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IJAIEM-2013-11-30-108

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					 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
        Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 11, November 2013                                       ISSN 2319 - 4847

          Mathematical Modeling and Experimental
         Validation of Performance Characteristics of
                  Solar Photovoltaic Modules
                                    Dr. Jayashri Vajpai1, Mr. Harish Kumar Khyani2
     1
         Associate Professor, Electrical Engg. Department, Faculty of Engineering, J.N.V. University, Jodhpur, Rajasthan, India,
                          2
                            Associate Professor, Electrical Engg. Department, JIET, Jodhpur, Rajasthan, India,



                                                    ABSTRACT
This paper presents the development of a MATLAB/Simulink model for the solar PV cell, module and array. The
simulation of photovoltaic module for obtaining the performance characteristics has also been carried out in this
paper. The developed model is then simulated and validated experimentally using PSS1237 solar panel. The
experimental results obtained, exhibited a good agreement with the simulated data.

Key words: Photovoltaic Module, Simulation, MATLAB/Simulink.

1. INTRODUCTION
Several mathematical models for computer simulation of PV systems have been built over the past four decades [1]. These
models describe the output characteristics in terms of the major governing parameters. The output of the PV systems is
affected mainly by the solar insolation, cell temperature, and load voltage. MATLAB/Simulink software has been used for
the modeling and simulation in this paper.
The main contribution of this paper is to implement a generalized PV model that can be adapted to model different types
of PV Cells, Arrays and Modules and validate it by comparing its performance with a practically available Module.
Moreover, the simulated model is in the form of masked block, with a user-friendly icon and dialog box in the same way
as standard MATLAB/Simulink block libraries or other component-based electronics simulation software packages. This
masked block can be easily used in circuits involving PV systems. The process of model development and testing is
described in the following sections.

2. STATE OF ART
Research work on solar photovoltaic systems has shown exponential growth in the past few years, with these systems
becoming increasingly commercially feasible. Numerical modeling has proved to be a valuable tool in understanding the
operation of these systems. Tsai, Tu, and Su [2] have suggested four different types of generalized MATLAB models to
examine the effect of solar irradiance and cell temperature and to optimize the generalized model. The first complete
solar photovoltaic power electronic conversion system in circuit-based simulation model to simulate the electrical
behavior of the PV systems in a grid connected application has been designed by González-Longatt [3]. A
MATLAB/Simulink based study of PV cell, PV module and PV array under different operating conditions and load has
been carried out by Nema et al [4]. Ramos Hernanz, et. al. [5] have analyzed the performance of solar cells and developed
a complete model to simulate the electrical behavior of the PV systems. Surya Kumari and Sai Babu have also carried out
mathematical modeling and simulation of PV Cell in MATLAB/Simulink Environment to find the parameters of the
nonlinear I–V equation by adjusting the curve at three operating conditions: open circuit, maximum power, and short
circuit points [6]. Electrical characteristics of PV Array have been obtained as a function of temperature by Bhatt and
Thakker [7]. In a paper by Alsayid and Jallad, a MATLAB/Simulink /PSIM based simulation of PV cell, PV module and
PV array has been carried out and compared with 50W solar panel [8]. MATLAB/Simulink based modeling of modules
with the output power of 60W and 64W have been attempted by Mohammed [9]. Richhariya and Pachori have designed a
user friendly solar cell model with irradiance and cell temperature as input parameters, by using Matlab/Simulink and
have verified it with a commercial module [10]. Ramos-Hernanz et. al. [11] have compared two PV Simulation Models in
time domain by using MATLAB/Simulink, to achieve an I-V curve similar to the manufacturer’s data sheet. However,
these models have been developd with a large number of assumptions, some of which are even practically unrealistic.

3. DEVELOPMENT OF MATHEMATICAL MODEL FOR A PHOTOVOLTAIC MODULE
The use of equivalent electric circuits and mathematical equations makes it possible to model the characteristics of a PV
cell and simulate it. The same model can also be extended for modeling a PV module and an array. It is important to
build a generalized model that is suitable for scaling at all levels of model, i.e. the PV cell, module, and array. A

Volume 2, Issue 11, November 2013                                                                                       Page 295
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
        Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 11, November 2013                                       ISSN 2319 - 4847

generalized PV model has hence been developed using MATLAB/Simulink to illustrate and verify the nonlinear I-V and
P-V output characteristics of PV module.
In order to make the generalized model easier to identify and understand, a masked model is designed to have a dialog
box, in which the parameters of PV module can be configured in the same way as the standard Simulink block libraries.

3.1 MODELING OF A PV CELL
General mathematical description of I-V output characteristics for a PV cell has been studied for over the past four
decades [2]. The PV cell is usually represented by the single diode model. The single diode equivalent circuit of a solar
cell is as shown in Figure1.




                                           Figure 1 Single Diode Model of a Solar Cell

It primarily consists of a current source that generates photo-current (Iph), which is a function of incident solar
irradiation and cell temperature and a diode that represents p–n junction of the solar cell. In practical solar cells, the
voltage loss on the way to the external contacts is observed. This voltage loss is expressed by a series resistance RS.
Furthermore, leakage current is described by a parallel resistance RSH [12].

The voltage-current characteristic equation of a solar cell [13] is given as follows:




It is a nonlinear mathematical equation. Where IPH is a light-generated current or photocurrent, IS is the saturation
current, q (= 1.6 ×10−19C) is the magnitude of charge on an electron, k (= 1.38 ×10−23J/K) is Boltzmann’s constant, A is
ideality factor, RS is a series resistance and RSH is a shunt resistance. But the series loss and the leakage to ground, is
usually neglected to simplify the analysis, i.e., RS = 0 and RSH = ∞
The photo-generated current IPH is given by:



where, ISC is the short-circuit current at 25°C and 1kW/m2, KI is the short-circuit current temperature coefficient, TC is
the working temperature, TRef is the reference temperature, and G is the solar insolation in kW/m2.
The saturation current IS is represented by:




where, IRS is the reverse saturation current at a reference temperature and a solar radiation and EG is the band-gap energy
of the semiconductor material used.
The reverse saturation current IRS is given by:




   Finally, the output current of the PV cell after neglecting the effect of RS & RSH is as follows:



   This equation forms the basis of model development.

3.2 MODELING OF PV MODULE AND ARRAY

Volume 2, Issue 11, November 2013                                                                            Page 296
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
        Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 11, November 2013                                       ISSN 2319 - 4847

Since a typical PV cell produces less than 2W at 0.5V approximately, therefore the cells must be connected in series-
parallel configuration on a module to produce enough power. A PV array is a group of several PV modules which are
electrically connected in series and parallel circuits to generate the required current and voltage.
The equation no. 5 can be modified by including these circuits to obtain the output current of a PV module. Hence
The reverse saturation current IRS and the final output current of a PV module with Np parallel cells and Ns series cells is
given as follows:




   The circuit of an ideal PV module with Np parallel cells and Ns series cells is shown in Figure2.




                                           Figure 2 Ideal Model of PV Module


4. REFERENCE PV MODULE
PSS1237 PV Module, commercially available from (Easy Photovoltaic Private Limited, Ghaziabad, Uttar Pradesh), is
taken as the reference module for simulation. The details of manufacturer’s data sheet of this module are given in Table 1
[14]

                               Table 1: Parameter Specifications of PSS1237PV Module
                                          Characteristics                      Specifications
                           Nominal Voltage (volts)                                    12
                           Open Circuit Voltage, Voc (volts)                          21
                           Voltage at Max. Power, Pmax (volts)                      16.8
                           Short Circuit Current, Isc(Amps)                         2.55
                           Current at Max. Power, Imax (Amps)                        2.2
                           Max. Rated Power, Pmax (watts)                             37
                           No. of Cells/ module                                       36
                           Weight (Kg)                                               6.5
                           The electrical specifications are under test conditions of irradiance
                                  of 1kW/m2, cell temperature of 25°C and AM of 1.5
                                            Permissible range of error is ±3%

5. SIMULINK PV MODEL DEVELOPMENT
Using the equations given in section III, Simulink modeling is done as explained in the following steps:
Step- 1: Using equation no. 2, the photo generated current is modeled.
Step- 2: Using equation no. 3, the saturation current is modeled.
Step- 3: Using equation no. 6, the reverse saturation current of the module is modeled.
Step- 5: The output current of the module is modeled using equation no. 7.
Step- 5: The four models are finally interconnected as shown in Figure3.



Volume 2, Issue 11, November 2013                                                                             Page 297
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
        Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 11, November 2013                                       ISSN 2319 - 4847




                               Figure 3 MATLAB/Simulink Model of PV Cell/Module/Array

The final model shown in Figure3. It takes irradiation, operating temperature and module voltage as input parameters
and gives the output current and output voltage.

6. PERFORMANCE CHARACTERISTICS
Both I-V and P-V output characteristics of developed model have been simulated at standard test conditions i.e.
temperature = 298 K (250C) and irradiation G= 1kW/m2 as follows:

6.1 SIMULATION FOR DIFFERENT IRRADIATION LEVELS
Both I-V and P-V characteristics under different irradiation levels with constant temperature (250C) are obtained and are
shown in Figures 4(a) and 4(b).




               Figure 4(a) I-V Output Characteristics for            Figure 4(b) P-V Output Characteristics for
                        Different Irradiation Levels                             Different Irradiation Levels


6.2 SIMULATION FOR DIFFERENT TEMPERATURES
Both I-V and P-V characteristics under constant irradiation levels (1kW/m2) with varying temperatures are obtained and
are shown in Figures 5(a) and 5(b).

Volume 2, Issue 11, November 2013                                                                           Page 298
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
        Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 11, November 2013                                       ISSN 2319 - 4847




        Figure 5(a) I-V Output Characteristics for                     Figure 5(a) P-V output characteristics for
                  Different Temperatures                                           Different Temperatures

7. EXPERIMENTAL VALIDATION
The developed model has been validated through experimentation by using a simple variable resistive load and PSS1237
PV module. The circuit diagram of the proposed method and experimental setup are shown in Figure 6 and 7
respectively.




                   Figure 6 Circuit diagram                         Figure 7 Experimental Setup in the Field

In order to validate the MATLAB/Simulink model, an experiment has been performed under different conditions as
shown in Table 2.
                Table 2: Comparison of proposed model values with practical values at remarkable points

                                  Remarkable               Tilt angle: 26o, Tc : 55o
                                    points
                                                      Model Value       Practical Value
                                      Imax                2.55                2.08
                                     Vmax                 9.52               11.87
                                      Pmax                24.28              24.68

   This table depicts that the I-V and P-V simulation and experimental results show a good agreement in terms of current
at maximum point, voltage at maximum point and maximum power and also the error in maximum power is found to be
1.6% which is within the acceptable range of ±3% as specified in the manufacturer datasheet.

The simulated and experimental I-V and P-V characteristics of the solar PV module are shown in following Figures:




                            Simulated IV Curve                     Practical IV Curve

Volume 2, Issue 11, November 2013                                                                          Page 299
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
        Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 11, November 2013                                       ISSN 2319 - 4847




                           Simulated PV Curve                             Practical PV Curve

8. CONCLUSION
A generalized MATLAB/Simulink PV model to represent the performance of a PV cell has been developed and validated
in this paper and has been extended to model a PV module. The proposed model has been verified by comparing its
performance with a commercial module, PSS1237 available from Easy Photovoltaic Private Limited, Ghaziabad, (Uttar
Pradesh). The experimental results exhibited a good agreement with the simulation results. This paper also provides a
clear and concise understanding of the, I-V and P-V characteristics of PV module and the effect of change of Temperature
and Insolation levels on these characteristics. The proposed model is expected to serve as the basis model for carrying out
study by the researchers in the field of PV modeling.

REFRENCES
[1] G. Adamidis, G. Tsengenes and K. Kelesidis, “Three Phase Grid Connected Photovoltaic System with Active and
     Reactive Power Control using Instantaneous Reactive Power Theory”, Department of Electrical Engineering and
     Computer Engineering, Democritus University of Thrace, Spain, International Conference on Renewable Energies
     and Power Quality (ICREPQ’10) Granada (Spain), March 2010.
[2] H.L. Tsai, C.S. Tu, and Y.J. Su, “Development of Generalized Photovoltaic Model Using MATLAB/Simulink”,
     Proceedings of the World Congress on Engineering and Computer Science (WCECS ‘08) San Francisco (USA), 22nd
     to 24th October, 2008.
     http://www.iaeng.org/publication/WCECS2008/WCECS2008_pp846-851.pdf
[3] F.M.G. Longatt, “Model of Photovoltaic Module in Matlab”, 2nd International Conference on Iberoamerican
     Congress to Electrical Engineering Students, Electronics and Computing (II CIBELEC: 2005), Page(s): 1-5, 2005.
[4] S. Nema, R.K. Nema and G. Agnihotri, “MATLAB/Simulink Based Study of Photovoltaic Cells / Modules / Array
     and their Experimental Verification”, International Journal of Energy and Environment Vol.1, No. 3 Page(s): 487-
     500, 2010.
[5] R. Hernanz, C. Martín , Z. Belver, L. Lesaka, Z. Guerrero and P. Perez, “Modeling of Photovoltaic Module”,
     International Conference on Renewable Energies and Power Quality (ICREPQ’10) Granada (Spain), 23rd to 25th
     March, 2010.
[6] J.S. Kumari and C.H. Babu, “Mathematical Modeling and Simulation of Photovoltaic Cell using MATLAB/Simulink
     Environment”, International Journal of Electrical and Computer Engineering (IJECE) ISSN 2088-8708 Vol. 2, No.
     1, Page(s): 26 – 34, February 2012.
[7] H.G. Bhatt and R.A. Thakker, “Matlab Based Simulation of Photovoltaic Solar Cell and its Array at Different
     Temperature Values”, National Conference on Recent Trends in Engineering & Technology, B.V.M. Engineering
     College, Gujarat, Page(s): 1-4, 13-14 May 2011.
[8] B. Alsayid and J. Jallad, “Modeling and Simulation of Photovoltaic Cells/Modules/ Arrays”, International Journal of
     Research and Reviews in Computer Science (IJRRCS), ISSN 2079-2557 Vol. 2, No. 6, Page(s): 1327 – 1331,
     December 2011.
[9] S. Sheik Mohammed, “Modeling and Simulation of Photovoltaic Module using MATLAB/Simulink”, International
     Journal of Chemical and Environmental Engineering Vol. 2, No.5, Page(s): 350 – 355, October 2011.
[10] G. Richhariya and A. Pachori, “Modeling of Solar Cell” International Journal of Wind and Renewable Energy
     (IJWRE), Vol. No. 1 Issue 1 Page(s): 31-34, 2011.
[11] J.A.R. Hernanz, J.J. Campayo, J. Larranaga , E. Zulueta , O. Barambones, J. Motrico, U. Fernandez Gamiz, and I.
     Zamora, “Two Photovoltaic Cell Simulation Models in MATLAB/Simulink”, International Journal on Technical
     and Physical Problems of Engineering (IJTPE), ISSN 2077-3528 Vol. 4 No. 1 Issue 10 Page(s): 45-51, March 2012.
[12] N. Pandiarajan and Ranganath Mathu, “Mathematical Modeling of Photovoltaic Module with Simulink”,
     Department of Electrical & Electronic Engineering, SSN College of Engineering, TamilNadu, International
     Conference on Electrical Energy Systems (ICEES 2011), 3-5 Jan 2011.


Volume 2, Issue 11, November 2013                                                                            Page 300
 International Journal of Application or Innovation in Engineering & Management (IJAIEM)
        Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 11, November 2013                                       ISSN 2319 - 4847

[13] H.K Khyani (Under the guidance of Dr. J. Vajpai), “Modeling and Simulation of Solar Photovoltaic Systems”, M.E.
     Thesis, Electrical Engineering Department, Faculty of Engineering (M.B.M. Engineering College) JNV University,
     Jodhpur, Page(s):27-75, 2013.

[14] Solar PV Module [Online] Available: http://www.easyphotovoltech.com/solar-module.html


AUTHOR’S PROFILE:

            Dr. (Mrs.) Jayashri Vajpai is presently serving the Electrical Engineering Department of Jai Narain Vyas
            University, Jodhpur as Associate Professor. She is recipient of Sir Thomas Ward Memorial Gold Medal
            awarded by the Institute of Engineers and AICTE Career Award for Young Teachers. She has also won
            University Gold Medal and Seth Ram Kunwar Bangur Memorial Gold Medal. She has published more than a
            hundred papers in various International and National Journals, Conferences and Seminars. She is the reviewer
of several journals and on the editorial board of two International Journals. She is the presenter and subject expert of a
series of educational films on “Artificial Intelligence” being broadcast in the UGC Country-Wide Classroom Programme.
Her research interests include Soft Computing, Artificial Intelligence, Solar Energy Systems, Fault Diagnosis, Adaptive
Control and Image Processing. She has carried out several sponsored research projects in these areas.

            Harish Khyani, Associate professor, in EE Department, Jodhpur Institute of Engineering & Technology,
            Jodhpur received the B.E. degree in Electrical Engineering from Rajasthan University, Jaipur, Rajasthan,
            India in 2006 and M.E. degree in Control Systems from JNV University, Jodhpur, Rajasthan, India in 2013.
            His research interests are in the area of control systems, artificial intelligence, circuit analysis and synthesis
and solar energy systems. He has presented about 12 papers in various International and National onferences and Seminars.
He is a Life Member of the Indian Society of Technical Education.




Volume 2, Issue 11, November 2013                                                                               Page 301

				
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