IN DEGREE PROJECT TECHNOLOGY,FIRST CYCLE, 15 CREDITS

, STOCKHOLM SWEDEN 2017

Dimensioning of a Residential Microgrid in Sweden

JOAKIM LARSEN

TOBIAS TUNESTAM

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

Dimensioning of a Residential Microgrid in SwedenJoakim Larsen and Tobias Tunestam

Abstract—This project aims to evaluate through simulationsin Simulink whether an average power consuming, 4-personhousehold in Sweden, can be successfully supplied from amicrogrid system powered by solar panels. The goal is to achievea 48 V DC system and examine both its voltage stability and longterm power balance for stationary and transient conditions. Thesimulations are based on weather data such as temperature andsolar irradiation as well as an estimated consumption pattern forthe household. Loads and sources in the system are identified aswell as possible algorithms for communication between nodes.Two scenarios are tested, a standalone grid with optional energystorage and a system connected to the main grid. The resultsindicate that a Swedish household can not be supplied froma standalone microgrid due to low irradiation values, withoutan unreasonably large energy storage or change in consump-tion. Although a continuous power supply is missing, voltagestability and power balance is established for this scenario. Withconnection to the main grid all requirements above are met.The observed limitations of the methodology are analyzed. Forfuture projects a communication algorithm for load variation,synchronized with irradiation inputs, can be implemented in themodel. Also, simulations can be done for alternative geographicalconditions to yield different results where alternative renewablesources, such as wind and geothermal, can be included.

I. INTRODUCTION

S INCE the late 19th century, electrical power systems havemainly been adapted to run on Nikola Tesla’s alternating

current (AC) as opposed to direct current (DC) promoted byThomas Alva Edison. The most evident reason to produceand transmit power with AC is the simplification it bringsregarding voltage regulation and circuit breakers due to itsalternating properties and zero crossings [1].

AC systems enabled the use of magnetic transformers toincrease the voltage in long transmission lines to minimizelosses during transportation, which was not easily done withDC at that time. The zero crossings enabled the use of simplemechanical breakers, making it easier to isolate grid faults inorder to avoid major system failures [2].

The contemporary perception regarding the use of ACversus DC for power distribution is starting to shift towardsusing DC. Power sources producing DC, such as solar panelsand fuel cells, have become more frequent as well as theusage of DC-loads for household applications, such as LEDlights, computers and electrical vehicles [1], [3]. DC loadshave always been present but required individual convertersfor a connection to the standard AC grid. However, a DCbased system would make these energy consuming convertersredundant.

Short ranged, local DC-based grids, microgrids, are there-fore an alternative to establish a more effective and self-sufficient system where power is produced and consumedlocally. With this solution, unnecessary power consumingAC/DC-conversions can be avoided and a higher efficiency,

cleaner power quality and less material usage can be achieved[3].

These microgrids ensure a more stable power supply as theycan work both with and without a grid connection makingthem less vulnerable to grid failures, thus allowing connectedhouseholds to be more energy independent.

As mentioned, microgrids can be operated in two modes,island mode, more commonly referred to as standalone mode,and grid-connected mode. If the circumstances allow for it,microgrids are more frequently connected to the grid i.e. runin grid-connected mode. This ensures that the energy demandof the connected loads are met at all times. If power failureoccurs in the main grid the operation mode can always beswitched allowing the microgrid to be more resilient andenergy independent, ensuring a stable supply of power to theloads. If this happens or if the microgrid simply is located toofar from a main grid it will have to operate in island mode,entirely relying on its distributed generation (DG) units, suchas solar panels, wind turbines or fuel cells [4].

When in grid-connected mode, the main objective is tooperate the system to increase the economical benefits frombuying and selling electricity to the main grid. Operating instandalone mode the priorities change to make sure importantloads are supplied with power when necessary [5].

Previous studies about microgrids often prove to be moreextensive and detailed regarding the size and structure oftheir research [6] [7]. These studies include a larger set ofDG units and take into account more parameters regardingoperational costs for microgrids [4]. Here the goal normallyis to minimize these costs with different control methodsfor energy management and even out the effects of powerfluctuations from intermittent energy sources [5].

This project however, aims to study the power flow ina small microgrid consisting of a 4-person household withroof-based PV panels, an energy storage and optional gridconnection. The main objective is to construct a 48 V DC-based model of the microgrid in MATLAB Simulink andexamine voltage stability and long term power balance. Thesimulations are performed in both mentioned operation modesand an energy storage is implemented as a lead-acid batterybank with realistic charge/discharge dynamics.

May 15, 2017

II. MICROGRID COMPONENTS AND THEORY

This section describes and illustrates the topology for amicrogrid, and the theory behind the different components.

A. Buck-boost converter

The buck-boost converter is a DC-DC converter that caneither decrease (buck) or increase (boost) the input voltage.

As seen in Figure 1 the converter is an active switchedcircuit, which means that the current flow and voltage actdifferently depending on the controlled switch. When theswitch is on, energy is supplied directly to the load andcapacitor but also stored in the inductor. When the switch isoff, the inductor supplies energy to the capacitor and loadwhilst discharging. By controlling the amount of time theswitch is on or off, the circuit can either raise or lower the inputvoltage [8]. The relation between the in- and output voltageis given by the relation

D =Vo

Vi + Vo(1)

where D is the duty-ratio, i.e the relation between the time theswitch is on and off.

Fig. 1. The topology of a buck-boost converter

B. Energy storage

As the energy production from renewable sources usuallyfluctuate over time, it is wise to include an energy storagein the microgrid to be able to meet the also fluctuatingconsumption. Some of the most commonly grid connectedenergy storages used are: compressed air, fly wheels, lead-acidbatteries, sodium sulfur batteries and lithium-ion batteries [9].

The most realistic energy source for a small householdhowever are batteries which is why a lead-acid battery ischosen for simulations in this project.

C. Local energy source

Microgrids are often coupled with a local energy source e.gsolar, wind, hydraulic power, portable generators etc.

Solar power in the form of photovoltaic arrays (PV-arrays) isused in the project, essentially converting incoming irradiationinto usable electricity [10].

The PV-array has a convoluted relationship between celltemperature, irradiation and load which all affect the outputcurrent and voltage, thus also the output power [11].

The load supplied from the solar panel usually has a certainvoltage requirement but can handle a varying amplitude ofcurrent within certain limits. Between the solar panel and theload there is a converter connected that matches its outputvoltage to the load requirement while adapting its input voltagein order to ensure maximum power output from the PV-array.The latter is done by a maximum power point tracker (MPPT).The MPPT is a mathematical algorithm that makes sure theconverter works in such a way that the solar panels produce

as much power as possible by increasing the current, whilekeeping the specified voltage over the load [12]. In this projecthowever, a simplified MPPT is introduced using a formula thatgives roughly the same output ensuring maximum power fromthe PV-array.

For example, a 100 W solar panel without converter andMPPT has a nominal output voltage of 20 V and output currentof 5 A delivers power to a battery which require 15 V tocharge. The solar panel adjusts to the required voltage anddelivers 15 V and 5 A, i.e. the panels produce only 15 · 5 =75 W . However, with a MPPT and converter the solar panelcan deliver 20 V , decrease it to 15 V by increasing the outputcurrent to 100 W

15 V ≈ 6.67 A which the battery has no problemto accept. The output power from the solar panels becomesbecause of this 15 · 6.67 ≈ 100 W . The calculations are doneby applying Ohm’s law P = U · I

III. SIMULATION ENVIRONMENT, METHOD AND MODEL

Two different model types are used in order to achievethe desired results. This section shows the topology of thesemodels, describes different parameters and components, andpresents the calculations involved.

A. Simulation environment

To simulate the given conditions for the microgrid anintegrated tool for model-based-design in MATLAB, calledSimulink, is used. This block diagram environment is theplatform for all simulations in this project. Depending of thetype of model being used, the operation mode is set to eitherphasor, or continuous.

B. Method

The project starts with the gathering of irradiation andtemperature data for a suburb of Stockholm called Salem. Thisdata is retrieved from [13], [14] and is used to calculate themaximum power that can be provided from the solar panelsat any given time during the simulations. Data for July andJanuary are obtained in order to simulate both extremes interms of weather conditions.

To simulate load variations, i.e. the consumption patternin the household, a scheme for a hypothetical family is con-structed. In this scheme the family’s daily routine is describedto determine when different household appliances are activatedor turned off. Power consumption data for all the chosenappliances are integrated with the constructed scheme usingMicrosoft’s Excel. This way the total power consumptionof the household for every minute of the day is calculated.All appliances are assumed to run on DC for simplificationpurposes. The consumption data for these appliances areobtained from various well know retail companies in Sweden.The specific type of hardware is chosen roughly with regardsto the economic constraints of an average 4-person household.For consumption data of the different appliances, see [15]–[27].

To determine how much power constant loads consume perminute, minor calculations are necessary. The chosen model

of combined fridge/freezer has an average yearly consumptionof 233 kWh. The corresponding consumption per minute iscomputed as shown below:

233 kWh

year=

233 · 1000 · 60 Wmin

365 · 24 · 60 min(2)

The sizing of the heat pump is calculated using a measureof power per square meter living area (Pm2 ) according to[28], where an average level of isolation is assumed. Togetherwith an average living area for a 4-person household (Ahouse)according to [29], the sizing of the heat pump is computedas shown in equation 3. In average, during the simulated timeperiod of 24 hours, the heat pump is assumed to work on 60percent of installed capacity.

HPcapacity = Pm2 ·Ahouse (3)

where,HPcapacity is Heat Pump capacityAhouse = 122 m2

Pm2 = 45 W/m2

With requirements for ceiling heights according to [30] andassuming that the hypothetical house has two equally largefloors with an estimated attic ceiling height a 3D-model of thehouse is constructed using Solid Edge ST8. Size measurementsof the specific PV-Module used in the simulations, Bosch SolarEnergy c-si M60 NA42117 250W [31], is incorporated in themodel to compute the maximum number of modules that canbe placed on the roof. Figure 2 below shows the 3D-model,where the green rectangles symbolize the PV-modules. With ameasurement tool in the programming environment this areais computed to 39.44 square meters.

Fig. 2. 3D-Model of household incorporated with PV-panels

According to [32], lead-acid batteries are a common batterytype used in solar-powered microgrids. Based on [32], the

design of the battery system is calculated using the followingequation:

Bcapacity =Eday ·Dautonomy

ηrte ·DOD · Vbat(4)

where,Bcapacity is battery capacityEday is energy consumption per dayDautonomy is the number of days of autonomyηrte is the round-trip-efficiency of the batteryDOD is the battery’s Depth of DischargeVbat is the nominal voltage of the battery system

The energy consumption per day is computed to 92.1 kWhusing the daily scheme. According to [33], the minimumnumber of Days of autonomy for microgrids operating withoutgrid connection is 5 and varies depending on the amount ofsolar irradiation per square meter delivered to the PV-array.

To investigate the sizing of the battery during grid-connectedmode, Dautonomy is set to 1, due to the fact that large powerfailures in the national grid seldom last more than one day.The round-trip-efficiency (RTE) of the battery refers to theratio of the energy input and output from the energy storage,set to 90 percent according to [34]. The nominal voltage ofthe battery system is set to 48 V to match the desirable DCvoltage in the simulated system.

C. Models

1) Model 1: Model 1 works by computing the simulationequations using a variable-step solver integrated in Simulink.The step size in these calculations is relatively high, resultingin less accurate results but a faster simulation time. To sim-ulate one day, Excel-files consisting of data for temperaturevariations, solar irradiation values and load variation from thedaily scheme, are all reformatted to csv-files and imported toMATLAB. With this input data it takes several days to simulate24 hours. To avoid this the data that is changing each minuteis scaled down to fit in a time span of 0.1 seconds.

Figure 3 describes the detailed version of Model 1 operatingin island mode without an implemented energy storage.

The PV-array block in Figure 3 is pre-programmed togenerate an output voltage and current similar to that of realsolar panels with irradiation and temperature data as input. Thesettings in this block are adjusted to mimic the specific model[31]. The number of series-connected modules per string areset to 6 and the total number of parallel strings to 4 accordingto previous calculations from the 3D-model of the house.

The duty-cycle step computes the required duty-cycle tobe fed into the buck-boost in order to ensure an outputvoltage of 48 V. The consumption variation in the household isrepresented by a variable resistor whose values are computedusing the output voltage and current from the buck-boost steptogether with the load variation data from the daily schemeaccording to the following equation.

R =U2

Phouse(5)

Fig. 3. Model 1, microgrid in island mode without implemented energystorage

The battery is connected in the node between the PV-arrayand the buck-boost step. Figure 4 describes the battery modeland state of charge (SOC) control implemented.

Fig. 4. Battery model and SOC-control

The battery block is also pre-programmed and the settingsadjusted to mimic a lead-acid battery bank with a nominalvoltage of 48 V and a capacity of 2661 Ah calculated usingequation (4). The SOC-control monitors the SOC and is setto disconnect the battery when reaching values above 99.9percent or below 20 percent to avoid damage.

2) Model 2: Model 2 is inspired by [35] and works bycomputing with phasors i.e. calculating the equations withthe current and voltages maximum values. With a time stepof 60 seconds, the model is able to execute the calculationswith great speed, optimal for long-time simulations. Model 2requires approximately one second to simulate 24 real hours.

Figure 5 represents a conventional two-phase residence. Thepower consumed is represented as a current source connecteddirectly to the AC grid. The defined residence consumption isdivided randomly upon these two phases and then convertedwith the power equation into a current. The current values aretransferred into the associated current source where it by thepower equation consumed the appropriate power.

P = U · Icons (6)

Icons =P

U(7)

where,P is power the residence consumesU is voltage the grid supplies to the residenceIcons is current that represents the power consumption

Fig. 5. Split phase system with controlled current sources representing theresidence’s power consumption

On the roof of the house there is a PV-array, covering40 m2 of the roof’s surface, providing electricity to theresidence. The solar panels have the following specifications[31]:Pmp = 250 WVmp = 30.31 VImp = 8.25 AVoc = 37.9 VIsc = 8.82 Aγ = −0.44% ◦C -1

where,Pmp is maximum power delivered from the solar panelsVmp is voltage at maximum power productionImp is current at maximum powerVoc is open circuit voltageIsc is closed circuit currentγ is maximum power correction for temperature

It is assumed that the PV-array has a working MPPT andthe maximum power provided by the PV-array is calculated

according to [10]

Pmp =G

GrefPmp,ref [1 + γ(T − Tref )] (8)

where,Pmp is the power output with MPPTG is the incident irradianceGref is the 1000 Wm−2

Pmp,ref is the maximum power output under standard testingconditions

T is the temperatureTref is the temperature for standard testing condition

reference (25◦C)

The irradiation data used in the calculations, both for Model1 and Model 2, is observed from a Meteosat satellite. Tem-perature data is retrieved from the Swedish industry standardfor energy in buildings, SVEBY [14].

As the PV-array is connected to phase two of the house, itis reasonable to connect the battery to this phase as well. InModel 2 the battery is represented by a MATLAB functionblock (M-file block), as seen in Figure 6, that registers theenergy consumption and the PV-array’s energy production.If the production is higher than the consumption, the M-fileblock will convert the excess energy from the PV-array intoan equivalent direct current with a converter loss representedby an efficiency factor thus charging the battery. If the powerfrom the PV-array is lower than the house consumption, thebattery will discharge, providing the house with power equalto the difference between house consumption and the solarproduction until it reaches an unacceptable SOC. The batterythen disconnects and all the power the house needs will beprovided by the grid. The stored/supplied equivalent directcurrent is calculated by the following equation:

IDCeqv = η · conj(2PDC

V2) (9)

where,η is the product of the battery’s RTE and AC-DC

converter efficiencyPDC is the DC powerV2 is the phasor voltage over the second phase

Fig. 6. Battery saving excess current from the PV-array via an M-file block

IV. RESULTS

A. Model 1

From the simulations operating in continuous mode withModel 1 the following results are obtained.

Figure 7 shows the voltage stability over load withoutbattery implemented.

Fig. 7. Obtained voltage stability over variable load without battery imple-mentation

Figure 8 shows the acquired plot for the variable resistorsimulating load variation.

Fig. 8. Computed load variation

Figure 9 shows the power delivered from the PV-arraywithout battery implementation.

Fig. 9. Input power from PV-array

Figure 10 shows power consumed by the variable loadwithout battery implementation.

Fig. 10. Measurement of power consumed by load

Figure 11 shows voltage stability over load with batteryimplemented.

Fig. 11. Obtained voltage stability when battery implemented

B. Model 2

Figure 12 shows the amount of solar power delivered to thesecond phase with a working MPPT. The power is roughlywhat is to be expected during a summer day in Sweden.

Fig. 12. Delivered solar power with MPPT

Figure 13 illustrates the residence’s power consumption onthe second phase. The power consumption is successfullyrandomized over the two phases.

Figure 14 represent the amount of power delivered from thegrid to the second phase after the solar panels and battery isimplemented. The difference in load the second phase puts onthe grid is clear.

Fig. 13. Power consumption, second phase

Fig. 14. House consumption on the second phase after battery and solarpanels with a MPPT is implemented. As seen, no power is drawn from thegrid after the PV-array and battery is connected to the second phase.

As seen in Figure 15, the battery delivers current and there-fore power to the residence when the irradiance is deficientand stores excess solar power when irradiance surpasses theresidence’s power consumption. The excess solar power duringthe day is not sufficient enough to bring the battery back toits initial SOC.

Fig. 15. Battery discharge pattern

V. DISCUSSION

1) Model 1: When scaling down the minute by minutechanging input data for model 1 to 0.1 seconds, the simulationonly took a couple of minutes to complete. This was a decisivefactor for further work with the model. With some fine-tuningof parameter settings in the different components in the buck-boost and duty-cycle step both voltage stability and long term

power balance was obtained, as shown in Figures 7, 9 and10. Without battery implementation in the circuit, Figure 7clearly shows when the irradiation levels are high enoughfor the buck-boost step to be able to boost the power andprovide the desired 48 V over the resistor, i.e the house. Theopposite effect occurs when the irradiation input is too low inthe afternoon and the buck-boost converter’s input voltage istoo low for it to be able to deliver 48 V.

The load variation pattern, plotted in Figure 8, is as expectedwhen the control function for the variable resistor in thecircuit outputs a value according to Equation (5). ComparingFigures 9 and 10 it is evident that the buck-boost step hasconsumed some of the power supplied by the PV-array. Theoutput power from the array is on average 100 W after 0.02seconds and throughout the day. The power consumed by theload however, is on average 80 W. The buck-boost converterhas consumed 20 percent of the output power delivered by thesolar panels. According to [36], the efficiency of the convertershould be around 90-95 percent making the obtained lossesunreasonably high. This can be explained by the parametersettings in the buck-boost step. Since minimizing the lossesin the converter step is not in the scope of the project, theseresults are sufficient.

Model 1 met its limitations when simulating the battery dy-namics. As mentioned before, the battery is pre-programmedto simulate the dynamics of a real battery. It would normallytake several hours to drain the battery and reach a SOC of 20percent. When scaling down the simulations to 0.1 secondsthe battery will act as an infinite energy source. Due to theseobservations there is no further analysis of the apparently lowpower values shown in Figure 9 and 10.

2) Model 2: As evident in Figure 15 the power providedby the PV-array is not sufficient to provide the residence withenough power to sustain the second phase without a gridconnection. The battery’s SOC does not return to its initialstate and we can therefore see that if we were to simulate forseveral consecutive days, the battery would eventually have aninitial SOC equal to its lower limit. It would then charge upwhen the PV-array provides sufficient power but return to itslower SOC limit by the end of the day. To be able to have astandalone system we would need to incorporate more solarpower and/or lower the consumption. Note that it would benecessary to take the first phase into consideration as well,further increasing the amount of needed solar power.

It is possible that the current solar panels could havedelivered more power to the system. The model takes onlythe vertically incoming irradiation into consideration whichprovides less power compared to e.g. solar panels designedto track the sun’s movement and thus maximizing the powerproduction. Such a system is more expensive than passive solarpanels. It is also assumed that the PV-array’s inner temperatureis equal to the outside temperature. This is not the case inreality and does have an impact on the results.

As the incoming irradiation is measured with a satellitein orbit around the earth, it is quite clear that the incomingirradiation used in this project does not correspond to theactual incoming irradiation at ground level. It is less intensedue to clouds and the earth’s atmosphere.

These factors weighed together with the simplified MPPT-formula, converter simplifications and lack of consideration ofbattery dynamics would change the results of the simulationbut we argue that it does not have enough impact to changethe conclusion that the microgrid needs a grid connection.The most important impact factor is a change in consumptionand potentially an implementation of an algorithm usingcommunication to optimize the load behavior.

VI. CONCLUSION

The shown results is based on a summer day in Sweden andcomputations for input data matching that of a winter day isnot necessary to compile since such results does not changeany of the conclusions made in the project. For it to be relevantto study a winter day, the constructed power demand shouldbe met at all times from the PV-array and the battery. Basedon the results, this is not the case.

As mentioned, Model 1 met its limitations when a necessarydownscaling of the time array used to simulated 24 hoursin a reasonable time span caused the battery to act as aninfinite energy source. The downscaling causes the input datato vary much more dynamically than when using the minuteby minute changing csv-file input from the daily scheme. Thefact that the converter can handle such a small time stepand still outputs the desired voltage allows the conclusionto be made that voltage stability can be obtained even withsimulations in the original time scale. The same logic appliesfor the long term power balance. Furthermore, the fact thatthe system works with these transient conditions we concludethat it would support a stationary load and continuous energysupply.

As demonstrated with Model 2, the microgrid integratedwith a PV-array and batteries is not able to sustain theresidence with enough power for a stand alone system. Dueto the irradiation and temperature in Sweden it is necessary tohave a grid connection for power stability.

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