Mathematical Modeling and Simulation of Photovoltic Array

Amit Kumar Sharma. et. al. Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 6, Issue 3, (Part - 6) March 2016, pp.74-76
www.ijera.com 74|P a g e
Mathematical Modeling and Simulation of Photovoltic Array
Amit Kumar Sharma*, Ravinder Singh Chauhan**, Gaurav Rajoria**
*Department of Electrical Engineering, Rajasthan Technical University, Kota, India
** Department of Electrical Engineering, Jaipur National University, Jaipur, India
ABSTRACT
With the increasing demand of power and depleting resources, PV based power system has been a ray of hope
for the future energy scenario. The non-linear V-I Characteristics of PV module depends on solar irradiance and
other environmental factors. This paper deals with power electronics based simulation model for photovoltaic
integrated module. The model includes the real time behavior of the PV module. Detailed simulink modeling for
PV module along with numerical values has been presented. The simulation model has been verified for 36 W
PV modules. The proposed model has been found to exhibit better and accurate result for any irradiance and
temperature variations
.Keywords – Photovoltic Module, Simulink Model, V-I Characteristics
I. INTRODUCTION
A photovoltaic (PV) module converts
solar energy into electrical energy. The basic
components of a photovoltaic module include
photovoltaic cell, DC-DC converter, storage
battery, etc. PV cells includes grouped/individual
panels or modules, depending on the requirement
and rating of the system under consideration.
Panels can be grouped to form large photovoltaic
arrays. The term array is usually employed to
describe a photovoltaic panel (with several cells
connected in series and/or parallel) or a group of
panels. Most of time one are interested in modeling
photovoltaic panels, which are the commercial
photovoltaic devices. This paper focuses on
modeling photovoltaic modules or panels
composed of several basic cells. The term array
used henceforth means any photovoltaic device
composed of several basic cells. In the Appendix at
the end of this paper there are some explanations
about how to model and simulate large
photovoltaic arrays composed of several panels
connected in series or in parallel.
I. Modeling Of Photovoltic Arra
1.1 Ideal Photovoltic Cell
Fig. 1 shows the equivalent circuit of the
ideal photovoltaic cell. The basic equation from the
theory of semiconductors [1] that mathematically
describes the I-V characteristic of the ideal
photovoltaic cell is:
I= )-1 (1)
= )-1
where Ipv,cell is the current generated by the
incident light (it is directly proportional to the Sun
irradiation), Id is the Shockley diode equation,
I0,cell [A] is the reverse saturation or leakage
current of the diode [A], q is the electron charge
[1.60217646 ・ 10−19C], k is the Boltzmann
constant [1.3806503 ・ 10−23J/K], T [K] is the
temperature of the p-n junction, and a is the diode
ideality constant. Fig. 2 shows the I-V curve
originated from (1).
1.2 Modeling the Photovoltic Array
The basic equation (1) of the elementary
photovoltaic cell does not represent the I-V
characteristic of a practical photovoltaic array.
Practical arrays are composed of several connected
photovoltaic cells and the observation of the
characteri tics at the terminals of the photovoltaic
array requires the inclusion of additional
parameters to the basic equation [1]:
Fig. 1 Single-diode model of the theoretical
photovoltaic cell and equivalent circuit of a practical
photovoltaic device including the series and parallel
resistances.
RESEARCH ARTICLE OPEN ACCESS

Fig. 2 Characteristic I-V curve of a practical photovoltaic
device and the three remarkable points: short circuit (0,
Isc), maximum power point (Vmp, Imp) and open-circuit
(Voc, 0).
I= [exp ( )-1] - (2)
Where Ipv and I0 are the photovoltaic and
saturation currents 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 current and cells connected in series
provide greater output voltages. If the array is
composed of Np parallel connections of cells the
photovoltaic and saturation currents may be
expressed as: Ipv=Ipv,cellNp, I0=I0,cellNp. In (2)
Rs is the equivalent series resistance of the array
and Rp is the equivalent parallel resistance. This
equation originates the I-V curve seen in Fig. 3,
where three remarkable points are highlighted:
short circuit (0, Isc), maximum power point (Vmp,
Imp) and open-circuit (Voc, 0).The light generated
current of the photovoltaic cell depends linearly on
the solar irradiation and is also influenced by the
temperature according to the following equation
[6]:
(3)
Where Ipv,n [A] is the light-generated current at
the nominalcondition (usually 25 ◦C and
1000W/m2), T = T – Tn(being T and Tn the
actual and nominal temperatures [K]), G [W/m2] is
the irradiation on the device surface, and Gn is the
nominal irradiation.The diode saturation current I0
and its dependence on the temperature may be
expressed by (4) [3]
exp[q ( )] (4)
where Eg is the bandgap energy of the
semiconductor (Eg ≈ 1.12 eV for the
polycrystalline Si at 25 ◦C [4], [3]), and I0,n is the
nominal saturation current:
(5)
with Vt,n being the thermal voltage of Ns series-
connected cells at the nominal temperature Tn.
1.3 Improving the Model
The photovoltaic model described in the
previous section can be improved if equation (4) is
replaced by:
= (6)
This modification aims to match the open-
circuit voltages of the model with the experimental
data for a very large range of temperatures. Eq. (6)
is obtained from (5) by including in the equation
the current and voltage coefficients KV and KI.
II. SIMULATION MODELS AND
RESULTS OF THE PHOTOVOLTIC
ARRAY
Fig.3 shows the photovoltaic model circuits
implemented with MATLAB/SIMULINK (using
the SymPowerSystems blockset) circuit models
work perfectly and may be used in the simulation
of power electronics converters for photovoltaic
systems.
Fig. 3 Photovoltic Circuit Model built with
MATLAB/SIMULINK

I-V curve of solar array plotted by varying
voltage applied across the solar array and
measuring the corresponding current flowing
through it
P-V characteristics Similarly, an accurate P-
V curve obtained by varying voltage across the
solar array and values of power recorded on X-Y
plot as shown in figure
III. CONCLUSION
This paper has analyzed the development
of a method for the mathematical modeling of
photovoltaic arrays. The objective of the method is
to fit the mathematical I-V equation to the
experimental remarkable points of the I-V curve of
the practical array. The method obtains the
parameters of the I-V equation by using : open-
circuit voltage, short-circuit current, maximum
output power, voltage and current at the maximum
power point, current/temperature and
voltage/temperature coefficients.
REFERENCES
[1] H. S. Rauschenbach. Solar cell array
designhandbook. Van Nostrand Reinhold,
1980.
[2] J. A. Gow and C. D. Manning.
Development of a photovoltaic array
model for use in power electronics
simulation studies. Electric Power Applic
tions, IEE Proceedings, 146(2):193–200,
1999.
[3] N. Pongratananukul and T. Kasparis. Tool
for automated simulation of solar arrays
using general-purpose simulators. In Proc.
IEEE Workshop on Computers in Power
Electronics, p. 10–14, 2004.
[4] J. Hyvarinen and J. Karila. New analysis
method for crystalline silicon cells. In
Proc. 3rd
World Conference on
Photovoltaic Energy Conversion, v. 2, p.
1521–1524, 2003.
[5] Jenifer A., Newlin Nishia R., Rohini G.,
Jamuna V., “Development of MATLAB
Simulink Model for Photovoltaic Array”,
Proc. of IEEE International Conference on
Computing, Electronics and Electrical
Technologies , pp. 436-442, 2012
[6] Balakrishna S., Nabil A., Rajamohan G.,
Kenneth A. S., Ling C. J., “The Study and
Evaluation of MPPT Systems”, Proc. of
International Conference on Energy and
Environment, Malaysia, 2006
[7] D.S. Chan, Theory and implementation of
multidimensional discrete systems for
signal processing, doctoral diss.,
Massachusetts Institute of Technology,
Cambridge, MA, 1978.

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