Research Article An Improved PSO-Based MPPT Control ...

Research ArticleAn Improved PSO-Based MPPT Control Strategy forPhotovoltaic Systems

M Abdulkadir A H M Yatim and S T Yusuf

Department of Electrical Power Engineering Faculty of Electrical Engineering Universiti Teknologi Malaysia81310 Skudai Johor Bahru Malaysia

Correspondence should be addressed to M Abdulkadir amusa2liveutmmy

Received 1 March 2014 Accepted 28 May 2014 Published 16 June 2014

Academic Editor Cooper H Langford

Copyright copy 2014 M Abdulkadir et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents a control strategy proposed for power maximizing which is a critical mechanism to ensure power track ismaximized Many tracking algorithms have been proposed for this purpose One of the more commonly used techniques is theincremental conductance method In this paper an improved particle swarm optimization- (IPSO-) based MPPT technique forphotovoltaic system operating under varying environmental conditions is proposed The approach of linearly decreasing schemefor weighting factor and cognitive and social parameter is modified The proposed control scheme can overcome deficiency andaccelerate convergence of the IPSO-based MPPT algorithm The approach is not only capable of tracking the maximum powerpoint under uniform insolation state but also able to find the maximum power point under fast changing nonuniform insolationconditionsThe photovoltaic systematic process with control schemes is created usingMATLAB Simulink to verify the effectivenesswith several simulations being carried out and then comparedwith the conventional incremental conductance technique Lastly theeffectiveness of the intended techniques is proven using real data obtained form previous literature With the change in insolationand temperature portrait it produces exceptional MPPT maximization This shows that optimum performance is achieved usingthe intended method compared to the typical method

1 Introduction

Energy is indispensable to human life Energy is not only ameasurement for economic and social improvement but alsoa fundamental human necessity Many countries are tryingto find means to solve energy problems such as dependingon energy importation minimization of environmental pol-lution global warming increasing cost of energy and energyinefficiency [1 2]

Photovoltaic (PV) system has gained wide popularityin the past decade as one of the renewable energy sourcesdue to the possibility of depletion of conventional energysources and its high cost as well as its negative effectson the environment One essential fundamental of all PVis the efficacy of its maximum power point tracking Theaspect has drawn immense enthusiasm from photovoltaicresearchers and industry experts being the most economicalmeans to enhance above all the photovoltaic system efficacyMaximum power point tracking is primarily an operatingpoint cocoordinating between the photovoltaic module and

the DC-DC converter Nonetheless maximum power pointtracking is not simple and easy to track because of thenonlinear I-V characteristics of the photovoltaic curve andthe effect of the changing weather situations (especiallyradiation and temperature) tracking the accurate maximumpower point (MPP) has been always an intricate issueThe tracking eventually is further sophisticated when allphotovoltaic modules do not experience constant radiation

For the past decades many MPPT algorithms have beenproposed in which many centered around obtaining opti-mum maximum power point [2ndash6] Among the renownedpower maximizing methods are Perturb and Observe (PampO)andor hill climbing and incremental conductance (IC) [7ndash9]These techniques nonetheless fail to track maximum powerpoint when the insolation level is not consistent for all PVsolar cells or the panel is partially shaded PampO techniquefrequently leads to wrongful conclusion oscillation aroundthe maximum power point and it generally needs to linkone or many modifications for general usage Incremental

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2014 Article ID 818232 11 pageshttpdxdoiorg1011552014818232

2 International Journal of Photoenergy

conductance techniques overcome these shortfalls of Perturband Observe techniques but need relatively elaborate detec-tion devices and the choice of the step and threshold is alsodistressing [10]

Recently numerous researchers have presented intelli-gent MPPT methods [5ndash11] for photovoltaic module arraysboth to track MPPs accurately and to improve the dynamicand steady-state tracking performanceHowever thesemeth-ods are applicable only to MPPT in photovoltaic 119888 modulearrays without shading Nevertheless the appearance ofmultipeak output curves because of partial module shadingin photovoltaic module arrays is common Therefore thedevelopment of an algorithm for accurately tracking the trueMPPs of complex and nonlinear output curves is crucialReference [12] presented a MPP tracker based on particleswarm optimization (PSO) for photovoltaic module arraysAlthough this tracker was capable of tracking global MPPsof multipeak characteristic curves because fixed values wereadopted for weighing within the algorithm the tracking per-formance lacked robustness causing low success rates whentracking global MPPs Even though the MPPs were trackedsuccessfully the dynamic response speed was low Thereforethis study used PSO and added improvements preventingit from being trapped in local MPPs (ie searching onlylocal MPPs) and enabling it to track global MPPs quicklyand consistently on the multipeak characteristic curves ofphotovoltaic module arrays

An alternative approach is to employ evolutionary algo-rithm (EA) techniques Due to its ability to handle nonlinearobjective functions [13] EA is envisaged to be very effective todeal withMPPTproblem Among the EA techniques particleswarm optimization (PSO) is highly potential due to itssimple structure easy implementation and fast computationcapability [13] Since PSO is based on search optimization inprinciple it should be able to locate theMPP for any type ofP-V curve regardless of environmental variations It can be usedto track theMPP of PV system as the search space of the PSOis reduced and hence the time required for convergence canbe greatly decreased

Interestingly one important feature of the PSO which isignored by researchers [5 6 13 14] is the searching speedthrough adaptive learning factors and inertia weight Lineardecreases in line with increasing iteration numbers wereadopted in this study for the weighting of the PSO formulasThe physical meaning of this modified weighting formulais that greater step sizes are used to increase the particlesearch velocity during the initial search because the distanceto the global optimum is relatively large This prevents anexcessively small step size from making local optimum trapsunavoidable

However 119908 decreases gradually as the number of iter-ations increases As the particles approach the MPP thisdecrease in 119908 causes the steps in the particle movementsto diminish enabling the particles to track the MPP moreaccurately In PSO equation the first term 119908(119905)V

119894(119905) is

exploited tomaintain the same direction inwhich the particlewas moving pristinely thereby controlling the convergingdemeanor of the particle swarm optimization In order toexpedite converging the inertia weight will be culled such

that the effect of V119894(119905) of the algorithm diminishes during

the operation Therefore the value of 119908 decrementing withtime is desirable To get refined solutions a very popularoption is to set the inertia weight initially to a bigger valuefor better exploration and then reduce it gradually Likewisethe cognitive and social parameter can also be modified asit affects the search ability of PSO Therefore power loss asa result of the oscillation is eradicated and the efficiency ofthe system increasesThe theoretical analysis and simulationresults presented illustrate the good performances of theproposed control schemes

2 System Overview

Photovoltaic system models have long time been an originfor the description of photovoltaic nature for researchersand professionals alike The utmost ordinary model usedto foresee energy generation in photovoltaic cell model isthe single diode circuit [3 15] An ideal photovoltaic cell iscomprised of a single diode connected in parallel with a lightcurrent source as depicted in Figure 1 A complete PV systemsimulation should fulfill the following criteria (a) it shouldbe simple and fast but able to correctively predict the I-Vand P-V characteristic curves including special conditionssuch as partial shading and (b) it should be an overall toolwhich can evolve and ratify a photovoltaic system design all-encompassing the power converter and the MPPT control asshown in Figure 2 [3 15 16]

3 Basic of Incremental Conductance and PSO

In this work the performance of the proposed CS will beevaluated in comparison to Perturb and Observation (PampO)and Particle Swarm Optimization (PSO) MPPT To facilitatediscussion that shall follow brief overviews of both methodsare presented here

31 Incremental Conductance (IC) The idea behind incre-mental conductance is to increasingly contrast the ratioof the derivative of conductance with the instantaneousconductance [1 17] It is derived from the fact that at MPPthe derivative of power with respect to voltage (119889119875119889119881) is infact zero that is

120597119875PV120597119881PV=

120597 (119881PV lowast 119868PV)

120597119881PV= 119881PV lowast

120597119868PV120597119881PV+ 119868PV = 0 (1)

where the change in photovoltaic current is 120597119868PV the changein photovoltaic voltage is 120597119881PV and 120597119875PV is the change inphotovoltaic power respectively

Equation (1) can be reconstructed as follows

120597119868PV120597119881PV= minus

119868PV119881PVasymp

Δ119868

Δ119881

(2)

where photovoltaic current and voltage Δ119868 and Δ119881 are theincrements respectively

International Journal of Photoenergy 3

PV module

IPV

VPV

Figure 1 Photovoltaic System

IPSO-based MPPT

Load

PWM

IPV

VPV

+

minus

Figure 2 Configuration of the proposed PV system

The key rules for incremental conductance can hence bederived from the P-V characteristics and written as follows[18 19]120597119875PV120597119881PVgt 0 if

119868PV119881PVgt minus

120597119868PV120597119881PV on the left of MPP

120597119875PV120597119881PV= 0 if

119868PV119881PV= minus

120597119868PV120597119881PV at the MPP

120597119875PV120597119881PVlt 0 if

119868PV119881PVlt minus

120597119868PV120597119881PV on the right of MPP

(3)

where MPP refers to maximum power pointUsing the rules in (3) it can be observed that the reference

signal is based on voltage 119881lowast As the rules in (3) are derivedusing P-V curve the current cannot be used as the finaloutput rather P-I characteristics curve is utilized The clearflow chart of this technique is reported in [1] The followingare the modification in respect of the standard incrementalconductance algorithm

32 Particle Swarm Optimization (PSO) Particle swarmoptimization (PSO) is a stochastic population-based EAsearch method modeled after the behavior of bird flocks[13] The PSO algorithm maintains a swarm of individuals(called particles) where each particle represents a candidatesolution Particles follow a simple behavior emulate the suc-cess of neighboring particles and its own achieved successesThe position of a particle is therefore influenced by the bestparticle in a neighborhood 119901best as well as the best solutionfound by all the particles in the entire population 119892best Theparticle position 119909

119894 is adjusted using [13]

119909119905+1

119894= 119909119905

119894+ V119905+1119894 (4)

where the velocity component V119894 represents the step size

The velocity is calculated by

V119905+1119894= 119908V119905119894+ 11988811199031sdot (119901best 119894 minus 119909

119905

119894) + 11988821199032sdot (119892best minus 119909

119905

119894)

119894 = 1 2 119873

(5)


xtminus1i

ti

xti

t+1i

xt+1i

Pbest i

Gbest

Figure 3 Movement of particles in the optimization process

where 119909119894denote the particle position for 119894 the velocity of

the particle at 119894 is represented by V119894 the number of iteration

is denoted by 119905 the inertia weight is represented by 119908 1199031

and 1199032are uniformly distributed random variables within

[0 1] and the cognitive and social coefficient are respectivelydenoted by 119888

1 1198882[14] The best position for the storage of the

119894th particle that has been found so far is denoted by variable119901best 119894 and the storage of the best position of all the particlesis represented by 119892best Figure 3 depicts the movement ofparticle in the optimization process

33 The Weakness of Conventional Particle Swarm Opti-mization-Based MPPT Techniques Conventional PSO is fastand accurate when searching for the output characteristiccurves of PVmodule arrayswith single peak values Howeverwhen somemodules are shaded weights in conventional PSOmust be readjusted appropriately based on various multipeakcurve characteristics If this is not performed excessively highor low weights result in tracking failure Thus conventionalPSO-based MPPT must be modified when some of themodules in a photovoltaic module array are shaded

4 IPSO-Based MPPT Technique

For the IPSO-based MPPT system designed the position ofthe particle is designated as the duty cycle of the power con-verter while the fitness value evaluation function was chosenas the produced power119875PV for the entire photovoltaic systemIn the proposed method overview more accurate MPPtracking is achieved despite the complex shading conditionswith the smaller particle number and where larger number ofparticles results in lengthy computation time Therefore forgood tracking speed and accuracy to be ensured a tradeoffshould be made According to some research at most thereexist 119898 MPPs in the P-V curve for photovoltaic moduleswhich consist of 119898 series connected photovoltaic cells [12]For initialization step of the particle swarm optimizationparticles could be established in the random range or beplaced on stationary position Mostly it makes more sense

to initialize the particles around it if there is data availableregarding the position of the global maximumpower point inthe search range In [12] the authors state that the minimumdisplacement between successive peaks is nearly 80 of 119881OCand also the peaks on the P-V curve occur nearly at multiplesof 80 of the module open voltage 119881OC Thus the numberof particle 119873 is selected in the photovoltaic system as thenumber of the series connected cellsThe search spaces of theparticles that cover [0 1] are initialized on definite point 0and 1 are the duty cycle minimum andmaximum value of thedc-dc converter used respectively

The objective of this IPSO-based MPPT method was toextract the maximum power 119875PV of the photovoltaic Toevaluate the fitness value which is the generated power afterthe controller output the pulse width modulation acts in lineto the particle position 119894 that denote the duty cycle stateand the photovoltaic voltage 119881PV and current 119868PV can bemeasured To calculate the fitness value119875PV of particle 119894 thesevalues can then be used However to obtain the right samplestime it should be noted that power converterrsquos settling timehas to be lesser than the evaluations time interspaces betweensubsequent particles

To address these problems linear decreases with increas-ing iteration numbers were adopted in this study for theweighting of the PSO formulas The physical meaning ofthis modified weighting formula is that greater step sizesare used to increase the particle search velocity during theinitial search because the distance to the global optimum isrelatively large This prevents an excessively small step sizefrom making local optimum traps unavoidable However 119908decreases gradually as the number of iterations increasesBecause the particles are now approaching the MPP thesedecreases in 119908 cause the steps in the particle movementsto shrink enabling the particles to track the MPP moreaccurately

In (5) in order to maintain the particle acceleratingin the same direction it was originally moving the firstterm 119908(119905)V

119894(119905) is therefore utilized where the converging

demeanor of the particle swarm optimization is controlledThe inertia weight will be chosen in order to accelerateconvergence such that the effect of V

119894(119905) diminished through

the process of the algorithmHence the choice of a decreasingvalue of 119908 with time is considered To get refined solutionsa typical option is to set the inertia weight initially to abigger value and slowly reduce it for better exploration Forthis reason here the term 119908 was used as linearly decreasingscheme as illustrated as follows

119908 (119905) = 119908max minus119905

119905max(119908max minus 119908min) (6)

In (6) the minimum and maximum bounds of 119908 weredenoted by 119908min and 119908max while the maximum allowednumber of iterations are denoted by 119905max Likewise the socialand cognitive terms can be remodelled In (5) the searchability of particle swarm optimization can be affected by thevalues of 119888

1and 1198882by changing the particle direction Selecting

1198881gt 1198882sampling with respect to the bearing of 119901best 119894

would be biased while selecting 1198881lt 1198882in the reverse case

sampling in respect to the bearing of 119892best will be preferred


IPSOinitialization

Determine the duty cycleto converter according to

the position of particle

Measure and

Better individualfness value

Calculate the power

Better globalfness value

All particleevaluated

Update particlesrsquovelocity and positionusing Eq (2) and (3)

Update

Update

Next particle

Sort particlesrsquoposition

Next iterationConvergencecriteria met

Output the dutycycle of the

Shadingpattern

changed

Yes

No

No

No

No

No

YesYes

Yes

Yes

Start

VPV(i)IPV(i)

PPV(i) = VPV(i) times IPV(i)

i = i + 1

i = 1

t = t + 1

Pbest i

gbest

gbest

Figure 4 Flowchart of the proposed IPSO-based MPPT algorithm

For these reasons these two terms are defined as continuouslyincreasing and continuously decreasing functions as in (7)and (8) respectively

1198881 (119905) = 1198881max minus

119905

119905max(1198881max minus 1198881min) (7)

1198882 (119905) = 1198882max minus

119905

119905max(1198882max minus 1198882min) (8)

Two convergence criteria are employed in this studyThe proposed IPSO-based MPPT method will halt and yieldthe 119892best solution if the maximum number of iterations isattained or if all the particles velocities become smaller thana threshold

Basically particle swarm optimization algorithms areutilized to address optimization difficulty that the optimumresult is time invariant However in this case the fitnessvalue which is the global maximum power point sometimesvaries or depends on environmental factors as well as loadingstates To search for the new global MPP again in these cases

the particles must be reinitialized Considering the changein insolation and shading pattern to be detected here thefollowing constraint is utilized In the proposed IPSO-basedtechnique the particles will be reinitializing whenever thefollowing condition is satisfied as shown in (9) Figure 4depicts the comprehensive flowchart of the proposed system

1003816100381610038161003816119875PV new minus 119875PV old

1003816100381610038161003816

119875PV oldge Δ119875 () (9)

where 119875PV new is the new photovoltaic power 119875PV old is thephotovoltaic power at global maximum point of the lastoperating point and Δ119875() is set to 10

41 Effect of Partial Shading A photovoltaic module is com-prised ofmany photovoltaic cells either connected in series toproduce a higher voltage or connected in parallel to increasecurrent Many photovoltaic cells are therefore connectedeither in series or in parallel to form a photovoltaic system


0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

7

8

Voltage (V)

Curr

ent (

A)

Unshadded photovoltaic moduleShadded photovoltaic module

(a)

0 2 4 6 8 10 12 14 16 18 20 220

10

20

30

40

50

60

70

80

90

100

110

Voltage (V)Po

wer

(W)

Unshadded PV moduleShadded PV module

Uniform irradiance

Partial shading

global MPP

local MPP

MPP

(b)

Figure 5 (a) shows I-V characteristic of PV system under shading and nonshading condition and (b) shows the P-V characteristic of PVsystem under shading and nonshading condition respectively

The P-V curve of photovoltaic cell would exhibit multipleMPPs under partial shading pattern because of the bypassdiodes as reported in [17ndash20] The photovoltaic modulecharacteristics under partial shading pattern connected atmodule terminal with bypass diodes can be described asbellows In partial shading pattern the shaded portion ofthe cells acts as a load rather than a generator and createsthe hot shot and hence the bypass diodes of these shadedcells will conduct to avert this bad situation [17] Multiplepeaks in the P-V curve would be obtained since the shadedmodules are bypassed The resulting I-V curves when thissystem is under different shading conditions are shown inFigure 5(a) Same process can then be used to get the P-V characteristic curves as illustrated in Figure 5(b) It canthen be noticed from Figure 5(a) that the global MPPcould happen depending on the type of shading pattern ineither the below or above voltage range For this reason theconventional MPPT algorithms will be very difficult to beapplied directly

5 Simulation Results and Discussion

To demonstrate the effectiveness of the proposed IPSO-basedMPPT technique simulations were performed appropriatelyThe simulation model parameters of the PVmodule used areshown in Table 1

In this paper the simulations were implemented usingMATLABSimulink model According to the design princi-ple the specification frameworks of the complete IPSO-basedMPPT algorithm are shown in Table 2 The photovoltaicmodule characteristic curves are simulated by arbitrary

Table 1 Simulation model parameters of ICO-SPC 100W photo-voltaic module [3]

Parameter ValueMaximum Power (119875max) 100WVoltage at 119875max (119881max) 173 VCurrent at 119875max (119868max) 579AOpen circuit Voltage (119881oc) 2076VShort circuit Current (119868sc) 687 ANumber of cells in series (119873

119904) 36

Number of cells in parallel (119873119901) 1

Table 2 Simulation parameter setting of the IPSO-based MPPT

Parameter ValueNumber of particles 3Minimum duty cycle 002Maximum duty cycle 098Sampling time 01 sMaximum iteration 3119882max 10119882min 011198621min 11198621max 121198622min 11198622max 16

setting the irradiation of the series connected photovoltaiccells under the effect of partial shading condition The


0 02 04 06 08 1 12 14 16 18 2085

09

095

1

105

Time (s) times106

Chan

ge in

irra

dian

ce (W

m2)

(a)

50

60

70

80

90

100

110

Pow

er (W

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)

Figure 6 (a) shows varying irradiance level and (b) shows maximum power due to irradiance variation

5

52

54

56

58

6

62

64

66

68

7

Curr

ent (

A)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(a)

10

11

12

13

14

15

16

17

18

Volta

ge (V

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)

Figure 7 (a) shows the current at maximum power under varying irradiance condition and (b) shows voltage at maximum power undervarying irradiance condition

photovoltaic module temperature is taken to be unchanged at25∘C during the simulation Unshaded photovoltaic modules

are thoughtout entirely radiated at 1000Wm2 Irradiationon shaded photovoltaic module is thoughtout constant andchange from 0 to 1000Wm2 For different shading patternsthe IPSO-based MPPT algorithms are tested and verifiedand the simulation results are presented in Figures 6 and 7respectively

From the computed power the duty cycles are updatedaccording to the proposed algorithmWhen there is a changein irradiation from 1000Wm to 950Wm2 the duty cyclesare recomputed using (4) and (5) for the tracking of newMPPThe search process is continuously changing the duty cycleswhen irradiation changes from high to low value that is950Wm to 900Wm2 new duty cycles are again computedusing (4) and (5) At 052 sampling period the steady


0 01 02 03 04 05 060

10

20

30

40

50

60

70

80

90

100

110

Time (s)

Pow

er (w

)

IPSOImproved ICPampO


003 0034 0038 0042 0046 00580

82

84

86

88

90

92

94

96

98

100

102

Time (s)

Pow

er (w

)

034 0342 0344 0346 0348 03598

985

99

995

100

1005

101

1015

102

Time (s)

Pow

er (w

)(a)

(b) (c)

Enlarge portion A

Enlarge portion B

(A) (B)

Figure 8 (a) depicts the performance comparison between IPSO modified IC and PampO (b) Enlarge portion A (c) Enlarge portion B

state value is attained As the duty cycles are reinitializedfor every change in irradiation a fast tracking speed andalmost zero steady state oscillations at MPP are attainedwhen compared to IncCond technique which makes IPSOalgorithm exceptional

Figure 8 compares the performance of IPSO modifiedIC and PampO For IPSO variables 119888

1and 1198882are chosen as

shown in Table 2 These values are chosen after extensivesimulation trials and thus the IPSO can be regarded aswell optimized The random numbers are generated by

MATLAB rand function The result indicates that initiallyIPSO requires a much longer time that is approximately200ms to settle at the first MPP After convergence bothalgorithms track the MPP perfectly and remain almostripple-free at steady state However during the power rampIPSO sustains a prolong oscillation compared to modifiedIC This is due to the smaller step sizes which forces theIPSO to utilize more samples in order to converge to MPPThis observation is consistent with discussions presentedin Section 4


0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

Time (s)

5

10

15

20

25

30

Tem

pera

ture

(∘C)

Irradiance

Temperature

Irra

dian

ce (W

m2)

Figure 9 Depict a sequence of a rapid irradiation and temperaturevariation [11]

Throughout the experiment the temperature is main-tained constant at 25∘C This value is very conservativeconsidering the PV cell string voltage is 2076V Furthermoreit can be seen that even with a small step-size PampO oscillate(around the MPP) with an average ripple of 100W On theother hand as modified IC continuously sticks to the MPPthe loss is almost zero The comparison between modified ICand IPSO is shown in Figure 9 For the initial MPP trackingIPSO requires 200ms In the case of retracking (after eachstep change in irradiance) IPSO requires approximately40ms to settle to a new MPP value compared to modifiedIC that needs 60msThemost probable reasons for the fasterresponse of modified IC is the larger step size due to theparticle flight

In a typical sunny day both the irradiance and tem-perature increase as the hour approaches the midday andthereafter decreases towards the evening To study the perfor-mance of theMPPT algorithms under these gradual changessuch environmental scenario is simulated over a period oftime Figure 10 presents the irradiance and temperatureprofile inwhich the irradiance and temperature are increasedor decreased within one second rise or fall time respectively

A sequence of very fast irradiance variables was depictedin Figure 9 For incremental step the power response time isequal to 43 s for modified IC algorithm for 95 in this caseis shown in Figure 10 and 32 s for IPSO algorithmThereforethis shows that for the rapid irradiance variation the IPSOresponded very fast compared to the modified incrementalconductance method Nonetheless the distinction amongthe maximized powers between these algorithms is also notnegligible as depicted in Figure 10 If it is based on thefinal value the relative error obtained between these twopowers is about 48 The algorithm may be better thanone another especially depending on the rate and speed of

0 20 40 60 80 100 120 1400

20

40

60

80

100

120

Time (s)

Pow

er (W

)Modified ICPSO

Figure 10 Comparison of proposedMPPT and conventional IC fordaily Malaysian profile

solar irradiance change but without necessarily also having agood response time [19] The difference becomes negligiblefor a significant time in terms of energy It is well knownthat a photovoltaic system becomes interesting for energyproduction that requires a significant time

Many researchers in the literature show that PSO algo-rithm is more inferior to other methods [19] In this simula-tion concurrently implementing the two algorithms in samegiven set of conditions proves that the IPSO-basedMPPT hasbetter efficiencies compared to modified IC and it is easierto implement The performance of IPSO method is found tobe excellent compared to modified IC especially in terms oftracking speed and steady state oscillationsThough in IPSOthe calculation of new duty cycles using (4) and (5) is simplerand does not take much time and the number of sensorsrequired will be less when experimenting However all twoalgorithms can be easily developed with the help of the lowcost microcontroller

6 Performance Evaluation and Comparison

Simulations evaluation of the proposed maximum powerpoint tracking techniques under varying insolation showsthat the photovoltaic module output power varies as inFigure 7(b) For the purpose of comparison a modifiedincremental conductance method and PampO method wasemployed to track the MPP and the tracking performanceof the IPSO-based MPPT method approach as shown inFigure 8 It is noticed that themaximumpower reached by thephotovoltaic systemwhile using proposed IPSO-basedMPPTalgorithm is more efficient than the incremental conductance


method For the practical judgment of the effectiveness ofthe maximum power point tracking techniques a varietyinsolation is assumed and the photovoltaic power responseis monitored for proposed method and compared with thework reported in [15] and the result was found to be as shownin Figure 10 It is now clear that the tracking steadfastness andspeed of proposedmaximumpower point tracking techniqueare better than that of incremental conductance also thetracking accuracy of the proposed techniques is superior tothat of the incremental conductance

7 Conclusion

In this paper an IPSO-based MPPT method for trackingMPP either in unshaded or shaded irradiance levels waspresented An IPSO-based MPPT model utilizing a boostconverter topology has also been presented In order tospeed up the searching technique a learning factor andinertia weight were adapted Linear decreases with increas-ing iteration numbers were adopted in this study for theweighting factor of the PSO formulas The physical meaningof this modified weighting formula is that greater step sizesare used to increase the particle search velocity during theinitial search because the distance to the global optimum isrelatively large This prevents an excessively small step sizefrom making local optimum traps unavoidable It has beendemonstrated that an improved particle swarm optimizationbased MPPT method for tracking MPP is highly robustto variations in the solar insolation The proposed controlscheme is verified using Simulink models The simulationresults indicate that the converter can track the maximumpower point of the photovoltaic system The obtained resultsalso confirmed that the convergence speed of the proposedmethod is high and the structure of the improved MPPTalgorithms is so simpleWith these results the control schemecan be utilized for reliable and high quality photovoltaicsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank the Ministry of HigherEducation MOHE Malaysia for the financial support andUniversiti Teknologi Malaysia UTM JB for providing thefacilities to conduct the research

References

[1] Y Zou Y Yu Y Zhang and J Lu ldquoMPPT control for PVgeneration system based on an improved IncCond algorithmrdquoProcedia Engineering vol 29 pp 105ndash109 2012

[2] P Bhatnagar and R K Nema ldquoMaximum power point trackingcontrol techniques state-of-the-art in photovoltaic applica-tionsrdquo Renewable and Sustainable Energy Reviews vol 23 pp224ndash241 2013

[3] M Abdulkadir A S Samosir and A H M Yatim ldquoModellingand simulation of maximum power point tracking of photo-voltaic system in Simulink modelrdquo in Proceedings of the IEEEInternational Conference on Power and Energy (PECon rsquo12) pp325ndash330 December 2012

[4] M A Eltawil and Z Zhao ldquoMPPT techniques for photovoltaicapplicationsrdquo Renewable and Sustainable Energy Reviews vol25 pp 793ndash813 2013

[5] H-T Yau C-J Lin and Q-C Liang ldquoPSO based PI controllerdesign for a solar charger systemrdquoThe Scientific World Journalvol 2013 Article ID 815280 13 pages 2013

[6] K-H Chao L-Y Chang and H-C Liu ldquoMaximum powerpoint tracking method based on modified particle swarmoptimization for photovoltaic systemsrdquo International Journal ofPhotoenergy vol 2013 Article ID 583163 6 pages 2013

[7] K-H Chao and Y-H Lee ldquoA maximum power point trackerwith automatic step size tuning scheme for photovoltaic sys-temsrdquo International Journal of Photoenergy vol 2012 Article ID176341 10 pages 2012

[8] K-H Tang K-H Chao Y-W Chao and J-P Chen ldquoDesignand implementation of a simulator for photovoltaic modulesrdquoInternational Journal of Photoenergy vol 2012 Article ID368931 6 pages 2012

[9] K Ding X Bian H Liu and T Peng ldquoA MATLAB-simulink-based PV module model and its application under conditionsof nonuniform irradiancerdquo IEEE Transactions on Energy Con-version vol 27 no 4 pp 864ndash872 2012

[10] K Ishaque Z Salam A Shamsudin and M Amjad ldquoA directcontrol based maximum power point tracking method forphotovoltaic system under partial shading conditions usingparticle swarmoptimization algorithmrdquoApplied Energy vol 99pp 414ndash422 2012

[11] I Houssamo F Locment and M Sechilariu ldquoMaximumpower tracking for photovoltaic power system developmentand experimental comparison of two algorithmsrdquo RenewableEnergy vol 35 no 10 pp 2381ndash2387 2010

[12] X Chen and Y Li ldquoA modified PSO structure resulting inhigh exploration ability with convergence guaranteedrdquo IEEETransactions on Systems Man and Cybernetics Part B vol 37no 5 pp 1271ndash1289 2007

[13] K Ishaque Z SalamM Amjad and S Mekhilef ldquoAn improvedparticle swarm optimization (PSO)-based MPPT for PV withreduced steady-state oscillationrdquo IEEE Transactions on PowerElectronics vol 27 no 8 pp 3627ndash3638 2012

[14] Y-H Liu S-C Huang J-W Huang and W-C Liang ldquoAparticle swarm optimization-based maximum power pointtracking algorithm for PV systems operating under partiallyshaded conditionsrdquo IEEE Transactions on Energy Conversionvol 27 no 4 pp 1027ndash1035 2012

[15] MAbdulkadir A S Samosir AHM Yatim and S T Yusuf ldquoAnew approach ofmodelling simulation ofmppt forphotovoltaicsystem in simulink modelrdquo ARPN Journal of Engineering andApplied Sciences vol 8 no 7 pp 488ndash494 2013

[16] M Abdulkadir A S Samosir and A H M Yatim ldquoModelingand simulation of a solar photovoltaic system its dynamics andtransient characteristics in LABVIEWrdquo International Journal ofPower Electronics and Drive System vol 3 no 2 pp 185ndash1922013

[17] R W Erickson and D Maksimovic Fundamentals of PowerElectronics Springer 2001

[18] H Heydari-doostabad R Keypour M R Khalghani and MH Khooban ldquoA new approach in MPPT for photovoltaic array


based on extremum seeking control under uniform and non-uniform irradiancesrdquo Solar Energy vol 94 pp 28ndash36 2013

[19] M A Abdullah A H M Yatim and C W Tan ldquoA study ofmaximum power point tracking algorithms for wind energysystemrdquo in Proceedings of the IEEE 1st Conference on CleanEnergy and Technology (CET rsquo11) pp 321ndash326 June 2011

[20] C-M Hong T-C Ou and K-H Lu ldquoDevelopment of intelli-gentMPPT (maximumpower point tracking) control for a grid-connected hybrid power generation systemrdquo Energy vol 50 no1 pp 270ndash279 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


conductance techniques overcome these shortfalls of Perturband Observe techniques but need relatively elaborate detec-tion devices and the choice of the step and threshold is alsodistressing [10]

Recently numerous researchers have presented intelli-gent MPPT methods [5ndash11] for photovoltaic module arraysboth to track MPPs accurately and to improve the dynamicand steady-state tracking performanceHowever thesemeth-ods are applicable only to MPPT in photovoltaic 119888 modulearrays without shading Nevertheless the appearance ofmultipeak output curves because of partial module shadingin photovoltaic module arrays is common Therefore thedevelopment of an algorithm for accurately tracking the trueMPPs of complex and nonlinear output curves is crucialReference [12] presented a MPP tracker based on particleswarm optimization (PSO) for photovoltaic module arraysAlthough this tracker was capable of tracking global MPPsof multipeak characteristic curves because fixed values wereadopted for weighing within the algorithm the tracking per-formance lacked robustness causing low success rates whentracking global MPPs Even though the MPPs were trackedsuccessfully the dynamic response speed was low Thereforethis study used PSO and added improvements preventingit from being trapped in local MPPs (ie searching onlylocal MPPs) and enabling it to track global MPPs quicklyand consistently on the multipeak characteristic curves ofphotovoltaic module arrays

An alternative approach is to employ evolutionary algo-rithm (EA) techniques Due to its ability to handle nonlinearobjective functions [13] EA is envisaged to be very effective todeal withMPPTproblem Among the EA techniques particleswarm optimization (PSO) is highly potential due to itssimple structure easy implementation and fast computationcapability [13] Since PSO is based on search optimization inprinciple it should be able to locate theMPP for any type ofP-V curve regardless of environmental variations It can be usedto track theMPP of PV system as the search space of the PSOis reduced and hence the time required for convergence canbe greatly decreased

Interestingly one important feature of the PSO which isignored by researchers [5 6 13 14] is the searching speedthrough adaptive learning factors and inertia weight Lineardecreases in line with increasing iteration numbers wereadopted in this study for the weighting of the PSO formulasThe physical meaning of this modified weighting formulais that greater step sizes are used to increase the particlesearch velocity during the initial search because the distanceto the global optimum is relatively large This prevents anexcessively small step size from making local optimum trapsunavoidable

However 119908 decreases gradually as the number of iter-ations increases As the particles approach the MPP thisdecrease in 119908 causes the steps in the particle movementsto diminish enabling the particles to track the MPP moreaccurately In PSO equation the first term 119908(119905)V

119894(119905) is

exploited tomaintain the same direction inwhich the particlewas moving pristinely thereby controlling the convergingdemeanor of the particle swarm optimization In order toexpedite converging the inertia weight will be culled such

that the effect of V119894(119905) of the algorithm diminishes during

the operation Therefore the value of 119908 decrementing withtime is desirable To get refined solutions a very popularoption is to set the inertia weight initially to a bigger valuefor better exploration and then reduce it gradually Likewisethe cognitive and social parameter can also be modified asit affects the search ability of PSO Therefore power loss asa result of the oscillation is eradicated and the efficiency ofthe system increasesThe theoretical analysis and simulationresults presented illustrate the good performances of theproposed control schemes

2 System Overview

Photovoltaic system models have long time been an originfor the description of photovoltaic nature for researchersand professionals alike The utmost ordinary model usedto foresee energy generation in photovoltaic cell model isthe single diode circuit [3 15] An ideal photovoltaic cell iscomprised of a single diode connected in parallel with a lightcurrent source as depicted in Figure 1 A complete PV systemsimulation should fulfill the following criteria (a) it shouldbe simple and fast but able to correctively predict the I-Vand P-V characteristic curves including special conditionssuch as partial shading and (b) it should be an overall toolwhich can evolve and ratify a photovoltaic system design all-encompassing the power converter and the MPPT control asshown in Figure 2 [3 15 16]

3 Basic of Incremental Conductance and PSO

In this work the performance of the proposed CS will beevaluated in comparison to Perturb and Observation (PampO)and Particle Swarm Optimization (PSO) MPPT To facilitatediscussion that shall follow brief overviews of both methodsare presented here

31 Incremental Conductance (IC) The idea behind incre-mental conductance is to increasingly contrast the ratioof the derivative of conductance with the instantaneousconductance [1 17] It is derived from the fact that at MPPthe derivative of power with respect to voltage (119889119875119889119881) is infact zero that is

120597119875PV120597119881PV=

120597 (119881PV lowast 119868PV)

120597119881PV= 119881PV lowast

120597119868PV120597119881PV+ 119868PV = 0 (1)

where the change in photovoltaic current is 120597119868PV the changein photovoltaic voltage is 120597119881PV and 120597119875PV is the change inphotovoltaic power respectively

Equation (1) can be reconstructed as follows

120597119868PV120597119881PV= minus

119868PV119881PVasymp

Δ119868

Δ119881

(2)

where photovoltaic current and voltage Δ119868 and Δ119881 are theincrements respectively


PV module

IPV

VPV


IPSO-based MPPT

Load

PWM

IPV

VPV

+

minus





120597119875PV120597119881PV= 0 if

119868PV119881PV= minus

120597119868PV120597119881PV at the MPP

120597119875PV120597119881PVlt 0 if



(3)





119909119905+1

119894= 119909119905

119894+ V119905+1119894 (4)




119905

119894) + 11988821199032sdot (119892best minus 119909

119905

119894)

119894 = 1 2 119873

(5)


xtminus1i

ti

xti

t+1i

xt+1i

Pbest i

Gbest




















119908 (119905) = 119908max minus119905

119905max(119908max minus 119908min) (6)







IPSOinitialization



Measure and


Calculate the power




Update

Update

Next particle




Shadingpattern

changed

Yes

No

No

No

No

No

YesYes

Yes

Yes

Start

VPV(i)IPV(i)


i = i + 1

i = 1

t = t + 1

Pbest i

gbest

gbest



1198881 (119905) = 1198881max minus

119905

119905max(1198881max minus 1198881min) (7)

1198882 (119905) = 1198882max minus

119905

119905max(1198882max minus 1198882min) (8)





1003816100381610038161003816

119875PV oldge Δ119875 () (9)




0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

7

8

Voltage (V)

Curr

ent (

A)


(a)

0 2 4 6 8 10 12 14 16 18 20 220

10

20

30

40

50

60

70

80

90

100

110

Voltage (V)Po

wer

(W)


Uniform irradiance

Partial shading

global MPP

local MPP

MPP

(b)








119904) 36






0 02 04 06 08 1 12 14 16 18 2085

09

095

1

105

Time (s) times106

Chan

ge in

irra

dian

ce (W

m2)

(a)

50

60

70

80

90

100

110

Pow

er (W

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)


5

52

54

56

58

6

62

64

66

68

7

Curr

ent (

A)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(a)

10

11

12

13

14

15

16

17

18

Volta

ge (V

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)






0 01 02 03 04 05 060

10

20

30

40

50

60

70

80

90

100

110

Time (s)

Pow

er (w

)



003 0034 0038 0042 0046 00580

82

84

86

88

90

92

94

96

98

100

102

Time (s)

Pow

er (w

)

034 0342 0344 0346 0348 03598

985

99

995

100

1005

101

1015

102

Time (s)

Pow

er (w

)(a)

(b) (c)

Enlarge portion A

Enlarge portion B

(A) (B)








0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

Time (s)

5

10

15

20

25

30

Tem

pera

ture

(∘C)

Irradiance

Temperature

Irra

dian

ce (W

m2)





0 20 40 60 80 100 120 1400

20

40

60

80

100

120

Time (s)

Pow

er (W

)Modified ICPSO








7 Conclusion




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


PV module

IPV

VPV


IPSO-based MPPT

Load

PWM

IPV

VPV

+

minus





120597119875PV120597119881PV= 0 if

119868PV119881PV= minus

120597119868PV120597119881PV at the MPP

120597119875PV120597119881PVlt 0 if



(3)





119909119905+1

119894= 119909119905

119894+ V119905+1119894 (4)




119905

119894) + 11988821199032sdot (119892best minus 119909

119905

119894)

119894 = 1 2 119873

(5)


xtminus1i

ti

xti

t+1i

xt+1i

Pbest i

Gbest




















119908 (119905) = 119908max minus119905

119905max(119908max minus 119908min) (6)







IPSOinitialization



Measure and


Calculate the power




Update

Update

Next particle




Shadingpattern

changed

Yes

No

No

No

No

No

YesYes

Yes

Yes

Start

VPV(i)IPV(i)


i = i + 1

i = 1

t = t + 1

Pbest i

gbest

gbest



1198881 (119905) = 1198881max minus

119905

119905max(1198881max minus 1198881min) (7)

1198882 (119905) = 1198882max minus

119905

119905max(1198882max minus 1198882min) (8)





1003816100381610038161003816

119875PV oldge Δ119875 () (9)




0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

7

8

Voltage (V)

Curr

ent (

A)


(a)

0 2 4 6 8 10 12 14 16 18 20 220

10

20

30

40

50

60

70

80

90

100

110

Voltage (V)Po

wer

(W)


Uniform irradiance

Partial shading

global MPP

local MPP

MPP

(b)








119904) 36






0 02 04 06 08 1 12 14 16 18 2085

09

095

1

105

Time (s) times106

Chan

ge in

irra

dian

ce (W

m2)

(a)

50

60

70

80

90

100

110

Pow

er (W

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)


5

52

54

56

58

6

62

64

66

68

7

Curr

ent (

A)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(a)

10

11

12

13

14

15

16

17

18

Volta

ge (V

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)






0 01 02 03 04 05 060

10

20

30

40

50

60

70

80

90

100

110

Time (s)

Pow

er (w

)



003 0034 0038 0042 0046 00580

82

84

86

88

90

92

94

96

98

100

102

Time (s)

Pow

er (w

)

034 0342 0344 0346 0348 03598

985

99

995

100

1005

101

1015

102

Time (s)

Pow

er (w

)(a)

(b) (c)

Enlarge portion A

Enlarge portion B

(A) (B)








0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

Time (s)

5

10

15

20

25

30

Tem

pera

ture

(∘C)

Irradiance

Temperature

Irra

dian

ce (W

m2)





0 20 40 60 80 100 120 1400

20

40

60

80

100

120

Time (s)

Pow

er (W

)Modified ICPSO








7 Conclusion




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


xtminus1i

ti

xti

t+1i

xt+1i

Pbest i

Gbest




















119908 (119905) = 119908max minus119905

119905max(119908max minus 119908min) (6)







IPSOinitialization



Measure and


Calculate the power




Update

Update

Next particle




Shadingpattern

changed

Yes

No

No

No

No

No

YesYes

Yes

Yes

Start

VPV(i)IPV(i)


i = i + 1

i = 1

t = t + 1

Pbest i

gbest

gbest



1198881 (119905) = 1198881max minus

119905

119905max(1198881max minus 1198881min) (7)

1198882 (119905) = 1198882max minus

119905

119905max(1198882max minus 1198882min) (8)





1003816100381610038161003816

119875PV oldge Δ119875 () (9)




0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

7

8

Voltage (V)

Curr

ent (

A)


(a)

0 2 4 6 8 10 12 14 16 18 20 220

10

20

30

40

50

60

70

80

90

100

110

Voltage (V)Po

wer

(W)


Uniform irradiance

Partial shading

global MPP

local MPP

MPP

(b)








119904) 36






0 02 04 06 08 1 12 14 16 18 2085

09

095

1

105

Time (s) times106

Chan

ge in

irra

dian

ce (W

m2)

(a)

50

60

70

80

90

100

110

Pow

er (W

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)


5

52

54

56

58

6

62

64

66

68

7

Curr

ent (

A)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(a)

10

11

12

13

14

15

16

17

18

Volta

ge (V

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)






0 01 02 03 04 05 060

10

20

30

40

50

60

70

80

90

100

110

Time (s)

Pow

er (w

)



003 0034 0038 0042 0046 00580

82

84

86

88

90

92

94

96

98

100

102

Time (s)

Pow

er (w

)

034 0342 0344 0346 0348 03598

985

99

995

100

1005

101

1015

102

Time (s)

Pow

er (w

)(a)

(b) (c)

Enlarge portion A

Enlarge portion B

(A) (B)








0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

Time (s)

5

10

15

20

25

30

Tem

pera

ture

(∘C)

Irradiance

Temperature

Irra

dian

ce (W

m2)





0 20 40 60 80 100 120 1400

20

40

60

80

100

120

Time (s)

Pow

er (W

)Modified ICPSO








7 Conclusion




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


IPSOinitialization



Measure and


Calculate the power




Update

Update

Next particle




Shadingpattern

changed

Yes

No

No

No

No

No

YesYes

Yes

Yes

Start

VPV(i)IPV(i)


i = i + 1

i = 1

t = t + 1

Pbest i

gbest

gbest



1198881 (119905) = 1198881max minus

119905

119905max(1198881max minus 1198881min) (7)

1198882 (119905) = 1198882max minus

119905

119905max(1198882max minus 1198882min) (8)





1003816100381610038161003816

119875PV oldge Δ119875 () (9)




0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

7

8

Voltage (V)

Curr

ent (

A)


(a)

0 2 4 6 8 10 12 14 16 18 20 220

10

20

30

40

50

60

70

80

90

100

110

Voltage (V)Po

wer

(W)


Uniform irradiance

Partial shading

global MPP

local MPP

MPP

(b)








119904) 36






0 02 04 06 08 1 12 14 16 18 2085

09

095

1

105

Time (s) times106

Chan

ge in

irra

dian

ce (W

m2)

(a)

50

60

70

80

90

100

110

Pow

er (W

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)


5

52

54

56

58

6

62

64

66

68

7

Curr

ent (

A)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(a)

10

11

12

13

14

15

16

17

18

Volta

ge (V

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)






0 01 02 03 04 05 060

10

20

30

40

50

60

70

80

90

100

110

Time (s)

Pow

er (w

)



003 0034 0038 0042 0046 00580

82

84

86

88

90

92

94

96

98

100

102

Time (s)

Pow

er (w

)

034 0342 0344 0346 0348 03598

985

99

995

100

1005

101

1015

102

Time (s)

Pow

er (w

)(a)

(b) (c)

Enlarge portion A

Enlarge portion B

(A) (B)








0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

Time (s)

5

10

15

20

25

30

Tem

pera

ture

(∘C)

Irradiance

Temperature

Irra

dian

ce (W

m2)





0 20 40 60 80 100 120 1400

20

40

60

80

100

120

Time (s)

Pow

er (W

)Modified ICPSO








7 Conclusion




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 2 4 6 8 10 12 14 16 18 20 220

1

2

3

4

5

6

7

8

Voltage (V)

Curr

ent (

A)


(a)

0 2 4 6 8 10 12 14 16 18 20 220

10

20

30

40

50

60

70

80

90

100

110

Voltage (V)Po

wer

(W)


Uniform irradiance

Partial shading

global MPP

local MPP

MPP

(b)








119904) 36






0 02 04 06 08 1 12 14 16 18 2085

09

095

1

105

Time (s) times106

Chan

ge in

irra

dian

ce (W

m2)

(a)

50

60

70

80

90

100

110

Pow

er (W

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)


5

52

54

56

58

6

62

64

66

68

7

Curr

ent (

A)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(a)

10

11

12

13

14

15

16

17

18

Volta

ge (V

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)






0 01 02 03 04 05 060

10

20

30

40

50

60

70

80

90

100

110

Time (s)

Pow

er (w

)



003 0034 0038 0042 0046 00580

82

84

86

88

90

92

94

96

98

100

102

Time (s)

Pow

er (w

)

034 0342 0344 0346 0348 03598

985

99

995

100

1005

101

1015

102

Time (s)

Pow

er (w

)(a)

(b) (c)

Enlarge portion A

Enlarge portion B

(A) (B)








0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

Time (s)

5

10

15

20

25

30

Tem

pera

ture

(∘C)

Irradiance

Temperature

Irra

dian

ce (W

m2)





0 20 40 60 80 100 120 1400

20

40

60

80

100

120

Time (s)

Pow

er (W

)Modified ICPSO








7 Conclusion




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 02 04 06 08 1 12 14 16 18 2085

09

095

1

105

Time (s) times106

Chan

ge in

irra

dian

ce (W

m2)

(a)

50

60

70

80

90

100

110

Pow

er (W

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)


5

52

54

56

58

6

62

64

66

68

7

Curr

ent (

A)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(a)

10

11

12

13

14

15

16

17

18

Volta

ge (V

)

02 04 06 08 1 12 14 16 18 2Time (s) times106

(b)






0 01 02 03 04 05 060

10

20

30

40

50

60

70

80

90

100

110

Time (s)

Pow

er (w

)



003 0034 0038 0042 0046 00580

82

84

86

88

90

92

94

96

98

100

102

Time (s)

Pow

er (w

)

034 0342 0344 0346 0348 03598

985

99

995

100

1005

101

1015

102

Time (s)

Pow

er (w

)(a)

(b) (c)

Enlarge portion A

Enlarge portion B

(A) (B)








0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

Time (s)

5

10

15

20

25

30

Tem

pera

ture

(∘C)

Irradiance

Temperature

Irra

dian

ce (W

m2)





0 20 40 60 80 100 120 1400

20

40

60

80

100

120

Time (s)

Pow

er (W

)Modified ICPSO








7 Conclusion




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 01 02 03 04 05 060

10

20

30

40

50

60

70

80

90

100

110

Time (s)

Pow

er (w

)



003 0034 0038 0042 0046 00580

82

84

86

88

90

92

94

96

98

100

102

Time (s)

Pow

er (w

)

034 0342 0344 0346 0348 03598

985

99

995

100

1005

101

1015

102

Time (s)

Pow

er (w

)(a)

(b) (c)

Enlarge portion A

Enlarge portion B

(A) (B)








0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

Time (s)

5

10

15

20

25

30

Tem

pera

ture

(∘C)

Irradiance

Temperature

Irra

dian

ce (W

m2)





0 20 40 60 80 100 120 1400

20

40

60

80

100

120

Time (s)

Pow

er (W

)Modified ICPSO








7 Conclusion




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 20 40 60 80 100 120 140

200

400

600

800

1000

1200

Time (s)

5

10

15

20

25

30

Tem

pera

ture

(∘C)

Irradiance

Temperature

Irra

dian

ce (W

m2)





0 20 40 60 80 100 120 1400

20

40

60

80

100

120

Time (s)

Pow

er (W

)Modified ICPSO








7 Conclusion




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



7 Conclusion




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of














Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

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Research Article An Improved PSO-Based MPPT Control ...

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