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  • Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2013, Article ID 583163, 6 pageshttp://dx.doi.org/10.1155/2013/583163

    Research ArticleMaximum Power Point Tracking Method Based on ModifiedParticle Swarm Optimization for Photovoltaic Systems

    Kuei-Hsiang Chao, Long-Yi Chang, and Hsueh-Chien Liu

    Department of Electrical Engineering, National Chin-Yi University of Technology, No. 57, Section 2, Zhongshan Road,Taiping Distatrict, Taichung 41170, Taiwan

    Correspondence should be addressed to Kuei-Hsiang Chao; chaokh@ncut.edu.tw

    Received 9 June 2013; Accepted 20 September 2013

    Academic Editor: Adel M. Sharaf

    Copyright 2013 Kuei-Hsiang Chao et al. 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 study investigated the output characteristics of photovoltaic module arrays with partial module shading. Accordingly, wepresented a maximum power point tracking (MPPT) method that can effectively track the global optimum of multipeak curves.This method was based on particle swarm optimization (PSO).The concept of linear decreases in weighting was added to improvethe tracking performance of the maximum power point tracker. Simulation results were used to verify that this method couldsuccessfully track maximum power points in the output characteristic curves of photovoltaic modules with multipeak values. Theresults also established that the performance of the modified PSO-based MPPT method was superior to that of conventional PSOmethods.

    1. Introduction

    The output power of photovoltaic (PV) systems is heavilyinfluenced by irradiation and temperature. Thus, the outputpower of these systems presents nonlinear changes. Maxi-mum power point tracking (MPPT) must be incorporated tostabilize the output power at maximum power points. Thisresearch topic is critical for photovoltaic power generationsystems.

    The voltage feedback method [1] is the simplest of conve-ntionalMPPTmethods. However, this method requires priortesting of maximum power point (MPP) voltage. In add-ition, MPPs cannot be tracked when the photovoltaic mod-ules deteriorate and cause the MPPs to change unless re-measurement is performed. The framework of the constantvoltage tracking method [2, 3] is simple and does notrequire complex formulas.This method employs the extremesimilarity of MPP voltages under varying amounts of irra-diation, using MPP voltage under standard test conditionsas reference points to set the operation of the photovoltaicmodule arrays at these points. However, when the amount ofirradiation is low or when photovoltaic module temperatureschange, the difference in values between theMPP voltage andthe reference voltage becomes substantial, reducing tracking

    accuracy.Theperturb and observemethod [4] uses periodicalincreases or decreases in voltage to perturb the system. Ifthese perturbations increase the output power, the same trendis used to change (i.e., increase or decrease) voltage thefollowing time. If output power decreases, the reverse trendis used to change voltage. However, this method is unableto track MPPs accurately. In addition, the method osci-llates near the MPP and increases tracking losses, therebyaffecting power generation efficiency. These conventionalmethods only perform MPPT on module arrays with single-peak characteristic curves. When multipeak values appear inthe characteristic curves, thesemethods frequently track localMPPs and miss global MPPs.

    Recently, numerous scholars have presented intelligentMPPT methods [511] for photovoltaic module arrays, bothto track MPPs accurately and to improve the dynamic andsteady-state tracking performance. However, these methodsare applicable only to MPPT in photovoltaic module arrayswithout shading. Nevertheless, the appearance of multi-peak output curves because of partial module shading inphotovoltaic module arrays is common.Therefore, the devel-opment of an algorithm for accurately tracking the trueMPPs of complex and nonlinear output curves is crucial.Reference [12] presented a MPP tracker based on particle

  • 2 International Journal of Photoenergy

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    One module at 30% shadow ratio

    With no shadowTwo modules at 30% shadow ratio

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    VPV (V)

    IPV

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    Figure 1: I-V output characteristic curves in the four-series one-parallel module array with varying numbers of modules and shaderatios of 30%, as simulated by Solar Pro software.

    swarm optimization (PSO) for photovoltaic module arrays.Although this tracker was capable of tracking global MPPsof multipeak characteristic curves because fixed values wereadopted for weighing within the algorithm, the trackingperformance lacked robustness, causing low success rateswhen tracking global MPPs. Even though the MPPs weretracked successfully, the dynamic response speed was low.

    Therefore, this study used PSO and added improvements,preventing it from being trapped in local MPPs (i.e., search-ing only local MPPs) and enabling it to track global MPPsquickly and consistently on the multipeak characteristiccurves of photovoltaic module arrays.

    2. PV Module Array Characteristic Analysis

    Within photovoltaic power generation systems, photovoltaicmodules are typically connected to formmodule arrays usingseries and parallel methods.When certain modules malfunc-tion or are shaded, their electric current flow is impeded andhot spots occur, damaging the photovoltaic modules. Thus,bypass diodes, through which electric current circulates,are generally installed. This enables the other photovoltaicmodules to operate normally. However, when some modulesmalfunction or are shaded, the output voltage and current ofthe module arrays decrease, producing multipeak values inthe P-V and I-V output characteristic curves.

    To find out the output characteristics of series and parallelmodule arrays when some modules are shaded, a four-seriesone-parallel photovoltaic module array consisting of HIP2717 modules produced by Sanyo was investigated. Figures1 and 2 show the I-V and P-V output characteristic curves ofone, two, three, and four modules with 30% shading in thefour-series one-parallel module array, simulated using SolarPro software [13]. The figures show that shading on somemodules within the array causes the emergence of multipeakvalues in the output characteristic curves. In addition, themaximum output power points showed growing declines asthe number of shaded modules increased.

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    One module at 30% shadow ratio

    With no shadowTwo modules at 30% shadow ratio

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    PPV

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    Figure 2: P-V output characteristic curves in the four-series one-parallel module array with varying numbers of modules and shaderatios of 30%, as simulated by Solar Pro software.

    3. Particle Swarm Optimization

    PSO is an optimization theory presented by Kennedy andEberhart in 1995 [14]. The theory is an algorithm that usescollective intelligence; it belongs to a branch of evolutionarycomputation. The two scholars were inspired by the foragingbehavior of birds and applied this phenomenon to resolveproblems related to search and optimization [15, 16]. Eachbird flying in a space is called a particle. All particles movingin the space have fitness values mapped by an objective func-tion and individual velocities, which are used to determinethe direction and distance of their movement. Two memoryvalues influence themovement of the particles:best andbest.Each particle stores the best position it is currently seekingin an individual best memory position (best). Furthermore,memory intercommunication is present among the particles;the particle swarm compares individual positions to locatethe best position and stores this as the swarm best position(best). The particle swarm uses this method to revise thedirection and velocity of its movement continuously, therebyrapidly converging toward a global optimum.

    The PSO calculation process is as follows.

    (1) Set the number of particles, the maximum number ofiterations, the weight, and the learning factors.

    (2) Initialize the particle swarm and randomly assignpositions and velocities for each particle.

    (3) Substitute the initial positions into the objective fun-ction to assess the fitness values for each particle.

    (4) Compare the fitness values and the individual bestmemory positions (best) of each particle to selectbetter positions and update best.

    (5) Compare best and the swarm best memory valuebest. If best is superior to best, update best.

  • International Journal of Photoenergy 3

    Photovoltaic array

    MOSFETdriver

    Modified PSO-based MPPT

    controller

    DC/ACinverter Load

    PWM control signal

    Cin

    R1

    R2

    Cout

    V

    L

    D

    PV IPV

    Figure 3: System architecture for modified PSO-based MPPT control.

    (6) Use the core PSO formulas to update particle veloc-ities and positions. These formulas are shown asfollows:

    +1

    =

    + 1 rand1 () (best

    )

    + 2 rand2 () (best

    ) ,

    (1)

    +1

    = +1

    +

    .(2)

    In (1) and (2), and

    are the velocity and position ofparticle at iteration j, respectively. Variables rand1() andrand2() are random number generators that generate realnumbers between 0 and 1 randomly; these numbers are usedto strengthen the variability of the particle swarm. isthe weight; 1 and 2 are the learning factors; best is theindividual optimum of particle ; and best is the swarm orglobal optimum.

    (7) Stop tracking if the stop conditions are met. Other-wise, rerun Steps 4 through 6.The stop conditions areeither locating the global optimum or reaching themaximum number of iterations.

    The search efficiency and success rate of PSO are deter-mined primarily by the values assigned for the weights andthe learning factors [17]. When the weight is too high, theparticle search might lack accuracy because the movementstep sizes are too large. However, if the weight is low, par-ticle movement becomes slow, and the local optimum trapmight be unavoidable when facing multipeak values. Thus,weighting is typically based on the objective function.

    4. PSO-Based MPPT for PV Systems

    Conventional PSO is fast and accurate when searching forthe output characteristic curves of PV module arrays withsingle peak values. However, when somemodules are shaded,weights in conventional PSO must be readjusted appropri-ately based on various multipeak curve characteristics. If thisis not performed, excessively high or low weights result in

    tracking failure. Thus, conventional PSO-based MPPT mustbe modified when some of the modules in a photovoltaicmodule array are shaded.

    To solve these problems, linear decreases in line withincreasing iteration numbers were adopted in this study forthe weighting of the PSO kernel formulas. The modified wei-ghting formula is as follows:

    = (max min) ( )

    +min, (3)

    wheremax is the maximum weight, min is the minimumweight, is the maximum number of iterations, and is thecurrent iteration number.

    The 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, decreases gradually as the num-ber of iterations increases. Because the particles are nowapproaching the MPP, these decreases in cause the stepsin the particle movements to shrink, enabling the particles totrack the MPP more accurately.

    In addition, the output curve of the photovoltaic modulearray appears only in the first quadrant. Therefore, regionswith output power below zero cannot be optimum positions,and the lower limit for particle tracking is set to zero; thatis, particles automatically return to zero when tracking regi-ons with values of less than zero. This greatly reduces thetime wasted by particles tracking in erroneous regions. Thepredicate for these conditions is as shown in (4):

    best = {best , best > 0,

    0, best 0.(4)

    The bestvalue obtained in (4) is the solution of (2):

    best = +1

    .(5)

    Figure 3 shows the proposed system architecture formodified PSO-based MPPT control. This system contains

  • 4 International Journal of Photoenergy

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    Conventional PSO

    Gbe

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    (b)

    Figure 4: Simulation results for a four-series one-parallel modulearray with one module shaded 30% and one module shaded 55%and(a) P-V characteristic curve. (b) tracking comparison resultsbetween the conventional PSO (W = 0.4) and modified PSO-basedMPPT methods.

    two major subsystems: (1) a boost converter and (2) a MPPTcontroller. The MPPT controller is used to control the dutycycle of the boost converter [18], allowing the photovoltaicmodule array to output maximum power despite partialshading of some modules.

    5. Simulation Results

    MATLAB software [19] was used to simulate and comparethe application of the conventional and modified PSO-basedMPPT control methods to track photovoltaic module arraysin four shading situations.The first test situation involved onemodule with 30% shading and one module with 55% shadingin a four-series one-parallel module array. Figure 4(a) showsthis P-V characteristic curve, and Figure 4(b) shows theresults of a comparison between the conventional (with aweight of 0.4) and modified PSO-based MPPTmethods.Thefigures indicate that the P-V characteristic curve exhibitedthree peak values when the two modules in the sameseries had differing amounts of shade. In this situation, theconventional PSO-based MPPT method could track onlylocal maxima, whereas the modified PSO method couldtrack global MPPs. The modified PSO method also had afaster response speed than the conventional PSO method. Inthe second test situation, one module was shaded 25% andthe other (in another series) was shaded 30% in the four-series one-parallel module array. Figure 5(a) shows the P-V characteristic curve, and Figure 5(b) shows the results ofa comparison between the conventional (with a weight of0.4) and modified PSO-based MPPT methods. Under theseworking conditions, the P-V characteristic curve had twopeaks. The MPPT results in Figure 5(b) indicate that theconventional PSO method tracked the local optimum for

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    Gbe

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    Figure 5: Simulation results for a four-series one-parallel modulearray with one module shaded 25% and one module shaded 30%and (a) P-V characteristic curve. (b) tracking comparison resultsbetween the conventional PSO (W = 0.4) and modified PSO-basedMPPT methods.

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