSimulated

Jan

Feb

Mar

ch

April

May

June July

Aug

Sept Oct

Nov Dec

Dai

ly ra

diat

ion

(kW

hm

2d

)

Figure 3 Calibrated solar radiation

required AC power) and an ACDC converter (a rectifierfor the conversion of generated AC power in order to chargethe battery) as shown in Figure 4 The inverter used is bidi-rectional also known as power converter which maintainsenergy flow between AC and DC components since the flowcomes in two different directions (from AC to DC and fromDC to AC)

The flow from the solar array passes through the chargecontroller to charge the battery and at the same time supplyelectricity to the load through the inverter The actual ACpower obtained after the conversion from a solar array can beseen in Table 3 The charge controller monitors and controlsthe charging and discharging of the battery in order not toallow the battery to be damaged (due to overcharging oroverdischarging)

Another flow comes from diesel generator when the PVand the battery could no longer serve the load the generatorsupplies electricity direct to serve the load and at the sametime charge the battery through the rectifier That is how thedesigned hybrid system is expected to work

The system design was to be representative of the typeof residential systems that were likely to be installed inthe foreseeable future Hence the system was sized usingconventional simulation tool and representative insolationdata

31 Cost of Key Components (including Installation andLabour) and Interest Rate for Capital Investments

311 PV System Cost (US$ 2Wp) The cost of PV panelson the Nigerian market was estimated as US$ 0600Wpbased on prices cited by Nigerian suppliers (based on thecost of a module of 1210 times 808 times 35mm size generating 130watts of peak power (Wp DC) in controlled conditions) [34]This was adjusted upward to US$ 2Wp to account for othersupport components that are required also known as balanceof system (BOS) parts such as cables charge controller withmaximum power point tracker lightening protection anddeliverylabour and installation costs

8 Journal of Energy

Table3Re

sults

oftheh

ybrid

electric

ityprod

uctio

nbatte

rychargesup

plyexcesslossesandconsum

ption(kW)

Mon

th

Hybrid

PVdieselelectric

itygeneratio

nRe

ctifier

Batte

ryInverter

ACload

Electricity

generatedandsupp

liedcharging

the

batte

ryand

excessele

ctric

ityby

theh

ybrid

syste

m(kW)

Energy

received

byther

ectifi

erto

charge

theb

attery

(kW)

Energy

received

bytheb

attery

andsupp

liedto

theA

Cload

viainverter(kW

)

Energy

received

bythe

inverter

andsupp

liedto

the

ACload

(kW)

ACload

served

(kW)

Electricity

generatedlowastSupp

liedto

theload

lowastCh

arging

theb

attery

Losses

Excess

electricity

generated

Energy

inEn

ergy

out

Losses

Charge

Disc

harge

Losses

Energy

inEn

ergy

out

Losses

Janu

ary

271539

91862277

538799

0159

314164

2995

1725464

644

871

493928minus427515

66413

141514

31273589

1415

542148238

February

2527428

1695987

4897

000154

3415

872899

82246547

43435

446265minus379553

66712

135152

3121632

7135196

1940

344

March

2802411

1887039

533918

0154

3813

003014

72256311

4516

1488757minus411872

76885

1506288

1355615

150673

2148238

April

2629097

1827413

5093

320146

292206

2897

05246309

4339

6465936minus395701

70235

144131

1129713

7144174

2078940

May

2631846

187612

3535826

0179

2197

18314101

2670

4847053

488773minus419038

69735

1468844

1321921

146923

2148238

June

2522854

1804

867

528865

0177

188945

313288

266355

46933

4819

32minus408659

73273

1345553

1210967

134586

2078940

July

2544

529

1860281

5410

310167

143050

31466

6267531

4713

5493896minus420576

7332

01325833

1193214

132619

2148238

August

2565565

1849784

551749

0164

163868

324882

276211

48671

503078minus425589

77489

1270987

1143852

127135

2148238

Septem

ber

256819

51799896

5298

540171

238274

312814

265950

46864

482990minus409230

7376

01301553

11713

67130186

2078940

Octob

er2681092

1873098

5412

030184

266607

324375

275785

48590

492613minus422554

70059

1473828

1326414

1474

142148238

Novem

ber

2649461

181232

15297

430158

3072

39305717

2599

1945798

483945minus409988

73957

143333

71289968

143369

2078940

Decem

ber

266810

71868682

5414

490185

2577

91314356

2672

6847088

494361minus423486

70875

1438938

1295008

143930

2148238

Total

31505984

220177

686371469

1998

311474

93704875

3149880

554995

5816474minus495376

1862713

16773138

15095379

1677759

25293770

lowastIn

term

sofelectric

itysupp

lyandbatte

rychargethe

PVsupp

liese

lectric

ityto

theA

Cload

viathe

inverter

andchargesthe

batte

rydirectly

whereas

thed

ieselgenerator

supp

liese

lectric

ityto

theA

Cload

directly

andchargesthe

batte

rythroug

hther

ectifi

erassho

wnin

Table4

Also

the

batte

rysupp

liese

lectric

ityto

theA

Cload

throug

htheinverteras

show

nin

thistable

Journal of Energy 9

Multiple solar panelsmaking up a solar array Charge

controller

Control unit coordinates the power system and displays

the energy flow through the system

Converter contains both rectifier and inverter

Generator toconverter

disconnectswitch

Converter bypassswitch (selects

output aseither converteror generator)

Service box(main breaker

panel)

To loadsappliances

AC lightning arresters

Generator

Wires for automatic generator starterstoppersystem to start generator automaticallywhen the batteries are low and stop the

generator automatically when the batteries are fully charged

Multiple batteriesmaking up a battery

bank

Batteriesto converterdisconnect

switchCharge controller

to batteriesdisconnect

switch

DC lightningarrester

Solar tocharge

controllerdisconnect

switchCombiner box (combines multiplewires from solar array to just a few and

may contain breakers or fuses)

Figure 4 Photovoltaic hybrid power system structure [33]

Table 4 Results of each of the energy components of the hybrid system (PV and diesel) for electricity production supply and battery charging(kW)

Month

Electricity generated and supplied and batterycharge by the PV in hybrid system (kW)

Electricity generated and supplied and batterycharge by the diesel in hybrid system (kW)

Electricitygenerated

Supplied to the loadvia inverter

Charging thebattery directly

Electricitygenerated

Supplied to theload directly

Charging thebattery via rectifier

January 1538295 987628 239282 1177104 874649 299517February 1510492 971970 199718 1016936 724017 289982March 1705644 1094416 232446 1096767 792623 301472April 1554395 1045610 219627 1074702 781803 289705May 1488347 1049806 221725 1143499 826317 314101June 1333962 936894 215577 1188892 867973 313288July 1271351 905257 226365 1273178 955024 314666August 1230539 845398 226867 1335026 1004386 324882September 1343075 892323 217040 1225120 907573 312814October 1534355 1051274 216828 1146737 821824 324375November 1552498 1023349 224026 1096963 788972 305717December 1499299 1015452 227093 1168808 853230 314356Total 17562252 11819377 2666594 13943732 10198391 3704875

312 Converter Cost (US$ 0320Wp) The cost of a con-verter based on prices cited by Nigerian suppliers was US$0320Wp [35]

313 Battery Cost (US$ 180kWh) The cost of a 6V225Ahlead acid battery on the Nigerian market was found to be inthe range of US$ 172 [35] Including balance of system (BOS)components and labourinstallation costs the capital cost for

the battery arrays was adjusted upward to US$ 180kWhTheprecise number of batteries required for each option is thendetermined by the simulation

314 Generator Cost (US$ 1000kW) The capital cost ofthe genset includes the generator itself (usually diesel orgasoline) as well as BOS costs and labourinstallation costsOn the Nigerian local market a generator of smaller range

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 8: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

8 Journal of Energy

Table3Re

sults

oftheh

ybrid

electric

ityprod

uctio

nbatte

rychargesup

plyexcesslossesandconsum

ption(kW)

Mon

th

Hybrid

PVdieselelectric

itygeneratio

nRe

ctifier

Batte

ryInverter

ACload

Electricity

generatedandsupp

liedcharging

the

batte

ryand

excessele

ctric

ityby

theh

ybrid

syste

m(kW)

Energy

received

byther

ectifi

erto

charge

theb

attery

(kW)

Energy

received

bytheb

attery

andsupp

liedto

theA

Cload

viainverter(kW

)

Energy

received

bythe

inverter

andsupp

liedto

the

ACload

(kW)

ACload

served

(kW)

Electricity

generatedlowastSupp

liedto

theload

lowastCh

arging

theb

attery

Losses

Excess

electricity

generated

Energy

inEn

ergy

out

Losses

Charge

Disc

harge

Losses

Energy

inEn

ergy

out

Losses

Janu

ary

271539

91862277

538799

0159

314164

2995

1725464

644

871

493928minus427515

66413

141514

31273589

1415

542148238

February

2527428

1695987

4897

000154

3415

872899

82246547

43435

446265minus379553

66712

135152

3121632

7135196

1940

344

March

2802411

1887039

533918

0154

3813

003014

72256311

4516

1488757minus411872

76885

1506288

1355615

150673

2148238

April

2629097

1827413

5093

320146

292206

2897

05246309

4339

6465936minus395701

70235

144131

1129713

7144174

2078940

May

2631846

187612

3535826

0179

2197

18314101

2670

4847053

488773minus419038

69735

1468844

1321921

146923

2148238

June

2522854

1804

867

528865

0177

188945

313288

266355

46933

4819

32minus408659

73273

1345553

1210967

134586

2078940

July

2544

529

1860281

5410

310167

143050

31466

6267531

4713

5493896minus420576

7332

01325833

1193214

132619

2148238

August

2565565

1849784

551749

0164

163868

324882

276211

48671

503078minus425589

77489

1270987

1143852

127135

2148238

Septem

ber

256819

51799896

5298

540171

238274

312814

265950

46864

482990minus409230

7376

01301553

11713

67130186

2078940

Octob

er2681092

1873098

5412

030184

266607

324375

275785

48590

492613minus422554

70059

1473828

1326414

1474

142148238

Novem

ber

2649461

181232

15297

430158

3072

39305717

2599

1945798

483945minus409988

73957

143333

71289968

143369

2078940

Decem

ber

266810

71868682

5414

490185

2577

91314356

2672

6847088

494361minus423486

70875

1438938

1295008

143930

2148238

Total

31505984

220177

686371469

1998

311474

93704875

3149880

554995

5816474minus495376

1862713

16773138

15095379

1677759

25293770

lowastIn

term

sofelectric

itysupp

lyandbatte

rychargethe

PVsupp

liese

lectric

ityto

theA

Cload

viathe

inverter

andchargesthe

batte

rydirectly

whereas

thed

ieselgenerator

supp

liese

lectric

ityto

theA

Cload

directly

andchargesthe

batte

rythroug

hther

ectifi

erassho

wnin

Table4

Also

the

batte

rysupp

liese

lectric

ityto

theA

Cload

throug

htheinverteras

show

nin

thistable

Journal of Energy 9

Multiple solar panelsmaking up a solar array Charge

controller

Control unit coordinates the power system and displays

the energy flow through the system

Converter contains both rectifier and inverter

Generator toconverter

disconnectswitch

Converter bypassswitch (selects

output aseither converteror generator)

Service box(main breaker

panel)

To loadsappliances

AC lightning arresters

Generator

Wires for automatic generator starterstoppersystem to start generator automaticallywhen the batteries are low and stop the

generator automatically when the batteries are fully charged

Multiple batteriesmaking up a battery

bank

Batteriesto converterdisconnect

switchCharge controller

to batteriesdisconnect

switch

DC lightningarrester

Solar tocharge

controllerdisconnect

switchCombiner box (combines multiplewires from solar array to just a few and

may contain breakers or fuses)

Figure 4 Photovoltaic hybrid power system structure [33]

Table 4 Results of each of the energy components of the hybrid system (PV and diesel) for electricity production supply and battery charging(kW)

Month

Electricity generated and supplied and batterycharge by the PV in hybrid system (kW)

Electricity generated and supplied and batterycharge by the diesel in hybrid system (kW)

Electricitygenerated

Supplied to the loadvia inverter

Charging thebattery directly

Electricitygenerated

Supplied to theload directly

Charging thebattery via rectifier

January 1538295 987628 239282 1177104 874649 299517February 1510492 971970 199718 1016936 724017 289982March 1705644 1094416 232446 1096767 792623 301472April 1554395 1045610 219627 1074702 781803 289705May 1488347 1049806 221725 1143499 826317 314101June 1333962 936894 215577 1188892 867973 313288July 1271351 905257 226365 1273178 955024 314666August 1230539 845398 226867 1335026 1004386 324882September 1343075 892323 217040 1225120 907573 312814October 1534355 1051274 216828 1146737 821824 324375November 1552498 1023349 224026 1096963 788972 305717December 1499299 1015452 227093 1168808 853230 314356Total 17562252 11819377 2666594 13943732 10198391 3704875

312 Converter Cost (US$ 0320Wp) The cost of a con-verter based on prices cited by Nigerian suppliers was US$0320Wp [35]

313 Battery Cost (US$ 180kWh) The cost of a 6V225Ahlead acid battery on the Nigerian market was found to be inthe range of US$ 172 [35] Including balance of system (BOS)components and labourinstallation costs the capital cost for

the battery arrays was adjusted upward to US$ 180kWhTheprecise number of batteries required for each option is thendetermined by the simulation

314 Generator Cost (US$ 1000kW) The capital cost ofthe genset includes the generator itself (usually diesel orgasoline) as well as BOS costs and labourinstallation costsOn the Nigerian local market a generator of smaller range

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 9: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

Journal of Energy 9

Multiple solar panelsmaking up a solar array Charge

controller

Control unit coordinates the power system and displays

the energy flow through the system

Converter contains both rectifier and inverter

Generator toconverter

disconnectswitch

Converter bypassswitch (selects

output aseither converteror generator)

Service box(main breaker

panel)

To loadsappliances

AC lightning arresters

Generator

Wires for automatic generator starterstoppersystem to start generator automaticallywhen the batteries are low and stop the

generator automatically when the batteries are fully charged

Multiple batteriesmaking up a battery

bank

Batteriesto converterdisconnect

switchCharge controller

to batteriesdisconnect

switch

DC lightningarrester

Solar tocharge

controllerdisconnect

switchCombiner box (combines multiplewires from solar array to just a few and

may contain breakers or fuses)

Figure 4 Photovoltaic hybrid power system structure [33]

Table 4 Results of each of the energy components of the hybrid system (PV and diesel) for electricity production supply and battery charging(kW)

Month

Electricity generated and supplied and batterycharge by the PV in hybrid system (kW)

Electricity generated and supplied and batterycharge by the diesel in hybrid system (kW)

Electricitygenerated

Supplied to the loadvia inverter

Charging thebattery directly

Electricitygenerated

Supplied to theload directly

Charging thebattery via rectifier

January 1538295 987628 239282 1177104 874649 299517February 1510492 971970 199718 1016936 724017 289982March 1705644 1094416 232446 1096767 792623 301472April 1554395 1045610 219627 1074702 781803 289705May 1488347 1049806 221725 1143499 826317 314101June 1333962 936894 215577 1188892 867973 313288July 1271351 905257 226365 1273178 955024 314666August 1230539 845398 226867 1335026 1004386 324882September 1343075 892323 217040 1225120 907573 312814October 1534355 1051274 216828 1146737 821824 324375November 1552498 1023349 224026 1096963 788972 305717December 1499299 1015452 227093 1168808 853230 314356Total 17562252 11819377 2666594 13943732 10198391 3704875

312 Converter Cost (US$ 0320Wp) The cost of a con-verter based on prices cited by Nigerian suppliers was US$0320Wp [35]

313 Battery Cost (US$ 180kWh) The cost of a 6V225Ahlead acid battery on the Nigerian market was found to be inthe range of US$ 172 [35] Including balance of system (BOS)components and labourinstallation costs the capital cost for

the battery arrays was adjusted upward to US$ 180kWhTheprecise number of batteries required for each option is thendetermined by the simulation

314 Generator Cost (US$ 1000kW) The capital cost ofthe genset includes the generator itself (usually diesel orgasoline) as well as BOS costs and labourinstallation costsOn the Nigerian local market a generator of smaller range

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 10: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

10 Journal of Energy

(2ndash5 kVA) was priced at about US$ 991 [36] Including BOSand labourinstallation costs the total price was estimated ataround US$ 1000 per kW load

315 Fuel Cost (US$ 12L) The source for this estimate wasthe Nigerian official market rate as of October 2015

316 Interest Rate 75 Interest rates vary widely and can beparticularly high in developing countries having a profoundimpact on the cost-benefit assessment Interest rates onNigerian commercial bank loans may be between 6 and75 An estimate of 75 was selected for this case study

4 Energy Losses in Stand-Alone PVDieselHybrid Systems

Stand-alone PVdiesel hybrid systems are designed to betotally self-sufficient in generating storing and supplyingelectricity to the electrical loads in remote areas Figure 5shows an energy flow diagram for a typical PVdiesel hybridsystemThe following equation (23) shows the energy balanceof a PVdiesel hybrid system

119864IN asymp 119864OUT (23)

The energy that has to be supplied from the generator can bedetermined as

119864MG = 119864LOAD + 119864LOSSR minus 119864PV (24)

The energy that has to be supplied from the photovoltaic canbe determined as

119864PV = 119864LOAD + 119864LOSSCC + 119864LOSSB + 119864LOSSI minus 119864MG (25)

The objective of this study (efficient energy balance) is tominimize the energy that has to be supplied from auxiliaryenergy source (diesel generator) by the addition of PV panelsAdditionally the motor generator should be operated near itsnominal power to achieve high fuel efficiency by the inclusionof battery bank As shown in (24) and (25) energy losses areflowing into the energy demand and supply of the systemtherefore it is necessary to identify the energy losses in thesystem A classification of all relevant energy losses in astand-alone PV hybrid system is given as capture losses andsystem losses [37] Capture losses account for the part of theincident radiation energy that remains uncaptured andwhichis therefore lost within a global energy balance Captureor irradiation losses translate the fact that only part of theincoming irradiation is used for energy conversion Systemlosses define systematic energy losses that are due to thephysical properties of the system components or the entireinstallation Energy conversion losses constitute importantcontributions to this category [38]

System losses cover all energy losses which occur duringthe conversion of generated energy into usable AC electricityIn this study only the energy conversion losses were consid-ered to assess the potential of the designed hybrid systemThe losses are indicated in Figure 5

DC =photovoltaic

energy

PV chargecontroller

losses

Batterylosses

Inverterlosses

AC load demand

Rectifierlosses

AC sim

motor generatorenergy

EPV

EBBin

EBBout

EMG

Eload

Figure 5 Energy flow diagram for a typical PVdiesel hybrid system[37]

5 Results and Discussion

The design provides an interesting example of how optimalcombinations of photovoltaic and diesel generation withappropriate energy storage yielded multiple gains a shift torenewable energy a reliable supply for household energyneeds and lower overall cost of energy

51 Results

511 Designed Hybrid System To overcome the problem ofthe climatic changes to ensure a reliable supply withoutinterruption and to improve the overall system efficiency ahybrid system (that comprised a PV system the diesel powersystem and storage battery as backup sources) is essential asshown in Figure 4 The reasons for the inclusion of batterybank in this design are due to fluctuations in solar radiationand also for the generator to operate at optimum efficiencybecause continued operation of generator at lower loads orsevere variation in the load results in an inefficient engineperformance and one of the options for the loadmanagementis to integrate battery bank (which becomes a load whencharging to improve the generator efficiency) to improvethe overall system efficiency Considering various types andcapacities of system devices (PV array diesel generator andbattery size) the configurations which can meet the desiredsystem reliability are obtained by changing the type and sizeof the devices systemsThe configurationwith the lowest LCEgives the optimal choice Therefore the optimal sizing of thehybrid system (PV-diesel generator-battery system) in termsof reliability economy and environment is shown in Tables 35 and 6 respectively This was determined through rigorousmathematical computations

From the design results the PV power supply is between800 h and 1900 h while the radiation peak is between1200 h and 1400 h as can be seen in the supplementarydata Between 1200 h and 1400 h there is no deficit in thesystem and the PV energy supplies the load and chargesthe battery thereby reducing the operational hours of thediesel generator and the running cost of the hybrid energy

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 11: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

Journal of Energy 11

Table5Com

parativ

ecostsof

hybrid

power

andsta

nd-alone

generatorsup

plysyste

ms

Con

figuration

PVcapacity

(kW)

Generator

capacity

(kW)

Num

bero

fbatte

ries

(6V225

Ah)

Con

verter

capacity

(kW)

Initial

capital

(US$)

Ann

ual

generator

usage(ho

urs)

Ann

ual

quantityof

diesel(L)

Totaln

etpresent

cost(U

S$)for

20years

Costo

fenergy

(US$kWh)

Renewable

fractio

n

PV+generator+

batte

ry15

54

1655

41048

5011

5716

192231

0745

059

Generator

+batte

rymdash

54

3055

14450

5298

9183

210146

0815

000

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 12: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

12 Journal of Energy

Table 6 Comparative emissions of hybrid power and stand-alone generator supply systems

Configuration Pollutant emission (kgyr) Fuel consumption(Lyr)

Operational hour ofdiesel generator (hryr)CO

2CO UHC PM SO

2NO119909

PV + generator + battery 15052 372 412 28 302 332 5716 5011Generator + battery 24183 597 661 45 486 533 9183 5298Note PM refers to total particulate matter UHC refers to unburned hydrocarbons

Figure 6 The optimization results from HOMER for hybrid PVdiesel energy system

system as well as the pollutant emissions There is likely tobe deficit in other remaining hours due to poor radiationand the deficit is being completed by either the battery orthe diesel generator The result of the demand met by thehybrid energy system (PVdiesel) over the course of the yearis shown in the supplementary data it shows how the sourceswere allocated according to the load demand and availabilityIt was observed that the variation is not only in the demandbut also in the availability of solar resources The battery orthe diesel generator compensates the shortage depending onthe decision mode

512 Results from HOMER The derivations from the devel-oped software were compared to HOMER optimizationmethod and the same inputs used in calculations by thedeveloped software were used by HOMER which producedthe same results with the developed software as shown inFigure 6 (Figure 6 compared with Table 5) Therefore theresults from the software can be used as comparison andpointof reference

52 Discussion

521 Overall Energy Production and Utilization From thedesign solar power will not replace the need for dieselgenerator for this remote residential home but could offset aportion of the diesel fuel used Although the residential loadsprovide the best possible match with PV output (since theseloads typically peak during daytime and afternoon hours)there is still need for a backup with diesel generator (duringthe raining season and cloudy days)

In the solar resources apart from the month of Februarythat has 28 days the month of March has the highest globaland incident solar (207568 kWhm2 213213 kWhm2) whilethe month of August has the least global and incident solar(159232 kWhm2 153817 kWhm2) as shown in Table 7

Table 7 Solar resources for the studied zone

Month Global solar(kWhm2)

Incident solar(kWhm2)

Power generatedwith 15 kW PVarray (kW)

January 173783 192285 1538295February 176292 188814 1510492March 207568 213213 1705644April 198460 194312 1554395May 197020 186037 1488347June 178982 166744 1333962July 168215 158916 1271351August 159232 153817 1230539September 166994 167880 1343075October 182472 191792 1534355November 175089 194054 1552498December 165744 187409 1499299Total 2149851 2195273 17562252

In the hybrid system configuration the sizing was done infavour of PV system (to overcome the problem of the climaticchanges) and in order to accommodate the load demand forall the months excess electricity was generated by the PVsystemThe excess electricity generated differs frommonth tomonth and depends on the incident solar The highest excesselectricity is observed inMarch (38130 kW) while the least isin the months of July (14305 kW) and August (163868 kW)the two months most affected by raining season

In the month of March the PV generated the highestelectricity (1705644 kW) and supplied to the load via inverterthe highest electricity (1094416 kW) This was because themonth of March has the highest global and incident solar(207568 kWhm2 213213 kWhm2) while in the month ofAugust the PV generated the least electricity (1230539 kW)

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 13: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

Journal of Energy 13

and supplied to the load via inverter the least electricity(845398 kW) and this was due to least global and incidentsolar (159232 kWhm2 153817 kWhm2) In this month ofAugust to ensure a reliable supply without interruptionthe diesel due to the low electricity generated by the PV(caused by low incident solar) supplies to the load the highestelectricity (1004386 kW) and charges the battery via rectifier(to improve the overall system efficiency) In the monthof August battery charging (503078 kW) and discharging(minus425589 kW) are highest due to low supply coming from thePVThegenerator becomesONoften to serve theAC load andat the same time charge the battery (which is a DC load bat-tery becomes a load when charging) It is worthwhile notingfrom Table 3 that the PV-diesel hybrid solution supported bybattery storage produces 17562 kWhyr (59) from solar PVarray and 13944 kWhyr (41) from diesel generator makinga total of 31506 kWhyr (100)

522 Energy Flows One of the main objectives of this studywas to produce a detailed experimental accounting of energyflows through the hybrid system In particular my interest isin quantifying all system losses

Hybrid PVDiesel System with Battery For the PV part ofthe hybrid system device losses include PV charge controllerlosses DC-AC conversion losses both for energy flowingdirectly to the load and for energy transiting through the bat-tery and storage round-trip losses On the generator side theAC-DC conversion losses affect electrical energy that doesnot flow directly to the load The reason for these losses onthe generator side is that the hybrid systemwas designed to becycle chargingmeaning that the diesel generator is allowed tocharge the battery

All losses through the hybrid system are classified asfollows

(i) PV charge controller losses(ii) Battery storage losses(iii) Rectifier (battery charger conversion) losses(iv) Inverter losses

PV charge controller losses are due to the DCDC conversionefficiency (converting energy generated by the PV to chargethe storage battery) DCDC conversion losses are generatedduring the control of the flow of current to and from thebattery by the PV charge controller Result shows that thelosses are minimal when compared to other componentlosses (storage losses inverter and rectifier losses) as shownin Table 3

Storage losses comprise all energy losses within a batteryThey are described by the charge and discharge efficiencies ofthe battery as well as the self-discharge characteristics In themonth of August the battery charging and the discharging aswell as its losses (due to charge and discharge efficiencies) arehighest due to the fact that diesel becomesONoften to chargethe battery when the battery reaches its maximum point ofcharge the diesel stops while the battery starts dischargingin order to power the load and once the battery reachesits minimum point of discharge it stops discharging and

the diesel comes ON again The process continues the sameway until the PV starts to generate electricity to supply itto the load and charge the battery otherwise it returns tothe diesel charging the battery Results of the design showthat the storage battery was charged with 227093 kWhyr and314356 kWhyr by the PV and diesel system respectivelymaking a total charge of 5816474 kWhyr while the batterydischarged (supplied) to the load via the inverter a total dis-charge of minus4953761 kWhyr having losses of 862713 kWhyras shown in Tables 3 and 4

Battery charger conversion losses are due to the rectifierrsquosACDC efficiency ACDC conversion losses are generatedduring battery charging from an AC source In the month ofAugust the rectifier receives the highest electricity from thediesel generator due to the monthrsquos least global and incidentsolar (159232 kWhm2 153817 kWhm2) and this affects theproduction from the PV at this point the diesel comes ONin order to ensure a reliable supply without interruptionResults of the design show that the rectifier was suppliedwith 3704875 kWhyr and rectified to the battery with3149880 kWhyr having losses of 554995 kWhyr as shownin Tables 3 and 4

Inverter losses are due to the inverterrsquos DCAC efficiencyDCAC inverter losses occur before the initially providedenergy can be consumed by an AC load It means that allelectrical energy that does not flow directly to the AC loadpasses through the inverter such as electricity flowing fromthe PV system electricity rectified to the battery and the onecoming from the battery In themonth of August the inverterreceives the least electricity from the PV and battery due tothe monthrsquos least global and incident solar (159232 kWhm2153817 kWhm2) Although the battery receives the highestcharging of 503078 kW from both the PV (226867 kW) anddiesel (rectified to the battery with 276211 kW) the inverterstill receives the least electricity because the diesel comesoften to supply the AC load and charge the battery thecharging of the battery by the rectifier shows how often dieselsupplies electricity to the load in this month of August asshown in Tables 3 and 4

In conclusion while the DCDC conversion efficiency isgenerally low the ACDC rectifier (battery charger conver-sion) efficiency is somewhat lower than the DCAC inverterefficiency as shown in Table 3

523 Economic Costs The capital cost of a PVdiesel hybridsolutionwith batteries is nearly three times higher than that ofa generator and battery combination (US$ 41048) but the netpresent cost representing cost over the lifetime of the systemis less than one-half of the generator and battery combination(US$ 192231) as shown in Table 5 The net present cost(NPC) of the PVdieselbattery hybrid system is slightly lowerthan the NPC of the dieselbattery combination as a resultof less fuel consumption and because fewer storage batteriesare needed and replacing batteries is a significant factor insystem maintenance

524 Environmental Pollution On the environmentalimpact perspective an increase in the operational hoursof diesel generator brings about increase in the fuel

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 14: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

14 Journal of Energy

consumption as well as an increase in GHG emissionwhereas a reduction in the operational hours of dieselgenerator brings about reduction in the fuel consumptionthereby a reduction in GHG emission Diesel system operatesfor 5298 hannum has a fuel consumption of 9183 Lannumand generates in kilogrammes (kg) the pollutant emissions asshown in Table 6 while in the hybrid PV-diesel system dieselgenerator operates for 5011 hannum has a fuel consumptionof 5716 Lannum and emits in kilogrammes the pollutantemissions annually into the atmosphere of the location of theresidence as shown in Table 6 Reducing fuel consumptionalso means less emission from the energy system as shownby the solar PV-diesel system which has the lowest pollutantemissions

6 Conclusion

This paper investigates the designing of a stand-alone hybridpower system focusing on photovoltaicdiesel energy systemwith energy storage in batteries Starting from the analy-sis of the models of the system components a completesimulation model is realized From the designed system adetailed experimental accounting of energy flows throughthe hybrid system was produced and all system losses causedby PV charge controller battery storage round-trip rectifierand inverter conversions were quantified and documentedResults show that PV charge controller losses are due tothe DCDC conversion efficiency and are generated duringthe control of the flow of current to and from the batteryby the PV charge controller while storage losses compriseall energy losses within a battery and are described by thecharge and discharge efficiencies of the battery as well asthe self-discharge characteristics In addition battery chargerconversion losses are due to the rectifierrsquos ACDC efficiencyand are generated during battery charging from an ACsource while inverter losses are due to the inverterrsquos DCACefficiency and occur before the initially provided energy canbe consumed by an AC load From the results it has proventhat the DCDC conversion efficiency is generally low whilethe ACDC rectifier efficiency is somehow lower than theDCAC inverter efficiency Also it has been demonstratedthat the use of hybrid PVdiesel system with battery (oneunit of 15 kW PV array one unit of 54 kW generator with 16units of battery) can significantly reduce the dependence onsolely available diesel resource The designed hybrid systemminimizes diesel operational hour and thereby reduces thefuel consumption which significantly affects (reduces) thepollution such as carbon emission thus reducing the green-house effect Although utilization of hybrid PVdiesel systemwith battery might not significantly reduce the total NPC andCOE it has been able to cut down the dependence on dieselOn the other hand it was also proven that the use of hybridPVdiesel system with battery would be more economical ifthe price of diesel increased significantly With a projectionperiod of 20 years and 75 annual real interest rate it wasfound that the use of hybrid PVdiesel system with batterycould achieve significantly lower NPC and COE as comparedto a stand-alone diesel system As a conclusion the hybridPVdiesel system has potential use in replacing or upgradingexisting stand-alone diesel systems in Nigeria

Nomenclature

119860 The surface area in m2119862acap119888 Annualized capital cost of a component119862arep119888 Annualized replacement cost of a

component119862aop119888 Annualized operating cost of a component119862acap119904 Annualized capital cost of solar power119862arep119904 Annualized replacement cost of solar

power119862aop119904 Annualized operating cost of solar power119862acap119892 Annualized capital cost of diesel generator119862arep119892 Annualized replacement cost of diesel

generator119862aop119892 Annualized operating cost of diesel

generator119862af 119892 Annualized fuel cost for diesel generator119862acap119887 Annualized capital cost of batteries power119862arep119887 Annualized replacement cost of batteries

power119862aop119887 Annualized operating cost of batteries

power119862acap119888 Annualized capital cost of converter power119862arep119888 Annualized replacement cost of converter

power119862aop119888 Annualized operating cost of converter

power119862cap Initial capital cost of the component119888CO2

Cost for emissions of carbon dioxide(CO2) ($t)

119888CO Cost for emissions of carbon monoxide(CO) ($t)

119888UHC Cost for emissions of unburnedhydrocarbons (UHC) ($t)

119888PM Cost for emissions of particulate matter(PM) ($t)

119888SO2

Cost for emissions of sulfur oxide (SO2)

($t)119888NO119909

Cost for emissions of nitrogen oxide(NO119909) ($t)

119862oc(119905) The cost of operating component119862rep Replacement cost of the componentCRF(119894 119877proj) Capital recovery factor119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1

kWh119864Needed(119905) The hourly load demand or energy needed

at a particular period of time119864REC-OUT(119905) The hourly energy output from rectifier

kWh119864REC-IN(119905) The hourly energy input to rectifier kWh119864SUR-AC(119905) The amount of surplus energy from AC

sources kWh119864DEG(119905) The hourly energy generated by diesel

generator119864PVG-IN(119905) The hourly energy output from inverter

(in case of SPV) kWh119864PVG(119905) The hourly energy output of the PV

generator

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 15: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

Journal of Energy 15

119864BAT-INV(119905) The hourly energy output from inverter(in case of battery) kWh

119864BAT(119905 minus 1) The energy stored in battery at hour 119905 minus 1kWh

119864LOAD(119905) The hourly energy consumed by the loadside kWh

119864CC-OUT(119905) The hourly energy output from chargecontroller kWh

119864CC-IN(119905) The hourly energy input to chargecontroller kWh

119864REC-OUT(119905) The hourly energy output from rectifierkWh

119864SUR-DC(119905) The amount of surplus energy from DCsource (PV panels) kWh

119864BAT(119905) The energy stored in battery at hour 119905kWh

119864IN Is equal to 119864PV + 119864MG119864OUT Is equal to 119864LOAD + 119864LOSS119864PV Energy generated by the PV array (kWh)119864MG Energy generated by the motor generator

(kWh)119864LOAD Energy supplied to the load (kWh)119864LOSS Energy losses (kWh) which comprise all

(119864LOSSCC + 119864LOSSB + 119864LOSSR + 119864LOSSI)119864LOSSCC Energy losses via charge controller (kWh)119864LOSSB Energy losses via battery (kWh)119864LOSSR Energy losses via rectifier (kWh)119864LOSSI Energy losses via inverter (kWh)119866(119905) The hourly irradiance in kWhm2119894 Interest rateINT( ) The integer function returning the integer

portion of a real value119872CO

2

Annual emissions of CO2(kgyr)

119872CO Annual emissions of CO (kgyr)119872NO

119909

Annual emissions of NO119909(kgyr)

119872PM Annual emissions of particulate matter(PM) (kgyr)

119872SO2

Annual emissions of SO2(kgyr)

119872UHC Annual emissions of unburnedhydrocarbons (UHC) (kgyr)

119873 Number of years119875 The PV penetration level factor119877proj Project lifetime119877comp Lifetime of the componentSFF( ) Sinking fund factor120578PVG The efficiency of PV generator120578DEG The diesel generator efficiency120578REC The efficiency of rectifier120578INV The efficiency of inverter120578DCHG The battery discharging efficiency120578CC The efficiency of charge controller120578CHG The battery charging efficiency

Competing Interests

The author declares no competing interests

References

[1] M Jovanovic ldquoAn analytical method for the measurement ofenergy systems sustainability in urban areasrdquo FME Transac-tions vol 36 no 4 pp 157ndash166 2008

[2] National Aeronautics and Space Administration (NASA)Atmospheric Science Data Center 2015 httpeosweblarcnasagovsse2012

[3] V A Ani Energy optimization at GSM base station sites locatedin rural areas [PhD thesis] 2015 httpwwwunnedungpublicationsfiles17774 ENERGY OPTIMIZATION AT GSMBASE STATION SITES LOCATED IN RURAL AREASpdf

[4] B S Borowy and Z M Salameh ldquoOptimum photovoltaic arraysize for a hybrid windPV systemrdquo IEEE Transactions on EnergyConversion vol 9 no 3 pp 482ndash488 1994

[5] R Dufo-Lopez and J L Bernal-Agustın ldquoDesign and controlstrategies of PV-diesel systems using genetic algorithmsrdquo SolarEnergy vol 79 no 1 pp 33ndash46 2005

[6] I Gross ldquoThe cost of diesel for Africarsquos mobile operators 2012may be the year that this bird comes home to roostrdquo November2011 httpwwwbalancingact-africacomnewsenissue-no-581

[7] MA Elhadidy ldquoPerformance evaluation of hybrid (windsolardiesel) power systemsrdquoRenewable Energy vol 26 no 3 pp 401ndash413 2002

[8] W Kellogg M H Nehrir G Venkataramanan and V GerezldquoOptimal unit sizing for a hybrid windphotovoltaic generatingsystemrdquoElectric Power Systems Research vol 39 no 1 pp 35ndash381996

[9] M A Elhadidy and S M Shaahid ldquoRole of hybrid (wind +diesel) power systems inmeeting commercial loadsrdquoRenewableEnergy vol 29 no 1 pp 109ndash118 2004

[10] M T Iqbal ldquoSimulation of a small wind fuel cell hybrid energysystemrdquo Renewable Energy vol 28 no 4 pp 511ndash522 2003

[11] M H Nehrir B J LaMeres G Venkataramanan V Gerez andL A Alvarado ldquoAn approach to evaluate the general perfor-mance of stand-alone windphotovoltaic generating systemsrdquoIEEE Transactions on Energy Conversion vol 15 no 4 pp 433ndash439 2000

[12] S H Karaki R B Chedid and R Ramadan ldquoProbabilistic per-formance assessment of autonomous solar-wind energy con-version systemsrdquo IEEE Transactions on Energy Conversion vol14 no 3 pp 766ndash772 1999

[13] C Protogeropoulos B J Brinkworth and R H MarshallldquoSizing and techno-economical optimization for hybrid solarphotovoltaicwind power systems with battery storagerdquo Inter-national Journal of Energy Research vol 21 no 6 pp 465ndash4791997

[14] L L Bucciarelli Jr ldquoEstimating loss-of-power probabilities ofstand-alone photovoltaic solar energy systemsrdquo Solar Energyvol 32 no 2 pp 205ndash209 1984

[15] S A Klein and W A Beckman ldquoLoss-of-load probabilities forstand-alone photovoltaic systemsrdquo Solar Energy vol 39 no 6pp 499ndash512 1987

[16] L Barra S Catalanotti F Fontana and F Lavorante ldquoAn ana-lytical method to determine the optimal size of a photovoltaicplantrdquo Solar Energy vol 33 no 6 pp 509ndash514 1984

[17] B Bartoli V Cuomo F Fontana C Serio and V SilvestrinildquoThe design of photovoltaic plants an optimization procedurerdquoApplied Energy vol 18 no 1 pp 37ndash47 1984

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 16: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

16 Journal of Energy

[18] L L Bucciarelli Jr ldquoThe effect of day-to-day correlation in solarradiation on the probability of loss-of-power in a stand-alonephotovoltaic energy systemrdquo Solar Energy vol 36 no 1 pp 11ndash14 1986

[19] P P Groumpos and G Papageorgiou ldquoAn optimal sizingmethod for stand-alone photovoltaic power systemsrdquo SolarEnergy vol 38 no 5 pp 341ndash351 1987

[20] V A Graham K G T Hollands and T E Unny ldquoA timeseries model for K

119905with application to global synthetic weather

generationrdquo Solar Energy vol 40 no 2 pp 83ndash92 1988[21] R J Aguiar M Collares-Pereira and J P Conde ldquoSimple

procedure for generating sequences of daily radiation valuesusing a library ofMarkov transitionmatricesrdquo Solar Energy vol40 no 3 pp 269ndash279 1988

[22] R N Chapman ldquoDevelopment of sizing nomograms for stand-alone photovoltaicstorage systemsrdquo Solar Energy vol 43 no 2pp 71ndash76 1989

[23] R N Chapman ldquoThe synthesis of solar radiation data for sizingstand-alone photovoltaic systemsrdquo in Proceedings of the 21stIEEE Photovoltaic Specialists Conference pp 965ndash970 OrlandoFla USA May 1990

[24] I Abouzahr and R Ramakumar ldquoLoss of power supply proba-bility of stand-alone photovoltaic systems a closed form solu-tion approachrdquo IEEE Transactions on Energy Conversion vol6 no 1 pp 1ndash11 1991

[25] A Mellit ldquoSizing of photovoltaic systems a reviewrdquo Revue desEnergies Renouvelables vol 10 no 4 pp 463ndash472 2007

[26] A Gupta R P Saini andM P Sharma ldquoSteady-state modellingof hybrid energy system for off grid electrification of cluster ofvillagesrdquo Renewable Energy vol 35 no 2 pp 520ndash535 2010

[27] S Ashok ldquoOptimised model for community-based hybridenergy systemrdquo Renewable Energy vol 32 no 7 pp 1155ndash11642007

[28] D K Lal B B Dash and A K Akella ldquoOptimization of PVWindMicro-Hydrodiesel hybrid power system in homer forthe study areardquo International Journal on Electrical Engineeringand Informatics vol 3 no 3 pp 307ndash325 2011

[29] K Sopian A Zaharim Y Ali Z M Nopiah J A B RazakandN SMuhammad ldquoOptimal operational strategy for hybridrenewable energy system using genetic algorithmsrdquo WSEASTransactions on Mathematics vol 7 no 4 pp 130ndash140 2008

[30] H Abdolrahimi and H K Karegar ldquoOptimization and sen-sitivity analysis of a hybrid system for a reliable load supplyin KISH IRANrdquo International Journal of Advanced RenewableEnergy Research vol 1 no 4 pp 33ndash41 2012

[31] T Lambert P Gilman and P Lilienthal ldquoMicropower systemmodeling with HOMERrdquo in Integration of Alternative Sourcesof Energy F A Farret and M G Simoes Eds chapter 15 JohnWiley amp Sons New York NY USA 2006

[32] V A Graham and K G T Hollands ldquoA method to generatesynthetic hourly solar radiation globallyrdquo Solar Energy vol 44no 6 pp 333ndash341 1990

[33] Off grid solar power system 2016 httprimstarorgrenewnrgoff grid solar power systemshtm

[34] Solar Power Systems ComponentsmdashSolar Panels Prices inNigeria httpwwwnaijatechguidecom200811solar

[35] The Solar Shop Ltd 2016 httpwwwsolarshopnigeriacom[36] Tiger Generators Model Prices Nigeria Technology Guide

2015 httpswwwnaijatechguidecom200803tiger-generators-nigeriahtml

[37] S Beverngen Mini Grid Kit Report EMS Strategy ReviewUniversity of Kassel Kassel Germany 2002

[38] D Mayer and M Heidenreich ldquoPerformance analysis of standalone PV systems from a rational use of energy point of viewrdquo inProceedings of the 3rd World Conference on Photovoltaic EnergyConversion pp 2155ndash2158 IEEE Osaka Japan May 2003

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Page 17: Design of a reliable hybrid (pv diesel) power system with energy storage in batteries for remote residential home

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


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