pysia

ngo

a r t i c l e i n f o

Article history:Received 3 December 2012Accepted 29 March 2013Available online 13 May 2013

Keywords:Genetic algorithm

tings, be it urban or rural [13]. Due to the many factors and benets,

nance costs, due to the fact that it does not rely on a minimal numberof moving parts. Furthermore, this technology heralds a clean andenvironmentally-friendly energy source. Another salient feature ofthe PV technology is its modularity, where instead of installing awhole new system whenever required; a current system can be up-graded accordingly within a short period of time [817]. Its benets

important renewable energy sources. Due to its importance, largee countries. How-is technoloinsured, antem shall

formed prior to its installation [2224]. The modeling ofmodule represents the important task in the whole PVpre-installation procedure.

Modeling of the PV cell is a mathematical description of the PVoutput currentvoltage (IV), and powervoltage (PV) relations. Ageneral equivalent circuit (model) that represents the operation ofthe PV cell is illustrated in Fig. 1. This model is called a single-diodemodel. A more detailed model is a two-diode model, which usestwo diodes to express the PN junction effect, and this model isshown in Fig. 2.

Corresponding author. Mobile: 60 12 239 4312; fax: +60 37 956 1378.E-mail addresses: mahmoud_kafa@yahoo.com, mahmoud@um.edu.my

Energy Conversion and Management 73 (2013) 1025

Contents lists available at

n

se(M.S. Ismail).both the public and private sectors are showing a tremendousamount of interest in the potential and capability of energy genera-tion from these devices [47]. One of the major advantages of PVtechnology is its long lifecycle time, with low operation and mainte-

PV power systems have been installed in multiplever, due to the high initial capital needed for thoptimal utilization of the solar energy should becise studies and simulation of the PV power sys0196-8904/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enconman.2013.03.033gy, thed pre-

be per-the PVsystem1. Introduction

Photovoltaic systems are one of the most popular renewable en-ergy sources in todays world. There are ubiquitous in numerous set-

and exibility makes it ideal for space and earth applications [16,18],and it is expected to grow in the near future, from small PV stand-alone site applications, to large PV grid connected systems [1921].

As previously mentioned, a PV power system is one of the moreSolar energyPV modelingRenewable energyPartial shadinga b s t r a c t

This paper details an improved modeling technique for a photovoltaic (PV) module; utilizing the optimi-zation ability of a genetic algorithm, with different parameters of the PV module being computed via thisapproach. The accurate modeling of any PV module is incumbent upon the values of these parameters, asit is imperative in the context of any further studies concerning different PV applications. Simulation,optimization and the design of the hybrid systems that include PV are examples of these applications.The global optimization of the parameters and the applicability for the entire range of the solar radiationand a wide range of temperatures are achievable via this approach. The Manufacturers Data Sheet infor-mation is used as a basis for the purpose of parameter optimization, with an average absolute error t-ness function formulated; and a numerical iterative method used to solve the voltage-current relation ofthe PV module. The results of single-diode and two-diode models are evaluated in order to ascertainwhich of them are more accurate. Other cases are also analyzed in this paper for the purpose of compar-ison. The MatlabSimulink environment is used to simulate the operation of the PV module, dependingon the extracted parameters. The results of the simulation are compared with the Data Sheet information,which is obtained via experimentation in order to validate the reliability of the approach. Three types ofPV modules, using different technologies, are tested for the purpose of this validation, and the resultsconrm the accuracy and reliability of the approach developed in this study. The effectiveness of themodel developed by this approach to predict the performance of the PV system under partial shadingconditions was also validated.

2013 Elsevier Ltd. All rights reserved.Department of Mechanical Engineering, Syiah Kuala University, Banda Aceh 23111, IndonesiaCharacterization of PV panel and global oparameters using genetic algorithm

M.S. Ismail a,, M. Moghavvemi a,b, T.M.I. Mahlia c,daDepartment of Electrical Engineering, University of Malaya, 50603 Kuala Lumpur, Malab Faculty of Electrical and Computer Engineering, University of Tehran, Tehran, IrancDepartment of Mechanical Engineering, Universiti Tenaga Nasional, 43000 Kajang, Selad

Energy Conversio

journal homepage: www.eltimization of its model

r, Malaysia

SciVerse ScienceDirect

and Management

vier .com/locate /enconman

Nomenclatures

a ideality factora1 ideality factor of diode 1a2 ideality factor of diode 2DV decision vectorDV1d decision vector-single-diode modelDV2d decision vector-two-diode modelDV1d-m decision vector-modied single-diode modelDV2d-m decision vector-modied two-diode modelErrorave average absolute errorG solar radiation (W/m2)Gj solar radiation (W/m2) at point jGSTC solar radiation (W/m2) at standard test conditionsID1 current of diode 1 (A)ID2 current of diode 2 (A)Ij (curve) current (A) read from curve at point jI current (A) at maximum power point

M.S. Ismail et al. / Energy Conversion anThe PV technology is readily available in the current market.

mp

Imp-STC current (A) at maximum power point at standard testconditions

I0 saturation current (A)I01 saturation current (A) of diode 1I02 saturation current (A) of diode 2Iph photon current (A)IPh-STC photon current at standard test conditionsIPV output PV current (A)Ipvn present value of output PV current (A)Ipvn + 1 next value of output PV current (A)Due to the sheer number of the different types of PV technologyavailable, the precise evaluation of different parameters of theequivalent circuit in real conditions of operation is imperative foran accurate and reliable modeling and simulation of PV systems[19,22,25].

Chouder et al. [19] and Sera et al. [26] used a single-diode mod-el to simulate the operation of a PV module. The authors dependedon the manufacturers data to initially determine the values of boththe series and shunt resistances. Moreover, the ideality factor, sat-uration current and photon current are also needed for this evalu-ation, in accordance to the relations they used. Most of themanufacturers do not provide values for these parameters, so anassumption for each of these parameters or iterative method shall

Fig. 1. Single-diode PV equivalent circuit.

Fig. 2. Two-diode PV equivalent circuit.be made. In the proposed genetic algorithm approach, part of these

ISCSTC short circuit current at standard test conditions (A)IV currentvoltageK Boltzmann constant (=1.38065 1023 J/K)KI current temperature coefcient (A/C)KV voltage temperature coefcient (V/C)Ns number of series cells in one PV panelp number of pointsPV photovoltaicP-V powervoltageQ electron charge (=1.6021765 1019 C)Rp shunt resistance (O)RS series resistance (O)T PN junction temperature (K)Tj ambient temperature at point j (K)TSTC temperature at standard test conditions

(=25 C or 298.15 K)Vj voltage at point j (V)Vmp voltage at maximum power point (V)Vmp-STC voltage at maximum power point (V) at standard test

conditionsVOC-STC voltage at open circuit (V) at standard test conditionsVPV output PV voltage (V)VT thermal voltage (V)VT1 thermal voltage of diode 1VT2 thermal voltage of diode 2

d Management 73 (2013) 1025 11variables and quantities are included in the decision vector of thegenetic algorithm, while others are computed according to differ-ent equations, which will be discussed at a later stage of this paper.

Ishaque et al. [22] used a two-diode model for the purpose ofmodeling a PV cell. This model computes more parameters, whichnecessitates certain assumption in the effort to simplify computa-tions. The iterative method was also used to calculate both the ser-ies and shunt resistances.

Ishaque and Salam [27] used a differential evolution method todetermine the model parameters of the PV modules. The effects oftemperature and irradiance were included, and the values for thedifferent parameters were calculated for each temperature or irra-diance. The global optimization of these parameters tting anyirradiance or temperature is not calculated in the presented ap-proach in this reference. Furthermore, ways to calculate the mod-els parameters when simultaneous change of temperature andirradiance occurs were also not discussed in this reference.

Shahat [28] developed a model for PV in order for it to be usedfor maximum power point identication. In this approach, theauthor depended on the assumed values for the ideality factor,and also on the assumption that the datasheet curve of the PV pa-nel is provided by the manufacturer to graphically calculate theseries resistance. The genetic algorithm used in the approach inthis reference is utilized only to determine the maximum powerpoint.

Zagrouba et al. [29] presented a method to identify the electri-cal parameters of PV solar cells and modules. A single-diode modelwas used in this study. Results produced by the Pasan cell testersoftware were used to validate the values obtained for the PV cellsparameters. This software does not provide values for all parame-ters. Furthermore, the temperature and radiation variations werenot taken into account while using this approach, and as men-tioned earlier; the values of these parameters are inuenced byvariations in temperature and radiation.

from the current population, and these individuals are used as par-ents to generate the children of the next generation [28,37].

n aWeidong et al. [30] used a simplied single-diode model todetermine the parameters of a PV module. The shunt resistancewas neglected in their approach. The graphical relationships be-tween both series resistance and ideality factor with temperaturechanges were also presented. These relations were used for theevaluation of the parameters. For validation purposes, the authorstook into account the maximum power point at certain radiationonly as the temperature changes; and as proven by authors ofRef. [27] , the values of these parameters vary with the variationof the radiation. As previously mentioned, not only the maximumpower point is taken into account in our approach; other points onthe IV curve at different temperatures and radiation levels are ta-ken into account as well.

Villalva et al. [31] suggested and developed an approach to ndthe parameters of a single-diode model of a PV module. An effec-tive method was proposed to t the mathematical IV curve tothe three characterizing points of any PV module (Isc point, Vocpoint and maximum power point). The model was validated bycomparison of simulation results with two practical PV arrays. Inorder to calculate the saturation current, a value for the idealityfactor was assumed, and remains unmodied later in the model.Furthermore, an iterative method was used to calculate both theseries and shunt resistances. The iteration is performed until cer-tain values of the series or shunt resistances render the power gen-erated by PV matches the maximum power at certaintemperatures and radiation. As it is known, the values of theseresistances depend on both temperature and radiation [27], sothe values obtained may not t the model, especially at low valuesof radiation (less than 400W/m2). In the developed approach inthis paper, the ideality factor, series and shunt resistances are partof the decision vector that are to be computed using genetic algo-rithm. Furthermore, different points at different radiation levelsand temperatures were used in calculations, and is not only limitedto the maximum power point at certain radiation or temperatures.

Jervase et al. [32] proposed a technique for improving the accu-racy of the solar cells parameters. The developed approach hingedon the fact that the specied values of these parameters were givenor calculated using one of the known extraction methods at certainconditions. The proposed genetic algorithmwas then used to renethese values. This may be applicable from a physical point of view,but it is inapplicable for PV applications, where other data are usu-ally provided by the manufacturer. Furthermore, the variations oftemperature and radiation were not taken into account in thiscontext.

Almonacid et al. [33] developed an articial neural network ap-proach to generate V-I curves of silicon-crystalline PV modules forany radiation or temperature values. This approach is capable ofpredicting the performance of the PV module, but a mathematicalmodel involving the different parameters is not provided by thisapproach.

The ability of the PV model to predict the performance of the PVsystem under partial shading should also be fullled. Several re-searches have studied the performance of the PV panel under par-tial shading [22,34,35]. The effectiveness of the two diode modeldeveloped in Ref. [22] was also validated under partial shadingconditions. The performance was checked under different shadingpatterns. Shaiek et al. [34] used a single-diode to express the oper-ation of the PV module, and the genetic algorithm was utilized tosearch for the global maximum power point under the shading ef-fect. In this work, the simulations were conducted with two panelsconnected in series, where one of them was assumed to be par-tially shaded. The simulations showed the ability of the geneticalgorithm to realize the global maximum power point. A way to

12 M.S. Ismail et al. / Energy Conversioobtain values of the PV model was not mentioned in this study,which prompted the authors to use typical values for theseparameters.Three main rules are used by genetic algorithm at each step toform the next generation from the present population, and theserules are: selection rules to select the individuals (parents) thatis considered the source for the next generation, crossover rulesthat combine two parents to produce children for the next gener-ation, and mutation rules that randomly apply changes to individ-ual parents to produce children [28].

In this paper, the genetic algorithm was programmed in twoways: MATLAB optimization Toolbox, and developed MATLABcode. This was done for the purpose of comparison.

2.1.1. Genetic algorithm using MATLAB global optimization ToolboxThis method involves a MATLAB code that is developed in order

to form the optimization tness function; the optimization Tool-box utilizes this le to run the genetic algorithm solver. Differentterminologies shall be specied for the purpose of optimization.Before specifying certain values for each of these terminologies,all of them were tested with regards to the accuracy of the resultsand their corresponding computation time. The following MATLABprescribed terminologies are selected in the genetic algorithmToolbox for the purpose of optimization in this paper:

Population type: double vector with populations size = 20. Fitness scaling: rank.The previous works discussed above indicated that the idealityfactor is one of the parameters that require major analysis for esti-mation. According to Ref. [28], a more accurate value for thisparameter can be obtained by curve tting, or by trial and error.This value estimation is inaccurate, due to the fact that it may ta certain IV curve only at certain temperatures or radiation, butis not inclusive of all temperatures and radiation levels.

In this study, the global optimization ability of the genetic algo-rithm was utilized in order to obtain the parameters of the PVmodel. Obtaining values for these parameters that are applicablefor the entire range of the solar radiation and a wide range of tem-peratures forms the purpose of this study. In order to achieve this,different points on the IV curve at different temperatures and dif-ferent radiation levels were used to calculate the optimized errorfunction, and MatlabSimulink was used to build the simulationmodel, depending on the values of the parameters obtained bythe optimization algorithm. The results of the simulation werecompared with real data obtained from the manufacturers data-sheet(s) for validation purposes. Different cases were also studiedin this paper for comparison purposes.

In a nutshell, the approach developed in this study realized theglobal optimization of the parameters of the PV model, with thevariation of temperature and radiation, which affects these valuesthat are being taken into consideration.

2. Materials and methods

2.1. Genetic algorithms

The genetic algorithms are methods used to solve constrainedand unconstrained optimization problems. They have been usedto solve optimization problems in engineering and the sciences[32,36], and are considered global methods for the purpose ofoptimization.

The population of individual solutions is repeatedly modied bygenetic algorithm. Individuals are randomly selected at each step

nd Management 73 (2013) 1025 Selection function: stochastic uniform reproduction. Reproduction: elite count: default (2), crossover fraction:default (0.8).

Mutation function: adaptive feasible. Crossover function: scattered migration. Migration: direction: forward, fraction: default (0.2), interval:default (20).

Algorithm settings: as default. Stopping criteria (defaults): generations: 100.

2.1.2. Genetic algorithm using developed MATLAB codeAs an alternative to the optimization Toolbox, a MATLAB code is

duly developed. This code includes both the genetic algorithm pro-gramming and the programming of the optimization tness func-tion. In this code, the initial population generation is formed byrandomly generating population members (possible solutions).Each possible solution is a code of the decision vector, taking intoaccount the upper and lower constraints. This initial generationevolves through successive iterations, and members of each gener-ation are evaluated in order to calculate the tness average error

function, with the member possessing the least error being se-lected. Fig. 3 details the owchart of the genetic algorithm process.

In this method, and after performing many executions, it wasdiscovered that a population size of 30 is adequate for the purposeof this paper, while the number of generations required to give themost optimal solution is 100. In most cases, the number of requiredgenerations is less than 60. It is also found that 0.9 is an appropri-ate rate for both cross-over and mutation.

2.2. Simulation

After using the genetic algorithm to obtain the optimized valuesfor the different PV model parameters that is needed to constructthe decision vector, MatlabSimulink is the simulation environ-ment that is used to simulate the operation of this PV module.The basic numerical model for the PV module used in the simula-tion is shown in Fig. 4. If a single-diode model is used, then the

f the

M.S. Ismail et al. / Energy Conversion and Management 73 (2013) 1025 13Fig. 3. Flow chart oFig. 4. Numerical modegenetic algorithm.l of the PV module.

contents of the numerical solution box in the gure becomeIph IDI.

Fig. 5 shows the details of a MatlabSimulink model of a PV-equivalent circuit. This block forms part of a whole PV system, andis illustrated in Fig. 6. In this study, the purpose of this system isto calculate the IV and PV characteristics of a typical PV panelfor validation purposes. This simulation model can be consideredpart of a total system, and in addition to the PV panel, this systemmay include a charge regulator, inverter, or any conditioning circuit.

Fig. 5 represents the inside details of the block called PV panelin Fig. 6. The other details of Fig. 6 are for measuring and displayingsignals, where the two external outputs of this block are called(V + PV and V PV), and are actually used for both voltage and cur-rent sensing in the simulation block, while the two additional out-puts appearing in Fig. 5 are internal outputs used for thecalculation of the PV panel current (Ipv = Iph ID1).

Different constants, variables and parameters of the model aredened through the MATLAB code executed in parallel with theSimulink model.

3. Theory and calculations

3.1. Mathematical modeling

Any model that is adopted to characterize the PV panel involvesseveral parameters that need to be calculated, depending on theexperimental data. The number of these parameters differs inaccordance to the adopted model. A single-diode model providesa good compromise between accuracy and simplicity [31], and ithas been used by several authors in previous research works[31,34]. Its effectiveness is proven, especially in the simulation ofPV modules with power converters. A two-diode model that takesinto account different conditions of the operation of a PV panel isalso used by different researchers for the purpose of modeling PVpanels.

The approach to calculate different parameters characterizingthe IV curve is as follows:

IPV IPh ID1 ID2 VPV IPVRsRP

1

Fig. 5. Main block of MatlabSimulink model.

14 M.S. Ismail et al. / Energy Conversion and Management 73 (2013) 1025Fig. 6. The PV system simulated by MatlabSimulink.

on anwhere [31,38]

ID1 Io1 exp VPV IPVRsa1VT1

1

;

ID2 Io2 exp VPIo1V IPVRsa2VT2

1

2

and IPh is the photon current generated by the incident light, and Io2are the reverse saturation currents of diode 1 and diode 2, a1 and a2are the diode ideality constants , VT1 and VT2 are the thermal volt-ages, considering one module and given as follows [31]:

VT1 VT2 Ns KTq 3

where Ns is number of series cells per module, q is the electroncharge (1.6021765 1019 C), K is the Boltzmann constant(1.38065 1023 J/K) and T is the PN junction temperature in Kel-vin (K).

The value of photon current (IPh) depends on the temperatureand solar radiation, and can be found using the following equation[31,39]:

IPh IPhSTC KIT TSTC GGSTC 4

where IPh-STC is the photon current at standard test conditions (solarradiation at standard test conditions (GSTC) = 1000W/m2, tempera-ture at standard test conditions (TSTC) = 25 C), and KI is the currenttemperature coefcient in (A/C), normally provided by the manu-facturer). IPh-STC can be found using the following equation:

IPhSTC ISCSTC RP RSRP 5

where ISC-STC is the short circuit current at standard test conditions(given by manufacture).

The reverse saturation current of any of the diodes (Io) can befound using the following equation [31]:

Io ISCSTC KIT TSTCexp VOCSTCKV TTSTC aVT

1

6

where VOC-STC is the open circuit voltage at standard test conditions(provided by the manufacturer), and KV is the voltage temperaturecoefcient (V/C). This is a modied relation that is used to calculatethe reverse saturation current, while taking into account the depen-dency of this current on temperature variations through short cir-cuit current and the open circuit voltage, and their respectivedependence on temperature. If dependency of open circuit voltageon solar radiation variation is taken into account, Eq. (6) becomes[27]

Io ISCSTC KIT TSTCexp VOCSTCKV TTSTC aV

T lnG=GSTC

aVT

1

7

The PV module output voltage (VPV) and output current (IPV) areinterdependent, so a numerical approach shall be used to calculatethe IV characteristic and the PV characteristic of the module forthe entire range of currents (from 0 to ISC), and for the entire rangeof voltages (from 0 to VOC). As surmised from Eq. (1), no direct solu-tion exists for this equation, since IPV is a function of (VPV and IPV),and VPV is function of (VPV and IPV). This interdependent relationshall appear in the developed algorithm.

3.2. Genetic algorithm implementation to evaluate PV moduleparameters

M.S. Ismail et al. / Energy ConversiAccording to Eqs. (1) and (2), which are used to represent thetwo-diode model, seven parameters are required to calculateeither the current or voltage output from the PV module. Theseparameters are Iph, Io1, Io2, a1, a2, RS, and Rp. Actually, if a1, a2,RS, and Rp are known, then according to Eqs. (4)(6), the valuesof Iph, Io1, and Io2 can be calculated. Therefore, there are two pos-sibilities in determining the values of Iph, Io1, and Io2 using the ap-proach developed in this paper. The rst possibility is byconsidering them to be within the decision vector, as they formthe specications of the PV module, and the genetic algorithmspecies values for each of them alongside other parameters. Theother possibility depends on the fact that their values can be calcu-lated if the ideality factor, the series and the shunt resistances areknown. In this case, values for the other parameters are speciedby the genetic algorithm, and their corresponding values areaccordingly calculated.

For a single-diode model, ve parameters are required to be cal-culated. As previously mentioned, if a1, RS, and Rp are known, thenIph and Io1 can be determined.

Different cases are tested for each model for comparison pur-poses, in order to nd the best case that accurately and preciselymodels the PV panel. Taking into account previous considerations,the decision vector used in the genetic algorithm for a two-diodemodel DV2d is given as:

DV2d a1; a2;Rs;Rp 8While the decision vector for a single-diode model DV1d is given as:

DV1d a1;Rs;Rp 9If the reverse saturation currents and the photon current are consid-ered within the decision vector, the modied decision vector for atwo-diode model DV2d-m is given as:

DV2dm Iph; Io1;Io2;a1; a2;Rs;Rp 10and the modied decision vector for a single-diode model DV1d-m isgiven as:

DV1dm Iph; Io1; a1;Rs;Rp 11The objective function is the average of absolute errors between theactual current (measured or from manufacturer datasheet) and thecalculated current. This error is calculated at different values ofvoltage, solar radiation and temperature. So

Errorave Xpj1

absIjcurve IjVj;Gj; Tj;DV=p 12

where p is the number of points taken into account, Ij(curve) is thecurrent measured or read from the manufacturer datasheet, Ij(Vj, -Gj, Tj, DV) is the current calculated at the voltage Vj, the solar radia-tion Gj, the temperature Tj, and the corresponding decision vectorDV values specied by the genetic algorithm.

To calculate the PV current Ij(Vj, Gj, Tj, DV), Eq. (1) or Eq. (2) shallbe used in accordance to the model used in the analysis. Theseequations do not have a direct solution, due to the fact that thePV current is a function of PV voltage and current, IPv = f(Ipv, Vpv).Instead, numerical methods should be used to solve any of thesetwo equations, with the NewtonRaphson method being chosenpreferred. The PV current Ipv that satises this equation at certainvoltage Vpv and certain values for other variables and constantscan be calculated by numerically solving the equation

hIpv ;Vpv Ipv f Ipv ;Vpv 0 13So, by NewtonRaphson

Ipvn1 Ipvn hIpv ;Vpv

0BB@

1CCA 14

d Management 73 (2013) 1025 15dhIpv ;VpvdIpv atIpvIpvn

where Ipvn is the present value, and Ipvn1 is the next value. The PVcurrent can be iteratively determined, and the number of iterationsis determined in such a way that the absolute error between thepresent calculated value and the previous one is less than a certainspecied tolerance.

In the following two subsections, a MATLAB code is developedto evaluate the average error tness function. This MATLAB codeis a function called that will be called by the optimization Toolboxwhenever the genetic algorithm Toolbox libraries is being used, orif it is included in the genetic algorithm developed code. In this

Table 1Specications of the analyzed three types of PV modules.

Parameter PV Type

Mono-crystalline Sanyo HIT 215 Poly-crystalline Kyocera KC200GT Thin-lm shell solar ST 40

Datasheet Simulation Datasheet Simulation Datasheet Simulation

Isc_stc (A) 5.61 5.61 8.21 8.209 2.68 2.68Voc_stc (V) 51.6 51.6 32.9 32.9 23.3 23.3Imp (A) 5.13 5.131 7.61 7.61 2.36 2.36Vmp (V) 42 42 26.3 26.3 16.9 16.9Pmax 215 215.5 200 200.2 39.9 39.88kV (V/C) 0.143 0.123 0.1KI (A/C) 0.00196 0.0032 0.00035Ns 72 54 42

0 5 10 15 20 25 30 350

1

2

3

4

5

6

7

8

9

Voltage (V)

Cur

rent

(A)

a = 1

a = 2

Increase a

Fig. 7. Effect of ideality factor variation on IV curve.

3

4

5

6

7

8

9

Cur

rent

(A)

Rs = 1 Ohm

Increase Rs

Rs = 0 Ohm

16 M.S. Ismail et al. / Energy Conversion and Management 73 (2013) 10250 5 10 150

1

2Volta

Fig. 8. Effect of series resistan20 25 30 35

ge (V)

ce variation on IV curve.

code function, different constants and parameters of the model aredened.

For different voltages, mainly at Vpv = 0, Vmp, and VOC V, and atdifferent solar radiation levels, mainly at G = 1000, 800, 600, 400,200 W/m2, and at different temperatures mainly at T = 25, 50,75 C, the PV current Ipv is calculated using Eq. (14). This currentis calculated at different points, with a number of these pointsequaling p, and the corresponding average error objective functionis calculated according to Eq. (12).

The lower and upper constraints for some of the variables con-structing the decision vector are common for the different types ofPV modules, while the remaining variables have lower and upperconstraints, according to the PV type and manufacturer. In thisstudy, the diode ideality constants (a1, a2) have lower and upperconstrains between 1 and 2. The series resistance RS usually haslower and upper constraints of between 0.01O and 1.2O, whilethe shunt resistance Rp usually has lower and upper constraints

of between 50 O and 1000 O, but these values can be alteredaccording to the results of the genetic algorithm.

Some PV manufacturers do not provide the datasheet illustrat-ing the IV and PV curves at different radiation levels or differenttemperature values. They only provide KV, KI, VOC-STC, ISC-STC andVmp, Imp at standard test conditions. In this case, Eq. (15)(18)can be used to calculate the open circuit voltage and the short cir-cuit current at different radiation levels and different temperatures[19]

ISCG; T ISCSTC G=GSTC KI T TSTC 15

VOCG; T VOCSTC KV T TSTC a VT lnG=GSTC 16

ImpG; T ImpSTC G=GSTC 17

VmpG; T VmpSTC KV T TSTC 18These equations can be used even when the data sheets are avail-able, instead of using datasheet curves to read currents at differentvoltages, radiation levels and temperature values. Actually, usingthese equations provide values of decision vector parameters thataccurately model the PV module, as illustrated in the followingsection.

Fig. 9. IV curves for Sanyo HIT 215 module from manufacturer at different solarradiation levels and T = 25 C.

3

6I V P

X: 0.0001173

X: 0.04421

Y: 5.61

2

2

2

2

1.0 kW/m2

M.S. Ismail et al. / Energy Conversion and Management 73 (2013) 1025 170 10 200

1

2

3

4

5

X: 0.003153

Y: 2.282

Cur

rent

(A)

Y: 4.533

X: 0.000209

Y: 3.411

X: 0.004196

Y: 1.158

0.8 kW/m

0.6 kW/m

0.4 kW/m

0.2 kW/mVolta

Fig. 10. Simulation IV curves for Sanyo HIT 215 mod4. Results and discussion

In order to validate the adopted model, the results of the simu-lation of the model using MatlabSimulink are compared with themanufacturers datasheet. Three types of PV modules, using differ-ent technologies, are used for this purpose, which include themono-crystalline (from Sanyo (HIT 215)), multi-crystalline (fromKyocera (KC200GT)), and thin-lm (from Shell Solar (ST 40)) types.Table 1 shows the constants and parameters for these types, withthe Data sheets downloaded from the companies web sites. On topof the datasheet values, this table also includes the simulation re-sults for these three types of PV modules at standard test condi-tions. It is fairly obvious from comparing these values that theresults of the simulation agree with the data sheet values.

0 40 50 60

X: 51.6

Y: 0.0005341

lot

X: 42

Y: 5.131

X: 48

Y: 0.0006842

X: 41.52

Y: 4.194

X: 41.33

Y: 3.162

X: 40.58

Y: 1.023

X: 41.23

Y: 2.094ge (V)

ule at different solar radiation levels and T = 25 C.

4.1. Effect of variation of parameters (a, RS, Rp)

The effect of varying different variables constructing the deci-sion vector on the characteristic curves of the PV module differs,and the effect of varying the ideality factor on the IV is shownin Fig. 7. It is obvious from the gure that increasing the ideality

factor decreases the values of voltage, current and consequently,power, at the maximum point. Fig. 8 shows the effect of varyingthe series resistance on the IV curve. This gure illustrates thatas the RS increases, the values of voltage, current and power atthe maximum point also decrease. In addition, it is also observedthat varying the values of both ideality factor and series resistancecaused a noticeable effect at the region of the maximum powerpoint. Finally, the effect of varying Rp on the IV curve of a PV mod-ule was also studied, but this effect was barely noticeable. Thesecomparisons were done on a Kyocera (KC200GT) panel, at standardtest conditions. This panel was also selected for the validation ofthe results of the developed approach.

Table 2Comparison between data sheet and simulation results for Sanyo HIT 215 module at different radiation levels.

Quantity G = 1 kW G = 0.6 kW G = 0.2 kW

Data sheet Simulation Abs. error Data sheet Simulation Abs. error Data sheet Simulation Abs. error

Voc (V) 51.6 51.6 0 50.43 50.47 0.04 47.94 48 0.06Isc (A) 5.61 5.61 0 3.4 3.411 0.011 1.145 1.158 0.015Imp (A) 5.13 5.131 0.001 1.98 2.094 0.114 0.905 1.023 0.118

Fig. 11. IV curves for Sanyo HIT 215 from manufacturer at different temper-atures and at G = 1 kW/m2.

5

6

X: 0.04004

Y: 5.708

X: 0.05028

Y: 5.61

18 M.S. Ismail et al. / Energy Conversion and Management 73 (2013) 10253

4

urre

nt (A

)0 10 20 30

1

2

Voltag

C

Fig. 12. Simulation IV curves for Sanyo HIT 215X: 42

Y: 5.131

X: 37.4

Y: 5.258

X: 33.89

Y: 5.224

T= 25 C4.2. Results of genetic algorithm

Different cases were taken into account while using the geneticalgorithm to extract the optimal parameters of the PV module. Thepurpose of analyzing different cases is to specify the most optimalcase that enables the extraction of the most precise parameters ofPV module model, which when used in the simulation program,provides the results that agrees with the datasheet information.

Case 1: The usage of a single-diode model and the optimizationis done using Toolbox optimization Matlab library:

In this case, a single-diode model and a Toolbox optimizationMatlab library were used. The results obtained from this case aredeemed the most accurate. The Diode ideality factor (a), seriesresistance (RS) and shunt resistance (Rsh) are the calculated param-eters using the genetic algorithm.

For a Mono-Crystalline PV (Sanyo HIT 215), the values of theparameters are [a = 1.178, RS = 0.782 O, Rsh = 852.177 O, with an0 40 50 60e (V)

X: 44.4

Y: 0.0408

X: 51.6

Y: 0.003395

T= 50 C

T= 75 C

at different temperatures and at G = 1 kW/m2.

average absolute error = 0.016615]. Fig. 9 shows the IV curves ta-ken from the manufacturer data sheet for the different radiationlevels, while Fig. 10 shows the simulation results that take into ac-count the values of the parameters being given before. The valuesof the voltages at maximum power points are read from the simu-lation PV curve, which were not provided by the manufacturer.From the two gures, one can observe the similarity of the resultsat different radiation levels. Table 2 summarizes a comparison be-tween the results of the two graphs at open circuit, short circuitand maximum points. The largest absolute error in the current oc-curs at the region of the maximum power point, and as it is obviousfrom the graphs and the table, it increases as the radiation de-creases, but still possesses small values. Fig. 11 shows the IVcurve for the same PV module at different temperatures, whileFig. 12 shows the simulation results for the same module. Detailedgraphs of error as function of voltage for different radiation levelsand different temperature values are illustrated later in thissection.

For a Multi-Crystalline PV (Kyocera Kyocera KC200GT), thevalues of the parameters are [a = 1.106, RS = 0.331 O,Rsh = 883.925 O, with an average absolute error = 0.0152]. Fig. 13shows the IV curve obtained from the manufacturer data sheetfor different temperature levels, while Fig. 14 shows the simulation

results that take into account the values of parameters that werepreviously provided. The values of the voltages at maximum powerpoints are read from the simulation PV curve, which are not pro-vided by the manufacturer. Table 3 summarizes a comparison be-tween the results of the two graphs at open circuit, short circuitand maximum points. From the two gures, one can observe thesimilarity of the results at different temperature levels. The largestabsolute error in the current occurs at the region of maximumpower point, and as it is obvious from the graphs and the table,it increases as radiation decreases, but still possesses small values.Fig. 15 shows the IV curves for the same PV module at differentradiation levels, while Fig. 16 shows the simulation results forthe same module. Table 4 summarizes a comparison between theresults of the two graphs at open circuit, short circuit and maxi-mum points.

For a thin lm PV (Shell Solar ST 40), the values of the param-eters are [a = 1.558, RS = 1.149 O, Rsh = 860.75 O, with an averageabsolute error = 0.0094]. Fig. 17 shows the IV curve taken fromthe manufacturers data sheet for different temperature levels,while Fig. 18 shows the simulation results, taking into accountthe values of the parameters given before. The values of voltagesat maximum power points are read from the simulation PV curve.

T=

T=

T=

M.S. Ismail et al. / Energy Conversion and Management 73 (2013) 1025 19Fig. 13. IV curves for Kyocera KC200GT from manufacturer at differenttemperatures and at G = 1 kW/m2.

0 5 10 150

1

2

3

4

5

6

7

8

9

Cur

ren

t (A)

X: 0.01773Y: 8.369

X: 0.01852Y: 8.209Voltag

Fig. 14. Simulation IV curves for Kyocera KC200GTable 5 summarizes a comparison between the results of the twographs at open circuit, short circuit and maximum points. Fromthe two gures, one can observe the similarity of the results at dif-ferent temperature levels. Furthermore, the manufacturer providesthe value for the series resistance, which equals to 1.14 O. This va-lue is consistent with the value that was computed using thedeveloped approach.

Case 2: Is similar to case 1, but the optimization is done via thedeveloped Matlab code.

For this case, a Kyocera module is also taken into account forcomparison purposes. The values of the parameters that are ex-tracted by the genetic algorithm code are [a = 1.107, RS = 0.3395,Rsh = 870.27 with an average absolute error = 0.0153]. For thiscase, Fig. 19 shows the IV curves for different radiation levels.The results of this gure can be compared with the results of theToolbox optimization, shown in Fig. 16. The comparison showsthat the corresponding values in the two gures are almost similar.Fig. 20 shows the value of the average absolute error as a functionof the number of generations. This graph is obtained via the devel-

20 25 30 35

X: 26.76Y: 0.006297

X: 29.83Y: 0.003111

X: 32.9Y: 0.02323

X: 26.3Y: 7.61

X: 23.03Y: 7.633

X: 20.16Y: 7.509

50 C

25 C

75 Ce (V)T at different temperatures and at G = 1 kW/m2.

oped Matlab code. It is obvious that after about fteen generations,the optimized function obtains its nal value.

used, and the Kyocera module is also used for comparison pur-poses. The values of the parameters extracted by the genetic algo-rithm code are [a1 = 1.112, a2 = 1.377, RS = 0.29 O, Rsh = 480.496 O,Io1 = 4.23 109 A, Io2 = 9.1478 109 A, with an average abso-lute error = 0.02]. For this case, Fig. 21 shows the IV curves for dif-ferent radiation levels. The results can be compared to the resultsof the Toolbox optimization that are shown in Fig. 16 for the caseof a single-diode model. The comparison shows that the corre-sponding values in the two gures are almost similar, while thesingle-diode model provides a more accurate result compared tothe datasheet values, with an average absolute error also beingsmaller.

The IV curves shown in case-1s results accurately match thedata sheet information for all radiation levels and temperature val-ues, along with all types of modules. The absolute error in the PVcurrent does not exceed 0.20 A, even in its worst case scenario(for Kyocera at temperature = 75 C), while in other cases, it isinvariably less. A detailed graph, illustrating the absolute error asa function of voltage for different radiation levels, and at tempera-tures equaling 25 C, is shown in Fig. 22, while Fig. 23 illustrates itfor different temperature levels at solar radiations equaling 1 kW/

Table 3Comparison between data sheet and simulation results for Kyocera KC200GT module at different temperature values.

Quantity T = 25 C T = 50 C T = 75 C

Data sheet Simulation Abs. error Data sheet Simulation Abs. error Data sheet Simulation Abs. error

Voc (V) 32.9 32.9 0 29.78 29.83 0.05 26.7 26.76 0.06Isc (A) 8.2 8.209 0.009 8.298 8.312 0.014 8.397 8.369 0.028Imp (A) 7.61 7.61 0 7.72 7.633 0.078 7.68 7.509 0.171

Fig. 15. IV curves for Kyocera KC200GT 215 module from manufacturer atdifferent solar radiation levels and T = 25 C.

Y Pl

20 M.S. Ismail et al. / Energy Conversion and Management 73 (2013) 1025Case 3: In this case, a two-diode model is used, and the decisionvector is made up of six parameters. The optimization Toolbox is

X: 0.02677X 0 5 10 150

1

2

3

4

5

6

7

8

9

Voltage

Cur

ren

t (A)

X: 0.01786Y: 3.284

X: 0.01754Y: 4.926

X: 0.05313Y: 1.642

X: 0.05313Y: 6.568

Y: 8.209

G=0.2 kW

G=0.4 kW

G=0.6 kW

G=0.8 kW

G=1.0 kW

Fig. 16. Simulation IV curves for Kyocera KC200GT 215 module a

Table 4Comparison between data sheet and simulation results for Kyocera KC200GT module at

Quantity G = 1 kW G = 0.6 kW

Data sheet Simulation Abs. error Data sheet

Voc (V) 32.9 32.9 0 32.07Isc (A) 8.2 8.209 0.009 4.9Imp (A) 7.61 7.61 0 4.62m2. These two graphs illustrate the agreement in values betweenthe datasheet information and the simulation results. It is also

20 25 30 35

X: 30.4Y: 0.007847

(V)

X: 26.2Y: 3.055

X: 26.23Y: 4.612

X: 26.27Y: 6.133

X: 32.9Y: 0.03252

X: 26.3Y: 7.61

X: 25.54Y: 1.52

ot

/m2

/m2

/m2

/m2

/m2t different solar radiation levels and T = 25 C (3 parameters).

different radiation levels.

G = 0.2 kW

Simulation Abs. error Data sheet Simulation Abs. error

32.12 0.05 30.46 30.4 0.064.926 0.026 1.595 1.642 0.0474.612 0.008 1.53 1.52 0.010

fairly obvious that the maximum error occurs at the region of themaximum power point, where the curvature of the curve is largelyaffected by the values of the PV parameters.

Certain value for each parameter was extracted using this ap-proach, which shows strong agreement of the results with the datasheet information. In this approach, solar radiation and tempera-ture variations were incorporated into the calculation while for-

results of the study presented in Ref. [27] for different types of PVmodules, although in the developed approach presented in thismanuscript, certain constant value was calculated for each param-eter for the whole range of solar radiation and temperatures. For athin-lm PV (ST40), authors of Ref. [27] found values for the seriesresistance to be within the range of (0.710.99 O), and presented avalue for this resistance, which equals to 0.092 O using the RS-model. In the developed approach in this manuscript, this valueequals to 1.149 O, and it is consistent with the value provided bythe manufacturer. The results are also consistent with results ofRef. [30], where the effect of the temperature on the ideality factorand series resistance was taken into consideration. Authors of Ref.[31] presented their results in a graphical form. The presentedcurves in this reference included the results of the absolute errorin the current for the approach developed in this reference, andthe results of another approach. The results were for the KyoceraPV module (KC200GT) at standard test conditions. The maximumrecorded absolute error in this reference was about 0.45 A, whileit was about 0.88 A for the other presented approach. In the devel-oped approach presented in this manuscript, it was about 0.02 A.The same comparison was conducted with the results of Ref.[22], where the maximum recorded absolute error for the currentwas about 0.2 A for the Kyocera PV module (KC200GT) at standardtest conditions, and it was greater than this value for the other twomethods presented in the same reference.

Many attempts were made to nd the execution time to obtainthe model parameters. It was found that this time, in most cases, itis less than 4 s. However, as this developed approach uses the spec-

Fig. 17. IV curves for shell solar ST 40 from manufacturer at differenttemperatures and at G = 1 kW/m2.

: 12.7: 2.23

XY

M.S. Ismail et al. / Energy Conversion and Management 73 (2013) 1025 21mulating the average absolute error tness function in order tocompute the optimized values for different parameters. A valuethat deals with the entire range for solar radiation and tempera-tures was therefore calculated for each parameter. In Ref. [27],the used approach enabled the computation of the values of theparameters that change with solar radiation variation and/or tem-perature variation. The results of this study are consistent with the

2

2.5

3

X: 0.02002Y: 2.68

XY

X: 0.01634Y: 2.6930 5 10 10

0.5

1

1.5

Volta

Cur

rent

(A)

T= 55 C

T= 70 C

T= 40 C

T= 25 C

Fig. 18. Simulation IV curves for shell solar ST 40

Table 5Comparison between data sheet and simulation results for Shell Solar ST 40 module at

Quantity T = 25 C T = 40 C

Data sheet Simulation Abs. error Data sheet

Voc (V) 23.3 23.3 0 22.03Isc (A) 2.68 2.68 0 2.683Imp (A) 2.36 2.36 0 2.35ications of any solar module given by the manufacturer to extractglobal values of the parameters that suit the entire range of solarradiation and temperature variations, these parameters can berstly calculated (off-line). This means that in this approach, thereis no need for real time modeling. In other approaches where theparameter values change with solar radiation and temperaturesvariations, real-time modeling is required. In these cases, the mod-

5 20 25 30X: 21.79Y: 0.003402

ge (V)

X: 16.9Y: 2.36

X: 23.3Y: 0.000122

X: 20.29Y: 0.005935

38

X: 15.41Y: 2.336

: 13.95: 2.308

X: 18.79Y: 0.003928

at different temperatures and at G = 1 kW/m2.

different temperature values.

T = 55 C

Simulation Abs. error Data sheet Simulation Abs. error

21.79 0.24 20.75 20.29 0.46

2.685 0.002 2.687 2.690 0.0032.336 0.006 2.323 2.308 0.015

0 5 10 15 20 25 30 350

1

2

3

4

5

6

7

8

9

X: 32.9Y: 0.02278

X: 0.03297Y: 8.209

X: 30.4Y: 0.01847

X: 0.03316Y: 6.568

X: 0.09801Y: 4.926

X: 0.09802Y: 3.284C

urre

nt (A

)

Voltage (V)

X: 0.09804Y: 1.642

X: 26.3Y: 7.595

X: 26.27Y: 6.123

X: 26.23Y: 4.609

X: 26.2Y: 3.055

X: 25.54Y: 1.52

G=1.0 kW/m2

G=0.8 kW/m2

G=0.6 kW/m2

G=0.4 kW/m2

G=0.2 kW/m2

Fig. 19. Simulation IV curves for Kyocera KC200GT 215 module at different solar radiation levels and T = 25 C using developed code for genetic algorithm.

Fig. 20. Average absolute error as a function of generation number.

0 5 10 15 20 25 30 350

1

2

3

4

5

6

7

8

9

X: 32.89

Y: 0.0001864

Voltage (V)

X: 30.59

Y: 0.006519

X: 0.0274

Y: 8.209

X: 0.0273

Y: 1.642

X: 0.02735

Y: 6.568

X: 0.02717

Y: 4.926

Cur

rent

(A)

X: 0.027

Y: 3.284

X: 26.3

Y: 7.63

X: 26.27

Y: 6.168

X: 26.23

Y: 4.653

X: 26.2

Y: 3.094

X: 25.54

Y: 1.545

G=1.0 kW/m2

G=0.8 kW/m2

G=0.6 kW/m2

G=0.4 kW/m2

G=0.2 kW/m2

Fig. 21. Simulation IV curves for Kyocera KC200GT 215 module at different solar radiation levels and T = 25 C (6 parameters).

22 M.S. Ismail et al. / Energy Conversion and Management 73 (2013) 1025

diation levels at T = 25 C for Sanyo HIT 215 module.

on and Management 73 (2013) 1025 23Fig. 22. Absolute error in PV current for different ra

M.S. Ismail et al. / Energy Conversieling approach shall be fast enough to deal with real timeoperation.

4.3. Validation of the results of the developed model for partial shading

In partial shading, different parts of the PV array are exposedupon different radiation levels. If the approach is able to providean accurate model of the PV panel at different solar radiation andtemperature values, this developed model can be satisfactorily ap-plied in the case of partial shading.

As it was earlier mentioned in this work, the developed ap-proach provides the parameters for the PV model that suit the en-tire range of the solar radiation and temperature uctuations. So,the developed model described in this work can be accurately usedfor this purpose. Actually, there is no need for real time modelingto be utilized while using the model developed by this approach,since this model is appropriate for different radiation and temper-ature levels. This is so due to the fact that there is no need to adaptthe values of models parameters to real time operation.

In order to validate the ability of this developed model to dealwith partial shading, a PV array conguration composed of 20 PVpanels and connected in series to form a string and three strings,are connected in parallel. This case was studied in detail by Ref.[22], where the SM55-Siemens PV panel was selected to validatethe partial shading modeling. The authors presented the resultsof the developed model in this reference where a two-diode modelis used alongside results of other previous studies. Four shadingpatterns affecting this array were assumed. Specic radiation lev-els for each shading pattern were selected, and different tempera-ture values were also considered. Fig. 24 shows the series parallelconnections of the 20 3 PV array, while Table 6 displays the sim-ulation results of this work for selected cases of partial shading

Fig. 23. Absolute error in PV current for different temperatupatterns at different temperatures alongside the results presentedin the same mentioned reference. The simulations showed satisfac-tory results compared to the results presented in this reference.Fig. 25 shows the PV curve of partial shading case 1, mentionedin Table 6.

The values of the parameters that were extracted by the geneticalgorithm for this panel are [a = 1.107, RS = 0.551, Rsh = 940.52with an average absolute error = 0.008]. The simulation results inthis manuscript that uses these parameters showed that this arrayis capable of generating 3292W, at a voltage of 347.2 V, at maxi-mum power point at standard test conditions. As provided by themanufacturers datasheet, the maximum power point voltage andcurrent at standard test conditions for this panel are 17.4 V and3.15 A, respectively. According to these specications, this arraycan produce a power of 3288W at 348 V, which are very close tothe simulation results, while the simulation results presented byRef. [22] for power and voltage are 3220W and 350 V, respectively.

re values at G = 1 kW/m2 for Sanyo HIT 215 module.

Fig. 24. The series parallel connections for the 20 3 array.

owe

[22

(W)

9.67.65.925.20

n aTable 6The voltage Vmp and the power Pmp outputs of a 20 3 PV array at global maximum p

Case T (C) Shading pattern 1 means 1000 W/m2 Two diode model

A B C D Vmp (V) Pmp

1 25 1 0.75 0.5 0.25 275 1352 25 0.75 0.5 0.2 0.1 177 863 50 0.8 0.6 0.4 0.2 243 964 75 0.9 0.6 0.3 0.1 158 93

24 M.S. Ismail et al. / Energy ConversioThe values for power and voltage under different shading pat-terns presented in Ref. [22] are the simulation results of ap-proaches, developed by the authors of this reference and theauthors of other studies, cited by the same reference.

The developed model in this manuscript showed accurate re-sults for the proposed (20 3) array under standard test condi-tions, as previously discussed. Furthermore, the SM55 PV panelmanufacturer provides a datasheet, including IV curves of onemodule at two radiation levels (1000 W and 800W), and threetemperature values (25, 45 and 60 C). The simulation results at(G = 1000 W/m2, T = 60 C) and at (G = 800W/m2, T = 45 C) areconsistent with the datasheets information.

5. Conclusions

In this paper, a modeling method based on the genetic algo-rithm is proposed. The values of the PV module parameters werecomputed in such a way that the error between the simulation re-sults and the data sheet information is minimized. A global optimi-zation for the values of the parameters was realized, so the valuesextracted using this algorithm are applicable for the entire range ofthe solar radiation and temperatures. The information provided bythe manufacturers data sheet of a certain PV module is the onlyrequirement for this approach. The MatlabSimulink environmentwas used to simulate the operation of the PV module using theparameters obtained by the genetic algorithm. The accuracy eval-uation of this approach was achieved by comparing the results ofthe simulation based on the extracted parameters with the manu-facturers data sheet information. The result validation was con-ducted for three types of PV modules from different technologies(mono-crystalline, poly-crystalline and thin-lm). Different caseswere also analyzed for the purpose of comparison. It was foundthat the error between the simulation results, based on the ex-

Fig. 25. The PV curve of caser point under different shading patterns at different temperatures.

] Results of studies presented in Ref. [22] Proposed approach

Articial neural network RS-model

Vmp (V) Pmp (W) Vmp (V) Pmp (W) Vmp (V) Pmp (W)

276.38 1383.1 271 1350.8 271.8 1376.8172.46 847.77 172 844.17 179.7 895.79241.01 964.26 236 940.89 254.99 1028.04150.35 885.98 156 914.9 147.86 885.11

nd Management 73 (2013) 1025tracted parameters and the data sheet was minuscule for differentsimulated types at different temperatures and different solar radi-ation. The most accurate results (achieving least error) were ob-tained using single-diode model with three extracted parameters(ideality factor, series resistance and shunt resistance). The photoncurrent and the saturation current of the model were calculateddepending on the optimally extracted parameters. The effective-ness of the model developed by this approach to predict the perfor-mance of the PV system under partial shading conditions was alsoapproved. The accurate modeling of any PV module is an importanttool required for any further studies concerning PV applications, sothis approach can be used as valuable tool for this exact purpose.

Acknowledgements

The authors would like to acknowledge the Ministry of HigherEducation of Malaysia and The University of Malaya, Kuala Lum-pur, Malaysia for the nancial support under UM.C/HIR/MOHE/ENG/21 (D000021-16001).

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Characterization of PV panel and global optimization of its model parameters using genetic algorithm1 Introduction2 Materials and methods2.1 Genetic algorithms2.1.1 Genetic algorithm using MATLAB global optimization Toolbox2.1.2 Genetic algorithm using developed MATLAB code

2.2 Simulation

3 Theory and calculations3.1 Mathematical modeling3.2 Genetic algorithm implementation to evaluate PV module parameters

4 Results and discussion4.1 Effect of variation of parameters (a, RS, Rp)4.2 Results of genetic algorithm4.3 Validation of the results of the developed model for partial shading

5 ConclusionsAcknowledgementsReferences