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    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME 19 MATLAB BASED MODELING OF A PV ARRAY AND ITS COMPARATIVE STUDY WITH ACTUAL SYSTEM FOR DIFFERENT CONDITIONS S.N.H. Faridi1 , Mohammed Aslam Husain2 , Abu Tariq3 , Abul Khair4 1,2,3,4 Department of Electrical Engineering, AligarhMuslimUniversity (AMU), Aligarh, INDIA ABSTRACT The paper presents the modeling of a photovoltaic array in Matlab/Simulink environment. The model is developed using basic circuit equations of the photovoltaic (PV) solar cells including the effects of solar irradiation and temperature changes. The equations of the model are presented in details. Firstly the mathematical modeling of a solar cell is done, then how a solar module, array and panel is obtained using that cell is shown clearly. Different characteristics of modeled PV panel and practical PV panel have been obtained for different parameters and comparison has been done. Solar PV panel is a nonlinear power source that needs accurate identification of optimal operating point. It is desired to operate Solar Photo Voltaic (SPV) panel at its maximum power output for economic reasons. This paper is useful to model, simulate and study the effect of changing ambient conditions of the photovoltaic arrays. The accuracy of Model is experimentally and practically verified. Keywords: SPV Array, Insolation, Temperature, Modeling, MATLAB Simulation. I. INTRODUCTION With the rapid increase in the demand of energy, it has become the need of time to switch over to the renewable energy sources. Development and utilization of renewable energy and green energy is necessary for sustainable development. The solar energy is the ideal green energy and a photovoltaic system (PVS) is the most simple and reliable way to produce electricity from the conversion of solar energy. The basic building device of SPV system is SPV cell. Many SPV cells are grouped together to form modules.SPV array may be either a module or a group of modules arranged in series and parallel configuration. The output of SPV system may be directly fed to the loads or may use a power electronic converter to process it. To study the converters and other connected performances it is necessary to proper model of SPV systems [2]. INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY (IJEET) ISSN 0976 – 6545(Print) ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME: www.iaeme.com/ijeet.asp Journal Impact Factor (2014): 6.8310 (Calculated by GISI) www.jifactor.com IJEET © I A E M E
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME 20 The main task of this paper is to develop a simulation model of SPV cell, module and array to reproduce the characteristics of existing SPV systems. Characteristics of developed models have been shown for different conditions. This text presents in details the equations that form the I-V model. The aim of this paper is to provide the reader with all necessary information to develop photovoltaic array models and circuits that can be used in the simulation for photovoltaic applications. II. MODELING OF PHOTOVOLTAIC CELL 2.1 Photovoltaic Cell The basic equation from the theory of semiconductors [1] that mathematically describes the I- V characteristic of the ideal photovoltaic cell is:       −−= 10 C C PhC kT qV eIII (1) Where: Iph is the short-circuit current that is equal to the photon generated current.         −= 10 kTc qVd d eII (2) Where, dI is the current shunted through the intrinsic diode, The diode current Id is given by the Shockley’s diode equation; Vd is the voltage across the diode (D). k is Boltzmann constant ,q is electron charge , OI is reverse saturation current of diode , CT is reference cell operating temperature (25 °C). 2.2 Modeling the photovoltaic array Practical arrays are composed of several connected photovoltaic cells and the observation of the characteristics at the terminals of the photovoltaic array requires the inclusion of additional parameters to the basic equation [1,11]: Fig.1: Single-diode model of the theoretical photovoltaic cell Fig. 2: Characteristic I-V curve of the photovoltaic cell.
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. The net cell current I is composed of the light However, if the load R is small, the cell operates in the region M the cell behaves as a constant current source, almost equal to the short circuit curre hand, if the load R is large, the cell operates on the regions P a constant voltage source, almost equal to the open Fig.3: A typical, current-voltage I-V points: short circuit (0, Isc), maximum = PhC II where Iph and I0are the photovoltaic and saturation currents thermal voltage of the array with Ns cells connected in series. Cells connected in parallel current and cells connected in series provide resistance of the array and Rp is the curve seen in Fig. 3. The equation (3) represents the practical SPV cell. Here the five parameters are RP. This equation can also be used to represent a series/parallel connected module by suitably modifying its parameters [2]. Eq. (3) describes the single- more sophisticated models that present better example, in [3–6] an extra diode is used to represent the a three-diode model is proposed to include the influence of effects which previous models. For simplicity the offers a good compromise between simplicity and accuracy [8] and has been used by several authors in always with the basic structure composed of a current source and a parallel Fig 4: Mathematical Modelling Implementation for Io cal Engineering and Technology (IJEET), ISSN 0976 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME 21 I is composed of the light-generated current Ipv and the diode current Id. However, if the load R is small, the cell operates in the region M-N of the curve Fig.3, where the cell behaves as a constant current source, almost equal to the short circuit curre hand, if the load R is large, the cell operates on the regions P-S of the curve, the cell behaves more as a constant voltage source, almost equal to the open-circuit voltage. V curve for a solar cell for different load and the three : short circuit (0, Isc), maximum power point (Vmax, Imax) and open-circuit (Voc, 0).       + −         −−         + P SCCAkT RIV q Ph R RIV eI c SCC 10 (3) are the photovoltaic and saturation currents of the array and Vt = thermal voltage of the array with Ns cells connected in series. Cells connected in parallel connected in series provide greater output voltages. Rs is the equivalent series is the equivalent parallel resistance. This equation originates The equation (3) represents the practical SPV cell. Here the five parameters are . This equation can also be used to represent a series/parallel connected module by suitably -diode model presented in Fig.1. Some authors have proposed that present better accuracy and serve for different purposes. 6] an extra diode is used to represent the effect of the recombination of carriers. In [7] model is proposed to include the influence of effects which are not considered by the single-diode model of Fig. 1 is studied in this paper. This offers a good compromise between simplicity and accuracy been used by several authors in previous works, sometimes with simplifications but basic structure composed of a current source and a parallel diode [2,9,10 Mathematical Modelling Fig 5: Mathematical Modeling Implementation for Ipv cal Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), diode current Id. N of the curve Fig.3, where the cell behaves as a constant current source, almost equal to the short circuit current. On the other S of the curve, the cell behaves more as for different load and the three remarkable circuit (Voc, 0). of the array and Vt = NskT/q is the thermal voltage of the array with Ns cells connected in series. Cells connected in parallel increase the Rs is the equivalent series equivalent parallel resistance. This equation originates the I-V The equation (3) represents the practical SPV cell. Here the five parameters are Iph, I0,Vt, RS, . This equation can also be used to represent a series/parallel connected module by suitably diode model presented in Fig.1. Some authors have proposed accuracy and serve for different purposes. For effect of the recombination of carriers. In [7] are not considered by the diode model of Fig. 1 is studied in this paper. This model works, sometimes with simplifications but diode [2,9,10]. Mathematical Modeling Implementation for Ipv
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. Fig 6: Mathematical Modelling Implementation for model current Im Fig 8: Circuitry Design for PV Array Manufacturers of SPV arrays, instead of the I data about electrical and thermal characteristics. adjusting photovoltaic array models cannot light-generated or photovoltaic current, the series and shunt the diode reverse saturation current, and the band All photovoltaic array datasheets bring basically the following open-circuit voltage Voc,n, the nominal power point Vmp, the current at the maximum power point Imp, the open circuit current/temperature coefficient KI , and the maximum information is always provided with reference to the nominal or standard temperature and solar irradiation. Some manufacturers provide I These curves make easier the adjustment and the equation. Basically this is all the information one can get Electric generators are generally classified as current or photovoltaic device presents an hybrid behavior, which may be of current or voltage source depending on the operating point. Datasheets only which is the maximum current available at the terminals of the practical ≈ Ipv is generally used in photovoltaic low and the parallel resistance is high. The light linearly on the solar irradiation and is also influenced by the temperature equation Ipv = ( Ipv,n + K1 cal Engineering and Technology (IJEET), ISSN 0976 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME 22 Mathematical Modelling Fig 7: PV array modeling Implementation for model current Im Circuitry Design for PV Array Fig 9: Mask of PV Array Manufacturers of SPV arrays, instead of the I-V equation, provide only a few experimental and thermal characteristics. Unfortunately some of the parameters adjusting photovoltaic array models cannot be found in the manufacturers’ data sheets, such as the generated or photovoltaic current, the series and shunt resistances, the diode ideality constant, current, and the band gap energy of the semiconductor. All photovoltaic array datasheets bring basically the following information: the nominal circuit voltage Voc,n, the nominal short-circuit current Isc,n, the voltage at th power point Vmp, the current at the maximum power point voltage/temperature coefficient KV, the short circuit current/temperature coefficient KI , and the maximum experimental peak output power Pmax,e. This always provided with reference to the nominal or standard test conditions (STC) of Some manufacturers provide I-V curves for several irradiation and temperature conditions. the adjustment and the validation of the desired mathematical equation. Basically this is all the information one can get from datasheets of photovoltaic arrays. Electric generators are generally classified as current or voltage sources. The practical hybrid behavior, which may be of current or voltage source Datasheets only inform the nominal short-circuit current (Isc,n), maximum current available at the terminals of the practical device. The assumption Isc Ipv is generally used in photovoltaic models because in practical devices the series resistance low and the parallel resistance is high. The light generated current of the photovoltaic cell depends diation and is also influenced by the temperature according to the Ipv = ( Ipv,n + K1∆T ) (4) cal Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), PV array modeling Mask of PV Array V equation, provide only a few experimental Unfortunately some of the parameters required for data sheets, such as the resistances, the diode ideality constant, information: the nominal circuit current Isc,n, the voltage at the maximum the short circuit experimental peak output power Pmax,e. This test conditions (STC) of and temperature conditions. validation of the desired mathematical I-V from datasheets of photovoltaic arrays. voltage sources. The practical hybrid behavior, which may be of current or voltage source circuit current (Isc,n), device. The assumption Isc models because in practical devices the series resistance is current of the photovoltaic cell depends according to the following
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME 23 where Ipv,n [A] is the light-generated current at the nominal condition (usually 25 ◦C and 1000W/m2), T = T − Tn,G [W/m2] is the irradiation on the device surface, and Gn is the nominal irradiation. Io= ூ௦௖,௡ା௄ଵ∆் ୣ୶୮ቀ ೇ೚೎,೙శ಼ೡ∆೅ ೌೇ೟ ቁି ଵ (5) The saturation current I0 of the photovoltaic cells that compose the device depend on the saturation current density of the semiconductor (J0, generally given in [A/cm2 ]) and on the effective area of the cells. The current density J0 depends on the intrinsic characteristics of the photovoltaic cell, which depend on several physical parameters such as the coefficient of diffusion of electrons in the semiconductor, the lifetime of minority carriers, the intrinsic carrier density, and others [7]. This kind of information is not usually available for commercial photovoltaic arrays. The value of the diode constant a may be arbitrarily chosen. Many authors discuss ways to estimate the correct value of this constant [8, 10,11]. Usually 1 ≤ a ≤ 1.5 and the choice depends on other parameters of the I-V model. Some values for a are found in [12] based on empirical analysis. As [8] says, there are different opinions about the best way to choose a. Because a expresses the degree of ideality of the diode and it is totally empirical, any initial value of a can be chosen in order to adjust the model. The value of a can be later modified in order to improve the model fitting if necessary. This constant affects the curvature of the I-V characteristic and varying a can slightly improves the model accuracy. TABLE 1 Parameters of the simulated model at nominal operating conditions Imp 7.61A Vmp 26.3V Pmax,m 200.143W Isc 8.21A Voc 32.9V I0,n 9.825 *10−8 A Ipv 8.214A A 1.3 Rp 415.405 KV −0.1230V/K KI 0.003 A/K Ns 54 The practical SPV cell has a series resistance Rse whose influence is stronger when the device operates in the voltage source region and a parallel resistance Rsh with stronger influence in the current source region of operation. The value of Rsh is generally high and some authors neglect this resistance to simplify the model [10, 11, 13]. The value of Rse is very low, and sometimes this parameter is neglected too [12-15]. The reference value of Rse is found from the V-I characteristics at reference conditions. The equation for variation of Rsh is found experimentally and curve fitting equation is given by equation (6). RSH= 3.6/(G-.086) (6)
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME 24 III. SIMULATION RESULT In order to test the validity of the model array with different Nss, Npp are drawn. I-V & P-V characteristics for varying insolation and temperature have been obtained. Fig 10: I-V curve for Nss=2,Npp=3 at different insolation Fig 11: p-v characteristics at variable solar insolation, 250 c Fig 12: I-V curve shows the comparison for Nss=1,Npp=1 & Nss=2,Npp=2 Figure 10 represents I-V characteristics of solar array at variable solar insolation, fig.11 represents P-V characteristics at variable solar insolation, similarly figures 12, 13, 14 and 15 show these variation for different Nss and Npp. Figure 16 and 17 show the I-V and P-V characteristics of the solar array for different temperatures.
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME 25 Fig 13: P-V curve shows the comparison Fig 14: P-V curve shows the comparison for Nss=1,Npp=1 & Nss=2,Npp=2 for Nss=3, Npp=1; Nss=2, Npp=1; Nss=1, Npp=1 Fig 15: I-V curve shows the comparison for Fig 16: I-V curve for Nss=2, Npp=3 Nss=3,Npp=1; Nss=2, Npp=1; Nss=1, Npp=1 at different temperature Fig 17: P-V curve for Nss=2, Npp=3 at different temperature IV. COMPARISION WITH PRACTICAL RESULTS TABLE 1 Parameters of the practicalmodel at 300W/m2 and 36o C Imp 0.53A Vmp 15.7V Pmax,m 8.32W Isc 0.6A Voc 18.5V
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME 26 Fig 19: Solar Panel and Pyranometer Fig 20: Practical Setup Fig 18: V-I curve for different values of Insolation Fig 19: Practical V-Icurve obtained for the simulated model for the above parameters for different values of Insolation From fig no.18 and 19, it is clear that the results of simulated model are almost same as that obtained from practical PV panel for different values of insolation. V. CONCLUSION This paper has analyzed the development of a method for the mathematical modeling of photovoltaic arrays and comparing the simulated results with the practical results of solar pv panel. The Matlab model of solar PV panel is first done and then its results are compared with the practical model. The comparison of both actual result and simulated results are almost same as shown in characteristic of solar panel. Then straightforward method has been proposed to fit the mathematical V-I curve to the remarkable points without the need to guess or to estimate any parameters. The proposed method has given a closed solution for the problem of finding the parameters of the five parameter model equation of a practical SPV module. This paper has presented in details the equations that constitute the single-diode photovoltaic I-V model and the algorithm necessary to obtain the parameters of the equation. This paper provides the reader with all necessary information to easily develop a single-diode photovoltaic array model using SIMULINK. The proposed simulated PV model can be used for further study of PV standalone and grid connected system. REFERENCES [1] H. S. Rauschenbach. Solar cell array design handbook.Van Nostrand Reinhold, 1980. [2] RamaprabhaR(2011) , PhD Thesis “Maximum Energy Extraction from solar photovoltaic array under partial shaded conditions” faculty of electrical engg anna university, Chennai. [3] J. A. Gow and C. D. Manning. Development of a model for photovoltaic arrays suitable for use in simulation studiesof solar energy conversion systems. In Proc. 6th International Conference on Power Electronics and Variable Speed Drives, p. 69–74, 1996.
    • International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 19-27 © IAEME 27 [4] N. Pongratananukul and T. Kasparis. Tool for automated simulation of solar arrays using general-purpose simulators.In Proc. IEEE Workshop on Computers in PowerElectronics, p. 10–14, 2004. [5] S. Chowdhury, G. A. Taylor, S. P. Chowdhury,A. K.Saha, and Y. H. Song. Modelling, simulation and performance analysis of a PV array in an embedded environment. In Proc. 42nd International Universities Power Engineering Conference, UPEC, p. 781–785, 2007. [6] J. Hyvarinen and J. Karila. New analysis method forcrystalline silicon cells. In Proc. 3rd World Conferenceon Photovoltaic EnergyConversion, v. 2, p. 1521–1524,2003. [7] Kensuke Nishioka, Nobuhiro Sakitani, Yukiharu Uraoka, and Takashi Fuyuki. Analysis of multicrystalline silicon solar cells by modified 3diode equivalent circuit model taking leakage current through periphery into consideration. Solar Energy Materials and Solar Cells,91(13):1222–1227, 2007. [8] C. Carrero, J. Amador, and S. Arnaltes. A single procedure for helping PV designers to select silicon PV module and evaluate the loss resistances. Renewable Energy, 2007. [9] E. Koutroulis, K. Kalaitzakis, and V. Tzitzilonis. Development of a FPGA-based system for real-time simulation of photovoltaic modules. Microelectronics Journal,2008. [10] GeoffWalker. Evaluating MPPT converter topologies using a matlab PV model. Journal of Electrical & Electronics Engineering, Australia, 21(1), 2001. [11] Mohammed Aslam Husain and Abu Tariq, “Modeling of a standalone Wind-PV Hybrid generation system using MATLAB/SIMULINK and its performance analysis”. IJSER Volume 4, Issue11, November‐2013. Pp. 1805-1811. [12] W. De Soto, S. A. Klein, and W. A. Beckman. Improvement and validation of a model for photovoltaic array performance. Solar Energy, 80(1):78–88, January 2006. [13] Glass.M.C., “Improved solar array power point model with SPICE realization,” in Proc. 31st Intersoc. Energy Convers. Eng.Conf. (IECEC), 1996, vol. 1, pp. 286–291. [14] Kuo.Y.C., Liang.T.J. and Chen.J.F., “Novel maximum-power- ointtracking controller for photovoltaic energy conversion system,” IEEE Trans. Ind. Electron., 2001, vol. 48, no. 3, pp. 594–601. [15] M. T. Elhagry, A. A. T. Elkousy,M. B. Saleh, T. F. Elshatter, and E. M. Abou-Elzahab. Fuzzy modeling of photovoltaic panel equivalent circuit. In Proc. 40th Midwest Symposium on Circuits and Systems, v. 1, p. 60–63, August 1997. [16] Ahmed A. A. Hafez, “Analysis and Design of Robust Cascaded PV System”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 5, 2013, pp. 20 - 35, ISSN Print : 0976-6545, ISSN Online: 0976-6553. [17] Mohammed Seddik, S. Zouggar, F.Z.Kadda, A. Aziz, M.L.Ahafyani and R.Aboutni, “The Automatic Voltage Control Developed for the Maximum Power Point Tracking of a PV System”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 5, 2013, pp. 173 - 183, ISSN Print : 0976-6545, ISSN Online: 0976-6553. [18] Manoj Kumar, Dr. F. Ansari and Dr. A. K. Jha, “Analysis and Design of Grid Connected Photovoltaic System”, International Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 2, 2012, pp. 69 - 75, ISSN Print : 0976-6545, ISSN Online: 0976-6553. [19] M D Goudar, B. P. Patil and V. Kumar, “A Review of Improved Maximum Peak Power Tracking Algorithms for Photovoltaic Systems”, International Journal of Electrical Engineering & Technology (IJEET), Volume 1, Issue 1, 2010, pp. 85 - 107, ISSN Print: 0976-6545, ISSN Online: 0976-6553.