1. IJEEE, Vol. 1, Issue 5 (October, 2014) e-ISSN: 1694-2310 | p-ISSN: 1694-2426
SIMULATION MODEL FOR PV ARRAY &
ITS CHARACTERISTICS
1Ekta, 2Maninder Kaur
1,2Electrical Department, Baba Banda Singh Bahadur Engineering College, Punjab, India
1ekku14@gmail.com, 2maninder.thakur@bbsbec.ac.in
Abstract—This paper presents the implementation of a
photovoltaic model using Matlab software, which can be
representative of PV cell module, and array for easy use
on simulation. The proposed model is designed with a
user-friendly icon and a dialog box like Simulink block
libraries. This makes the PV model easily simulated and
analyzed in conjunction with power electronics for a
maximum power point tracker. Taking the effects of
sunlight irradiance and cell temperature into consideration,
the output power and current characteristics of PV model
are simulated. This enables the dynamics of PV power
system to be easily analyzed, simulated and optimized.
Index Terms-photovoltaic model, Matlab-Simulink.
I. INTRODUCTION
With increasing concerns about fossil fuel deficit, sky
rocketing oil prices, global warming, and harm to
ecosystem and environment, the promising incentives to
develop alternative energy resources with high efficiency
and low emission are imperative. Among the renewable
energy resources, the energy through the photovoltaic (PV)
effect can be considered the most essential and pre
requisite sustainable resource because of the easy and
unending availability, and sustainability of solar energy[1].
Regardless of intermittency of the sunlight, solar energy is
widely available in the environment and completely free of
cost. Recently, photovoltaic array system is likely
recognized and widely utilized to the forefront in electric
power applications. It can generate DC electricity without
environmental impact and contamination when is exposed
to solar radiation. Being a semi conductive device, the PV
system is static, quite, and no moving parts, and these
make it have little operation and maintenance costs. Even
though the PV system is having high capital fabrication
cost and low conversion efficiency, the sky rocketing oil
prices make solar energy naturally viable energy supply
with potentially long-lasting benefits. PV module
represents the main power conversion unit of a PV
generator system. The output characteristics of a
photovoltaic module depends on
the solar insolation, cell temperature and output voltage of
PV module as we know that PV module has nonlinear
characteristics, it is beneficial to model it for the design
and simulation of maximum power point tracking
(MPPT)[9,10] for PV system applications. Almost all well-developed
PV models describe the output characteristics
mainly affected by the solar insolation, load voltage and
cell temperature. However, the equivalent circuit models
are implemented on simulation. However, the
SimPowerSystem tool in Matlab-Simulink package offers
wind turbine models but no PV model to integrate with
current electronics simulation. Thus, it is difficult to
simulate and analyse in the modeling of PV power system.
This motivated me to develop a model for PV cell,
array[1,2], and module using Matlab-Simulink. The main
feature of this paper is the implementation of a PV model
in the form of masked block, which has a user-friendly
dialog and icon in the same way of Matlab block libraries.
Recent works done by Ciobotaru (2007), Pandiarajan
(2012) and Jamri (2010), respectively [2], [3] and [4],
revealed some basic aspects of photovoltaic cell modelling.
They have adopted similar model of solar cell and carried
out some simulation works on their output characteristics
including power vs voltage and current vs voltage using
MATLAB/Simulink[10,11]. The output characteristics[8]
are similar showing a power that increases proportionally
to the voltage from an initial stage up to a certain threshold
after which it decreases rapidly down to zero.
II. PHOTOVOLTAIC MODEL AND ITS
GOVERNING EQUATIONS
Solar Energy is a good choice for electric power generation
and electromagnetic radiation of solar energy directly
converted into electrical energy by solar photovoltaic
module. Solar Module consists of solar cell. Solar cell is
basically a p-n junction fabricated in a thin wafer or layer
of semiconductor. The photovoltaic modules are made up
of silicon cells. The silicon solar cells gives output voltage
of around 0.7V under open circuit condition. When large
many such cells are connected in series we get a solar PV
module. Generally there are 36 cells in a module which
amounts for an open circuit voltage of approx 20V. The
current ratings of the modules depends on the area of the
individual cells. Higher the cell area, higher is the current
output of the cell, to obtain higher power output, the solar
PV modules are connected in series and parallel
combinations forming solar PV arrays. When exposed to
the sunlight, photons with energy higher than the band-gap
energy of the semiconductor are absorbed and create some
electron-hole pairs proportional to the incident irradiation.
With the influence of the internal electric fields of the p-n
junction, these carriers are pulled apart and creates a photo
current which is proportional to solar isolation.
Fig. 1: Equivalent electrical circuit of a PV device
International Journal of Electrical & Electronics Engineering ,6 www.ijeee-apm.com

2. PV system naturally exhibits a nonlinear V-I and P-V
characteristics which vary with the insolation and cell
temperature are shown as in Fig 2.a and Fig 2.b. Electrical
characteristic of PV module (Standard radiance level of
1000 W/m2).
Figure2.a V-I characteristic of PVmodule.
Figure2.b P-V characteristic of PV module
A general mathematical description of V-I output
characteristics for a PV cell has been studied for over past
four decades. An equivalent circuit-based model is mainly
used for the MPPT[2,3,10] technologies which consists of
a photo current, a parallel resistor, a diode, expressing a
leakage current and a series resistor denoting an internal
resistance to the current flow, is shown in Fig 1. The V-I
characteristic[8] equation of a solar cell is given as
I = Ipv, cell – Id (1)
Ipv, cell − Io, cell exp − 1 (2)
where Ipv, cell = Current generated by the Incident light
Id = Schottky diode equation,
Io, cell = Reverse Saturation or Leakage current of the diode,
q = Electron charge,
k = Boltzmann constant (1.3806503 × 10−23 J/K),
T(K) = Temperature of the P–N junction,
a = Diode ideality Constant.
III. BASIC V-I CHARACTERISTIC OF A
PRACTICAL PV DEVICE
In case of Practical PV Device Series Resistance (Rs) and
Parallel Resistance (Rp) of device are considered
as shown below
I=Ipv,cell−Io, cell exp − 1 − (3)
V = N ∗ ( ) Is Thermal Voltage
Ns = cells connected in series.
Generally, Series resistance, Rs, is assumed low and
parallel resistance, Rp, is assumed high.
Variation of Ipv with Temperature & Insolation[5,6]
I = I , n + K Δ ∗ (4)
PV Device depends linearly on the solar irradiation and the
temperature as shown above Equation (4).
Standard conditions are considered as follows
Where Tn = 25 ◦C and Gn =1000 W/m2
ΔT = T − Tn I , n = Nominal current
T = Actual Temperature,
Tn = nominal temperatures [K],
G = Actual irradiation (W/m2)
Gn = Nominal irradiation (W/m2)
Reverse saturation Current is calculated as (5)
I = , Δ
Δ (5)
Minimum Value of Parallel Resistance, Rp
V
Rp, min =
I , n + Imp
+
V , n + V
I_mp
(6)
I , n = I . n (7)
Where Isc,n = Nominal Current (short circuit)
Voc,n = Nominal Voltage (open circuit )
Vmp = Maximum Power Point Voltage
Imp = Maximum Power Point Current
Kv= Voltage Temperature Coefficient Ki=Current
Temperature Coefficient
Maximum value of Power is defined as
V + R I
Pmax, m = V I − exp
aV
− 1
−
V + R I
aV
= Pmax, e (8)
Basically, Pmax, m − Pmax, e = 0 (9)
Parallel Resistance (Rp) is defined as
Rp= ( )
{ _ , }
(10)
Where P max, e =Estimated power V = N ∗
IV. SIMULATION AND ANALYSIS OF PV MODEL
WITH ITS V-I AND P-V CHARACTERISTICS
The output V-I and P-V characteristics after simulation are
obtained as shown in Fig 3.
Figure 3: Simulated model of PV module with its V-I and PV
characteristics
Solar Module and Array Model
Since a PV cell produces less than 2W at 0.5V
approximately, the cells are connected in series-parallel
combinations on a module to produce enough high power.
The equivalent circuit for the solar module arranged in NP
parallel and NS series which is denoted by following
equations. The general equation for the current and voltage
of the array becomes
as follows.
www.ijeee-apm.com International Journal of Electrical & Electronics Engineering 7

3. I = NP IPH − NP IS[exp(q(V / NS + IRS / NP ) / kTCA)−1]−
(NPV / NS + IRS )/RSH
In fact, the PV efficiency is sensitive to small change in RS
but insensitive to variation in RSH . For a PV module or an
array, the series resistance becomes apparently imperative
and the shunt resistance approaches infinity which is taken
to be open. In many commercial PV products, these cells
are generally connected in series configuration to form a
PV module in order to obtain enough voltage. PV modules
are then arranged in series-parallel structure to achieve
desired higher power output. It can be shown that NS = NP
= 1 for a PV cell, NP =1 and Ns : series number of cells for
a PV module, and Ns and Np : series-parallel number for a
array of PV.
The mathematical equation of this model can be described
as
I = NP IPH − NP IS[exp(q(V / NS + IRS / NP ) / kTCA)−1]
The equivalent circuit is described on the following
equation
I = NP I PH − NP IS [exp(qV/NSkTC A)−1]
Simulation Model of PV array With its V-I And P-V
Characteristics
The PV simulated model of PV array with 6 PV modules
connected in series and its output V-I and P-V
characteristics are shown in Fig 4
Figure 4: Simulated model of PV array with its V-I and PV
characteristics
V. CONCLUSION
In summary, this paper dealt with the modelling of solar
energy conversion through photovoltaic effect. An
analytical model presented is constructed under Matlab-
Simulink and simulated for two effects: varying irradiance
and varying temperature. Finally, simulation results show
that more irradiance greatly increase the generation of
energy while big variation of temperature reduces the
current and power produced. This results obtained in form
of two fundamental graphs namely power characteristic
(power over voltage) and current characteristic (current
over voltage) are very similar to empirical results known
for solar system and this, further confirms the effectiveness
of the proposed model.
REFERENCES
[1] Alsayid, B., and Jallad, J. 2011. Modeling and
Simulation of Photovoltaic Cells Module Arrays.
International Journal of Research and Reviews in Computer
Science (IJRRCS). Vol. 2, No. 6, pp. 1327-1331.
[2] Gow, J. A. and Manning, C. D. 1999.
Development of a Photovoltaic Array Model for Use in
Power-Electronics Simulation Studies. IEEE Proceedings of
Electric Power Applications. Vol. 146, No. 2, pp. 193–200.
[3] Pandiarajan, N., Ramaprabha, R., and Muthu. R. 2012.
Application of Circuit Model for Photovoltaic Energy
Conversion System. Hindawi Publishing Corporation:
International Journal of Photo Energy, ID410401, 14 p.
[4] Jamri, M., S., and Wei, T., C. 2010. Modeling and
Control of a Photovoltaic Energy System Using the State
Space Averaging Technique. American journal of Applied
Sciences. ISSN 1546-9239. pp. 682-691.
[5] S. Rustemli, F. Dincer, Modeling of Photovoltaic Panel and
Examining Effects of Temperature in Matlab/Simulink.
[6] Kumar A., Kumar K., Kaushik N., Sharma S., Mishra S.
Renewable energy in India: Current status and future
Potentials // Renewable and Sustainable Energy Reviews. –
Elsevier, 2010. – No. 14(8). – P. 2434–2442.
[7] Gomez-Amo J. L., Tena F., Martı´nez-Lozano J. A.,
Utrillas M. P. Energy saving and solar energy use in the
University of Valencia (Spain) // Renewable Energy. –
Elsevier, 2004. – No. 29(5). – P. 675–685.
[8] B.K. Nayak, A.Mohapatra, B.Misra; Non Linear I-V Curve
Of PV Module: Impacts On MPPT And Parameters
Estimation
[9] Kinal Kachhiya; MATLAB/Simulink Model of Solar PV
Module and MPPT Algorithm.
[10] E.M. Natsheh, A. Albarbar. “photovoltaic model with MPP
tracker for standalone / grid connected applications”(2010)
International Journal of Electrical & Electronics Engineering ,8 www.ijeee-apm.com