modelling polycristallin photovoltaic cells using design...

Scientia Iranica D (2014) 21(6), 2273{2279

Sharif University of TechnologyScientia Iranica

Transactions D: Computer Science & Engineering and Electrical Engineeringwww.scientiairanica.com

Research Note

Modelling polycristallin photovoltaic cells using designof experiments

F.Z. Zerhounia;�, M.H. Zerhounia, M. Zegrara, M.T. Benmessaouda, A. Tilmatineband A. Boudghene Stamboulia

a. Department of Electronics, Faculty of Electrical Engineering, University of Sciences and Technology of Oran Mohamed Boudiaf,BP 1505, EL M'Naouer, USTO.M.B Oran (31000), Algeria.

b. Electrostatics and High Voltage Research Unit, IRECOM Laboratory, Djillali Liabes University of Sidi Bel-Abbes, 22000, Algeria.

Received 23 May 2012; received in revised form 14 February 2014; accepted 10 March 2014

KEYWORDSPhotovoltaicgenerator;Optimal power;Design of experiments;Solar radiation;temperature.

Abstract. Photovoltaic energy has, nowadays, an increased importance in electricalpower applications. However, the output power provided via the photovoltaic conversionprocess depends on solar irradiation and temperature. Tracking the Maximum Power Point(MPP) of photovoltaic (PV) systems is the most important part of the PV systems. In thispaper, modeling and parameter extraction methods are proposed to describe the optimalcurrent, voltage and power of the photovoltaic cells. The aim is to �nd a formula thatconsiders these factors and to study the interactions between these various factors. Thedesign of experiments is a powerful tool to understand systems and processes. Experimentsare often run so that the e�ect of one factor is unknowingly confused with the e�ectof another factor. A brief comparison between classic modeling is presented. In orderto model the optimal current, optimal tension and optimal power, a methodology ofexperimental design is presented. The obtained results show the merits of the proposedmathematical model, which makes the study of the interactions between various climaticfactors possible.

c 2014 Sharif University of Technology. All rights reserved.

1. Introduction

The consumption of fossil fuels has an environmentalimpact, in particular the release of carbon dioxide(CO2) into the atmosphere. CO2 emissions can begreatly reduced through the application of renewableenergy technologies, and renewable energy resourcesare su�cient to meet world energy requirements.Photovoltaic systems have become increasingly pop-ular and are ideally suited for distributed systems,as solar energy is the most abundant renewable re-source.

*. Corresponding author.E-mail address: zerhouni [email protected] (F.Z. Zerhouni)

2. Photovoltaic characteristics

There are three classic parameters that are very impor-tant for PV characteristics, namely, short-circuit cur-rent (Icc), open-circuit voltage (Voc) and the maximumpower point (Iopt; Vopt). The power delivered by aPV cell reaches a maximum value at the point (Iopt;Vopt). Solar photovoltaic (PV) arrays consist of manyNs cells connected in series to provide the requiredterminal voltage, and Ns cells, which are connectedin Np branches to provide the current ratings. PVpower systems do not have any moving parts, they arereliable, they require little maintenance and they donot generate pollutants or noise [1-8].

The voltage- current characteristic of a solar array

2274 F.Z. Zerhouni et al./Scientia Iranica, Transactions D: Computer Science & ... 21 (2014) 2273{2279

Figure 1. An equivalent circuit of a real photovoltaic cellwhere V and I are the output voltage and current of thePV module, respectively; Rs and Rsh are the series andshunt resistances.

in Figure 1 is given by Eq. (1) [1-8]:

I = Iph � Io:�exp

VdA:UT

� 1�� VdRsh

; (1)

with:

Vd = V +Rs:I; (2)

where V and I are the output voltage and currentof the PV module, respectively; Rs and Rsh are theseries and shunt resistances of the module, UT is thethermal voltage, Iph is the light-generated current, Iois the reverse saturation current, and A is an idealityfactor. In this studied case, a photovoltaic module isconstituted of 36 solar polycrystalline cells in series(Kyocera LA 361 K51), mounted 35� south.

P = V:I: (3)

The simulation result of the output module character-istics (Ns = Np = 1) using Eq. (1) and Eq. (3) isshown in Figure 2 [3-8]. Voc and Icc points are shownin Figure 2(a). The curve shows a MPP (MaximumPower Point), M , where the solar array operates moree�ciently (Figure 2(a)), which corresponds to theoptimal power, Popt, shown in Figure 2(b).

According to the maximum power transfer theory,the power P delivered to the load is maximum when thesource internal impedance matches the load impedancein a direct coupling. The peak Popt in Figure 2 isprovided by solving (4) [8]:

dPdI

=� 2:Rs:I +A:UT : ln�Icc � I + Io

Io

�� A:UT :IIcc � I + Io = 0: (4)

The current Iopt is the solution of Eq. (5):

Figure 2. Electrical characteristic of the module at solarradiation, Es = 100% and temperature, T = 25�C: a)I � V characteristic; and b) P � V characteristic.

Icc = Iopt + Io:

"exp

"(2:Iopt:Rs)A:UT

+Iopt

Icc � Iopt + Io#� 1#: (5)

The simulation results are shown in Figures 3 and 4.Figure 3 shows the characteristic curves at di�erentirradiances, Es, for a constant temperature. Thecharacteristic curves at di�erent temperatures for aconstant Es, is illustrated by Figure 4. Both �guresdemonstrate that the output characteristic of a solarmodule is crucially inuenced by solar radiation, Es,and temperature, T , conditions.

Due to the high cost of the photovoltaic generator,it is important to operate the modules close to theirmaximum power. So, in order to assure maximumpower transfer, the objective is to obtain the maximumpower point: Iopt, Vopt, Popt [8-13].

F.Z. Zerhouni et al./Scientia Iranica, Transactions D: Computer Science & ... 21 (2014) 2273{2279 2275

Figure 3. I � V and P � V characteristics of a solarmodule under varied solar irradiance and constanttemperature: a) I � V characteristic; and b) P � Vcharacteristic.

3. Experimental design methodology anddevelopment of the method

The methodology of the experimental designs allowsone to determine the number of experiments to beachieved according to a well de�ned objective, to studyseveral factors simultaneously, to reduce dispersionrelated to measurements, to appreciate the e�ects ofcoupling between factors, and, �nally, to evaluate therespective inuence of the factors and their interac-tions [7-10].

Finding mathematical models of good qualitywith minimum e�ort depends on how input factorintervals are selected. This method can be used, asfollows [14-19]:

Figure 4. I � V and P � V characteristics of a solarmodule under varied temperatures and constantirradiance: a) I � V characteristic; and b) P � Vcharacteristic.

� Selection of the most interesting and inuentialfactors;

� Determination of maximal, minimal and averagevalues of each factor;

� Carrying out a matrix of experiments with allpossible states and their corresponding responses.

Before starting the experiments, it is necessary to setthe best and suitable design which can model the pro-cess with the most possible precision. In this paper, theCentred Faces Composite design (CCF) is chosen whichallows the use of Response Surfaces Modelling (RSM).It is possible to determine a quadratic dependencebetween the output function to optimize (response) andthe input variables, ui (i = 1; � � � ; k):y = f(ui) = c0 +

Xciui +

Xcijuiuj +

Xciiu2i :

(6)

Knowing that �ui and ui0 are, respectively, the step ofvariation and the central value of factor i, the reduced


centred values of input factors may be de�ned by thefollowing relation:

xi = (ui � ui0)=�ui: (7)With these new variables, the output function becomes:

y=f(xi)=a0 +X

aixi +X

aijxixj +X

aiix2i :(8)

The coe�cients can be calculated or estimated by adata-processing program in such a way as to have aminimum variance between the predictive mathemati-cal model and the experimental results.

4. Software Modde 5.0

The software MODDE 5.0 (Umetrics AB, Umea, Swe-den) was used, which is a Windows program for thecreation and evaluation of experimental designs [20].The program assists the user for interpretation of theresults and prediction of the responses. It calculatesthe coe�cients of the mathematical model. In fact, itdraws the surfaces of response (RSM) and identi�esthe best adjustments of the parameters for processoptimisation.

Moreover, the program calculates two signi�cantstatistical criteria, which make it possible to validatethe mathematical model or not:

� The predictive power is given by Q2. This is ameasure of how well the model will predict theresponses for a new experimental condition.

� The goodness of �t parameter is given by R2.A good mathematical model must have criteria Q2 andR2, whose numerical values should be close to unity.

5. Results

The analysis of electric power, current and voltage wereachieved using a CCF experimental design with twofactors. In the experiments site in ORAN, used in thiswork, the domain of variation of each factor is:

� Solar radiation, ES : ESmin = 10%, correspondingto 100 W/m2, and ESmax = 100%, correspondingto 1 KW/m2;

� Temperature: Tmin = 20�C and Tmax = 50�C.Measurements of the three responses, i.e. power, Popt,current, Iopt, and voltage, Vopt, obtained according toa CCF design, are given in Table 1.

Once the experimental values of the responsesare measured, software MODDE.05 checks whetherexperimental results are \reasonable". It detects any\doubtful" measurement result.

Table 1. Obtained results.

Experiencen =�

Es[%]

T[�C]

Popt[W]

Vopt[V]

Iopt[A]

1 10 20 4.38 14.836 0.2952 100 20 49 16.528 2.9573 10 50 3.62 12.476 0.294 100 50 42.5 14.525 2.9265 10 35 4.07 13.904 0.2936 100 35 46.3 15.723 2.9477 55 20 27.298 16.737 1.6318 55 50 22.882 14.2 1.6119 55 35 25.107 15.467 1.62310 55 35 25.107 14.467 1.62311 55 35 25.107 14.467 1.623

The statistical tests achieved with MODDE.05lead to a valid mathematical model, since R2 and Q2reach higher values ranging between 0.991 and 1.000.The models suggested by MODDE.05 are:

- For power, Popt:

Popt =25:17 + 20:96E�s � 1:95T � � 0:07(E�S)2

� 0:17(T �)2 � 1:44(E�ST �): (9)- For voltage, Vopt:

Vopt =15:51 + 0:93E�S � 1:15T � � 0:77(E�S)2

� 0:12(T �)2 � 0:09(E�ST �): (10)- For current, Iopt:

Iopt =1:62 + 1:32E�S � 0:009T � � 0:003(E�S)2

� 0:02(T �)2 � 0:06(E�ST �): (11)

6. Discussions

The values of the coe�cients associated with the factorsshow the degree of the inuence of each factor. Thesigns indicate how much the response is inuenced.The coe�cients could also be plotted as shown inFigure 5. The latter shows that the ES e�ect ismore signi�cant than all the others. It arises frommathematical models that within the variation limitsof the selected intervals, ES is the most e�ective.This was con�rmed by iso-responses surfaces shown inFigure 6, where it could be veri�ed that factor ES ismore signi�cant than temperature. Furthermore, asexpected, the inuence of ES is positive and the one ofT is negative.

According to this power model, the operation setpoint, i.e. the optimum of the process corresponding to


Figure 5. Plotted coe�cients of the model.

Figure 6. Iso power contours P (W ) plotted by Modde 5based on the data of Table 1.

the maximum power, should be obtained for ES = 100and T = 20�C.

The design of the experiment model shows di-rectly the relationship between the climatic data: solarradiation, Es, temperature, T , and response, Popt. Itshows also interactions between these climatic factors.

7. Conclusion

In this work, we provide an approach to �nd optimalpower, optimal current and optimal voltage in order to�nd the MPP. The control variables considered for theoptimization include solar radiation and temperature.The aim is to show interactions between these variousfactors. This method can be applied to control a DC-DC converter device. An experimental design method-ology was employed for determining the optimum valueof each variable, using commercial software (MODDE,Umetrics, Sweden).

References

1. Ding, K., Zhang, J., Xingao, Xu, B.J. \A simpli�edmodel for photovoltaic modules based on improvedtranslation equations", Solar Energy, 101, pp. 40-52(2014).

2. Attivissimo, F., Di Nisio, A., Savino, M. and Spadav-

ecchia, M. \Uncertainty analysis in photovoltaic cellparameter estimation", IEEE Trans. on Instrumenta-tion and Measurement, 61(5), pp. 1334-1342 (2012).

3. Toledo, F.J., Blanes Jose, M., Garrigos Ausias, et al.\Analytical resolution of the electrical four-parametersmodel of a photovoltaic module using small perturba-tion around the operating point", Renewable Energy,43, pp. 83-89 (2012).

4. Peng, L., Sun, Y., Meng, Z. \An improved model andparameters extraction for photovoltaic cells using onlythree state points at standard test condition", J.l ofPower Sources, 248, pp. 621-631 (2014).

5. Cubas, J., Pindado, S. and Victoria, M. \On theanalytical approach for modeling photovoltaic systemsbehavior", J. of Power Sources, 247, pp. 467-474(2014).

6. Koran, A., LaBella, T. and Lai, J.-Sh. \High e�-ciency photovoltaic source simulator with fast responsetime for solar power conditioning systems evaluation",IEEE Trans. on Power Electronics, 29(3), pp. 1285-1297 (2014).

7. Li, Y., Huang, W., Huang, H., Witt, C.H., Chen, Y.,Fang, G. and Carroll, D.L. \Evaluation of methodsto extract parameters from current-voltage character-istics of solar cells", Solar Energy, 90, pp. 51-57 (2014).

8. Zerhouni, F.Z., Zerhouni, M.H., Zegrar, M., et al.\Proposed methods to increase the output e�ciencyof a photovoltaic (PV) system", Acta PolytechnicaHungarica, 7(2), pp. 55-70 (2010).

9. Zerhouni, F.Z., Zegrar, M., Benmessaoud, M.T., et al.\A novel method to optimize photovoltaic generatoroperation", International Journal of Energy Research,32(15), pp. 1444-1453 (2008).

10. Zerhouni, F.Z., Zegrar, M., Benmessaoud, M.T., et al.\Optimum load matching by an array recon�gurationin photovoltaic generators", Energy & Fuels, 24, pp.6126-6130 (2010).

11. Raghav, K., Qinhao, Z., Stanchina, W.E. et al.\Maximum power point tracking using model referenceadaptive control", IEEE Trans. on Power Electronics,29(3), pp. 1490-1499 (2014).

12. Wang, Feng, Wu, Xinke, Lee, Fred, C. et al. \Anal-ysis of uni�ed output mppt control in subpanel PVconverter system", IEEE Trans. on Power Electronics,29(3), pp. 1275-1284 (2014).

13. Benmessaoud, M.T., Zerhouni, F.Z., Zegrar, M., etal. \New approach modeling and a maximum powerpoint tracker method for solar cells", Computers &Mathematics with Applications, 60(4), pp. 1124-1134(2010).

14. Frigon, N.L. and Mathews, D., Practical Guide toExperimental Design, 1st Edn., Wiley (1996).

15. Tilmatine, A., Brahami, M., Miloua, F., Gouri, R.and Dascalescu, L. \Using experimental designs formodelling of intermittent air �ltration process", Fron-tiers of Electrical and Electronic Engineering in China,3(2), pp. 218-222 (2008).


16. Eriksson, L., Johansson, E., Kettaneh-Wold, N., Wik-strom, C. and Wold, S., Design of Experiments. Prin-ciples and Applications, Learnways AB, Stockholm(2000).

17. Hicks, C.R. and Turner Jr., K.V., Fundamental Con-cepts in the Design of Experiments, Oxford, OxfordUniversity Press (1999).

18. Taguchi, G. and Yokoyama, Y., Taguchi Methods: De-sign of Experiments, Dearborn, Michigan: AmericanSupplier Institute (1993).

19. Montgomery, D.C., Design and Analysis of Experi-ments, Wiley (2004).

20. MODDE 5.0, User guide and tutorial, Umetrics (1999).

Biographies

Fatima Zohra Zerhouni obtained her MS and PhDdegrees in electrical engineering from the Universityof Science and Technology, Mohamed Boudiaf, Oran(USTOMB), Algeria, where she is currently Professorand researcher, and also member of the Microsyst�emeset Syst�emes Embarqu�es Laboratory. She began herstudies in the �eld of power electronics and changedto environmental friendly production of energy. Shehas had a number of papers published in internationaljournals and presented at international and nationalconferences, and was awarded by CDER and theMinistry of Higher Education and Scienti�c Research,Algeria, for the best publication of 2010. Her researchinterests include renewable energy, fuel cells, powerelectronics, electrical storage systems and soft comput-ing control.

M'hamed Houari Zerhouni received his MS degreein electrical engineering from the University of Scienceand Technology, USTOMB, Mohamed Boudiaf, Oran,Algeria, where he is currently Professor and researcherwith the Department of Electronic Engineering, andalso member of the Microsyst�emes et Syst�emes Em-barqu�es Laboratory. He is currently pursuing his PhDin the �eld of PEMFC and solar energy, and has co-authored a number of papers published in internationaland technical journals and presented at internationaland national conferences. His research interests arepower electronics applied to photovoltaic energy sys-tems, including renewable energy, photovoltaic cellsand proton exchange membrane fuel cells, PEMFC.

Mansour Zegrar received his MS degree in electricalengineering from the University of Science and Tech-nology, Mohamed Boudiaf, Oran (USTOMB), Algeria,where he is Professor and researcher, and also memberof the Microsyst�emes et Syst�emes Embarqu�es Labora-tory. He is currently pursuing his PhD degree in the�eld of multilevel inverter, and solar energy. His teach-ing activities involve courses in switched-mode con-

verters, power electronic components, switched-modeconverter dynamics and EMC, as well as photovoltaicinterfacing issues. His research interests are renewableenergy and power electronics, including dynamic issuesin renewable energy systems and their grid integrationinvolving photovoltaic and fuel-cell systems.

Mohammed Tarik Benmessaoud received BS,MS and PhD degrees in engineering and electronicsfrom the University of Science and Technology, Oran(USTO-MB), Algeria, in 2000, 2006, and 2012, re-spectively. He is currently Professor in the electricaland electronics engineering faculty, as well as memberof the Materials and their Applications in ElectricalEngineering Laboratory, at the same institution.

His research interests include electronics, renew-able energy, solar cells, fuel cells, desalination, mate-rials and their applications in electrical engineering,theoretical and computational mathematical conceptswith applications in electrical engineering, neural net-works, genetic algorithms and optimization methods.

Amar Tilmatine received an MS degree in electricalengineering and the Magister (Dr. Eng.) degreefrom the University of Science and Technology, Oran,Algeria, in 1988 and 1991, respectively. He obtained aPhD degree, in 2004, from the Electrical EngineeringInstitute of Sidi Bel Abbes University, Algeria, wherehe teaches electric �eld theory and high-voltage engi-neering, and was Chairman of the Scienti�c Committeeof this institute for 3 years. He is currently Professor,senior IEEE member and Vice-chairman of the IEEEAlgerian subsection. He is also Director of the AP-ELEC Laboratory.

He visited the Electrostatics Research Unit of theUniversity Institute of Technology, Angoulême, France,at various times between 2001 and 2012, as invitedscientist for work on a joint research project involvingnew electrostatic separation technologies. His other�elds of interest are high-voltage insulation and gasdischarges.

Amine Boudghene Stambouli is a graduate of theUniversity of Science and Technology, Oran, Algeria, in1983. He received his MS and PhD degrees in modernelectronics and optoelectronics from the University ofNottingham, UK, in 1985 and 1989, respectively, Heis currently Professor of optoelectronics and materialsciences for environment and energy applications in theDepartment of Electronics at the University of Sciencesand Technology, Oran. His studies started in the �eldof high �eld electroluminescence and optoelectronicsand changed to environmental friendly production ofenergy. His research interests include photovoltaics,fuel cells, hybrid systems, and environment impacts.

Prof. Amine Boudghene Stambouli is a United


Nations consultant (Index 382958), member of manyscienti�c and industrial organizations and director ofseveral doctoral courses. He served as head of theelectronics department, vice rector of the university foralmost two years and, later, president of the scienti�ccouncil of the electrical and electronics engineeringfaculty. Prof. Amine Boudghene Stambouli haschaired several international conferences in the �eldof electrical engineering, and has been published in1 book and 3 polycopies. He has also had a num-ber of papers published in international journals andproceedings of international and national conferences,and is reviewer and editorial board member of several

international journals. He actively collaborates withresearch groups world-wide, including Algeria, Italy,Japan, France, USA, Germany, Turkey, England, SaudiArabia, Jordan, Morocco, Tunisia and Syria. He wasco-responsible, with Professor Enrico Travera, for theresearch team \Photovoltaics and Fuel Cells" betweenthe University of Roma Tor Vergata and the Universityof Sciences and Technology of Oran, and awarded bestpublication of 2009 by CDER and the Ministry ofHigher Education and Scienti�c Research of Algeria.He is co-responsible (Algerian side) for the Sahara SolarBreeder (SSB) project, with Pr. Koinuma (Japan side),and founder of the Sahara Solar Breeder Foundation.

modelling polycristallin photovoltaic cells using design...

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