40220140505003

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

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

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)

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.

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

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.

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.

40220140505003

More Related Content

What's hot

Viewers also liked

Similar to 40220140505003

More from IAEME Publication

Recently uploaded

40220140505003