International Journal of Advancements in Research & Technology, Volume 2, Issue 5, M ay-2013
ISSN 2278-7763
358
Modeling of PV Array and Analysis of Different Parameters
Subarto Kumar Ghosh1, Mohammad Hasanuzzaman Shawon2, Ashifur Rahman3 , Rifat Abdullah4
1
Lecturer at Daffodil International University, Dhaka, Bangladesh
Senior Lecturer at Daffodil International University, Dhaka, Bangladesh
3
Lecturer at Daffodil International University, Dhaka, Bangladesh
4
Lecturer at Daffodil International University, Dhaka, Bangladesh
E-mail: subarto@daffodilvarsity.edu.bd1
2
ABSTRACT
This paper defines a circuit-based simulation model for a PV array in order to allow and estimate the electrical behavior of a PV
array with respect changes on environmental parameter of temperature and irradiance. Taking the effect of sunlight irradiance,
cell temperature, shunt resistance and ideality factor into consideration the output current and power characteristics of PV model are simulated and optimized using the MATLAB/ simulink. An accurate PV array electrical model is presented based on the
Shockley diode equation. A particular typical 550W solar array was used for Standalone system analyzed.
Keywords : PV Modeling, Photovoltaic array, MATLAB simulink.
1 INTRODUCTION
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Photovoltaic’s (PVs) are arrays (combination of cells) that contain a solar voltaic material which converts solar energy into
electrical energy. PV cell is a basic device for Photovoltaic Systems. Such systems include multiple components like mechanical and electrical connections and mountings and various
means of regulating and (if required) modifying the electrical
output. Materials that are used for photovoltaic are monocrystalline silicon, polycrystalline silicon, microcrystalline silicon, cadmium telluride and copper indium selenide [1]. The
current and voltage available at the PV device terminals can be
directly used to feed small loads like lighting systems or small
DC motors. The output characteristics of PV module depends
on the solar irradiance, the cell temperature and output voltage of PV module. Since PV module has nonlinear characteristics, it is necessary to model it for the design and simulation of
maximum power point tracking (MPPT) for PV system applications. Almost all well-developed PV models describe the
output Characteristics mainly affected by the solar irradiance,
cell temperature, and load voltage [2]. The PV application can
be grouped depend the scheme of interaction with utility grid:
grid connected, stand alone, and hybrid.
processes. The monocrystalline and polycrystalline silicon
cells are the only found at commercial scale at the present
time. Silicon PV cells are composed of a thin layer of bulk Si or
a thin Si film connected to electric terminals. One of the sides
of the Si layer is doped to form the p–n junction. A thin metallic grid is placed on the Sunfacing surface of the semiconductor. Fig. 1 roughly illustrates the physical structure of a PV
cell. The incidence of light on the cell generates charge carriers
that originate an electric current if the cell is short circuited [4].
Char ges are generated when the energy of the incident photon is sufficient to detach the covalent electrons of the semiconductor—this phenomenon depends on the semiconductor
material and on the wavelength of the incident light [5].
2.2 Characterstics of Solar Cell
Solar cells naturally exhibit a nonlinear I-V and P-V characteristics which vary with the solar irradiation and cell temperature. The typical I-V and P-V characteristics of solar cell are
shown in figure 1.
The main contribution of this paper is the implementation
and modeling of a BP SX110 PV module in the form of
MATLAB Simulink on the basis of Shockley diode equation. .
2. BASIC PV CELL
2.1 Principles of Operation of Solar Cell
A photovoltaic cell is basically a semiconductor diode whose
p–n junction is exposed to light. Photovoltaic cells are made of
several types of semiconductors using different manufacturing
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Fig.1. Characteristics of solar cell
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International Journal of Advancements in Research & Technology, Volume 2, Issue 5, M ay-2013
ISSN 2278-7763
359
IV is maximum. Thus:
The fundamental parameters related to solar cell are short circuit current (I sc ), open circuit voltage (V oc ), maximum power
point (MPP), efficiency of solar cell and fill factor.
P max =V max . I max
2.2.1 Short Circuit Current
Short Circuit Current is the current corresponds to the short
circuit condition when the impedance is low and it is calculated when the voltage equals to zero.
P max =V oc .I sc . FF
(1)
I (at V=0) = I sc
I SC occurs at the beginning of the forward-bias sweep and is
the maximum current value in the power quadrant. For an
ideal cell, this maximum current value is the total current produced in the solar cell by photon excitation.
2.2.2 Open Circuit Voltage
Open Circuit Voltage is the voltage when the open circuit occurs and there is no current passing through the cell. The
Open circuit voltage is calculated when the voltage equals to
zero.
V (atI=0) = V oc
(2)
NKT
Iph
ln(
+ 1)
q
Io
(7)
Where FF is the fill factor given by Eq (4).
2.2.5 Efficiency
The solar cell power conversion efficiency can be
given as:
η=
P max V max . Im ax V max . Im ax
=
=
Pin
Pin
I (t ). Ac
(8)
Where Imax and Vmax are the current and voltage for maximum power, corresponding to solar intensity I(t).
3. MATHEMATICAL MODEL OF PV CELL
A general mathematical description of I-V output characteristics for a PV cell has been studied over the past four decades.
Such an equivalent circuit based model is mainly used for the
MPPT technologies. The equivalent circuit of the general model which consist of a photocurrent, a diode, a parallel resistor
expressing a leakage current, and a series resistor describing
an internal resistance to the current flow [8], is shown in Fig. 2
(3)
2.2.3 Fill Factor
The fill factor, also known as the curve factor is a measure of
sharpness of the knee in an I-V curve. It indicates how well a
junction was made in the cell and how low the series resistance has been made. It can be lowered by the presence of
series resistance and tends to be higher whenever the open
circuit voltage is high. The maximum value of the fill factor is
one, which is not possible. Its maximum value in Si is 0.88:
FF =
The maximum possible output can also be given as
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V OC is also the maximum voltage difference across the cell for
a forward-bias sweep in the power quadrant. Voc= Vm for
forward-bias power quadrant. The open circuit voltage can be
expressed as [7]:
Voc =
(6)
P max
V max
=
Voc.Isc Voc.Isc
(4)
A larger fill factor is desirable, and corresponds to an I-V
sweep that is more square-like. No power is generated under
short or open circuit.
The power output is defined as:
POUT =VOUT. IOUT
(5)
2.2.4 Maximum Power
The maximum power Pmax provided by the device is
achieved at a point on the characteristics, where the product
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Fig. 2: circuit diagram of the PV model [3]
The voltage current characteristic equation of a solar cell is
given as:
q.(V + IRs)
(V + IRs)
(9)
− 1) −
N .K .T
Rsh
Where, Iph is a light-generated current or photocurrent, Io is
the cell saturation of dark current, q (= 1.6 ×10−19C) is an electron charge, k (= 1.38 ×10−23J/K) is a Boltzmann’s constant, T is
the cell’s working temperature, N is an ideal factor, R sh is a
shunt resistance, and Rs is a series resistance. Photo current
mainly depend on the solar irradiance and cell’s temperature,
which is described as
(10)
Iph = ( Iscr + Ki * ( Ic + 273.15 − Tr )) * G
I = Iph − Io(exp
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International Journal of Advancements in Research & Technology, Volume 2, Issue 5, M ay-2013
ISSN 2278-7763
360
Where, Iscr is a cell’s short current at a 250c and 1kw/m2, Ki is
a cell’s short circuit current temperature coefficient, Tr cell’s
reference temperature, G solar irradiance in kw/m2.
Also the cell’s saturation current varies with cell temperature,
which is described as
Io = I oR * (
Tc 3
) * exp(
Tref
Tc = (( NOCT − 20) *
1
1
− )
Tref Tc
)
K .N
q * Eg (
G
) + (Ta )
0.8
(11)
(12)
Where, I OR is the cell reverse saturation current at a reference
temperature and a solar irradiance, NOCT is a nominal operating cell temperature, eg is the band gap energy of the semiconductor used in the cell. The ideality factor N dependent on
PV technologies. The complete behavior of PV cells are described by five model parameters (Iph, N, I s , R sh ) which is representative of a physical PV cell/module. These five parameters of PV cell/module are in fact related to two environmental
parameters of solar irradiance & temperature and owing to
non-linear nature of Eq. (11).
Fig.3 Simulation model for calculation of Iph
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4. PV CELL MODELLING
A PV array model based on the mathematical model of solar
cell is developed using MATLAB/Simulink blocks [9]. The
essential input parameters such as V m , I m , V oc , I sc , N s , KI, T c
and G are taken from the manufacturer’s datasheet for the
typical 110W modules selected for analysis for standalone system
TABLE 1
Specification of the simulated module
Parameter
Variable
Value
Maximum power
Pm
110W
Voltage@ Pm
Vm
32.9V
Current@ Pm
Im
3.34A
Short circuit current
Isc
3.69A
Open circuit voltage
Voc
41.2V
Temp. coeff of Voc
β
-0.38%/0c
Temp. coeff of Isc
α
0.065%/0c
NOCT
470C
Normal operating
cell temperature
Fig. 4: Simulation model for Calculation of Is
The performance of solar cell is normally evaluated under the
standard test condition (STC), where an average solar spectrum at AM 1.5 is used, the irradiance is normalized to
1000W/m2, and the cell temperature is defined as 25 ºC.
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Fig. 5: Simulation model for standalone PV array system
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International Journal of Advancements in Research & Technology, Volume 2, Issue 5, M ay-2013
ISSN 2278-7763
5. SIMULATION RESULT
The blocks of the model are developed using MATLAB
/Simulink based on Equation (9).The BP SX110 PV modules
are chosen for modeling. The typical electrical characteristics
of BP SX110 are given in table 1. These modules consist of 72
polycrystalline silicon solar cells electrically configured as two
series strings of 36 cells each. The blocks developed using
MATLAB/simulink for the PV module is shown in figures 3,4,
and 5.
The I-V characteristics and P-V characteristics curves obtained from the simulation for BP SX110 PV modules at
Tc=25°C (298.15 °K) and G=1 are presented in figures 6, 7, 8, 9,
10, 11, 12 and 13
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5.2 Variation of Ideality Factor
Fig. shows ‘V-I & PV characteristics’ of a PV cell for three different values of N corresponding to 1, 1.25 & 1.50 respectively.
It can be observed that as we increase the value of N the open
circuit voltage of cell decreases and this fact may effectively be
used in simulation of a PV module
5.1 Variation of Solar Irradiance
The two environmental conditions of Solar Irradiance and
Temperature govern output of a PV Cell. The
Matlab/simulink is used to demonstrate behavior of PV module under varying solar irradiance. The photon generated current I ph is in fact related with solar Irradiance G as in Eq. (10).
The output of the Matlab/simulink function is shown various
irradiation levels
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Fig. 8: variation of IF (V vs I)
Fig. 6: variation of Ir (V vs I)
Fig. 9: variation of N (Ideality factor) (V vs P)
Fig. 7: variation of Ir (V vs P)
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5.3 Variation of Shunt Resistance
The simulation is produced for two different values of Rsh as
10 Ω., 50 Ω and 1 kΩ. It is observed that the smallest value of
Rsh causes PV module current to fall more steeply indicating
higher power loss and low Fill Factor. The resultant V-I characteristics curve is shown below
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International Journal of Advancements in Research & Technology, Volume 2, Issue 5, M ay-2013
ISSN 2278-7763
Fig. 10: variation of Rsh (V vs I)
362
Fig. 12: variation of Tc (V vs I)
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Fig. 13: variation of Tc (V vs P)
Fig. 11: variation of Rsh (V vs P)
5.4 Variation of Operating Temperature
The effect of varying temperature on PV cell output is twofold:
(i) It affects short circuit current ‘I sc ’ of Cell (ii) It changes saturation current of the diode in PV cell approximately as cubic
power. Obviously from Eq. (11) the saturation current of diode
of PV Cell is highly temperature dependent and it increases
with increase in temperature and is taken care by
Matlab/Simulink. To study the effect of Temperature variation on PV Module output
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International Journal of Advancements in Research & Technology, Volume 2, Issue 5, M ay-2013
ISSN 2278-7763
363
6. CONCLUSION
In this paper, a PV array has been modeled in
MATLAB/SIMULINK environment. A generalized mathematical description of a PV array has been followed in order to
model PV array. Four parameters are chosen in order to characterize PV array. These four parameters are solar irradiation,
cell operation temperature, shunt resistance and ideality factor. Finally this paper presents a comprehensive analysis of
different parameters for a PV array. This study will be extended in focus of grid connected PV system in future research
area.
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