International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 3, March 2013)
Modelling and Simulation of photovoltaic module considering
single-diode equivalent circuit model in MATLAB
Dominique Bonkoungou1, Zacharie Koalaga2, Donatien Njomo3
1,2
Laboratory of Materials and Environment (LAME)/ Faculty of Sciences/ University of Ouagadougou/P.O. Box 7021
Ouagadougou/ Burkina-Faso
1,3
Environmental Energy Technologies Laboratory (EETL)/ Faculty of Sciences/ University of Yaounde 1/ P.O. Box 812
Yaounde/ Cameroon
Among these methods, in view of its quadratic
convergence and enhanced accuracy, Newton Raphson’s
method remains attractive with the number of variables
being limited to five parameters and their partial
derivatives easily obtainable. In this work, we elaborate a
MATLAB script file program, which uses Newton
Raphson’s method to compute the five parameters of the
single diode model of illuminated solar cells. The results
obtained by simulation show the consistency between the
data and obtained the parameters given by the
manufacturer, namely: short circuit current (I SC), open
circuit voltage (VOC) and maximum power point (Pmpp). For
instance, these parameters can be used for quality control
during production or to provide insights into the operation
of the devices, thereby leading to improvements in devices.
Abstract— This paper presents a photovoltaic (PV) cell to
module simulation model using the single-diode five
parameter models. The model was implemented in MATLAB
software and the results have been compared with the data
sheet values and characteristics of the PV module in Standard
Test Conditions (STC). Parameters values were extracted
using Newton Raphson’s method from experimental Current
(I)-Voltage (V) characteristics of Solarex MSX60 module. The
results obtained are in good agreement with the experimental
data provided by manufacturer. The approach can thus, be
very useful for researchers or engineers to quickly and easily
determine the performance of any photovoltaic module.
Keywords—
Matlab
Photovoltaic, Simulation,
software,
Newton
Raphson,
I. INTRODUCTION
An accurate knowledge of solar cell parameters from
experimental data is of vital importance for the design of
solar cells and for the estimates of their performance. Thus,
different solar cell models have been developing to
describe their electrical behavior, but the electrical
equivalent circuit is a convenient and common way in most
simulation studies. The five parameters of interest in the
equivalent circuit are the photo-current (IPV), series
resistance (RS), diode saturation current (I0), parallel
resistance (RSH) and the ideality factor (A). The currentvoltage relationship of a solar cell is described by a
mathematical equation that is both implicit and nonlinear,
therefore; the evaluation of these parameters has been the
subject of investigation of several authors. While some
authors use numerical analysis methods to solve the
implicit nonlinear equation of I-V relation [1-3], others use
analytical methods with a series of simplifications and
approximations [4-6].
II. MODELLING OF PHOTOVOLTAIC MODULE
Solar cell is basically a p-n junction fabricate in a thin
wafer or layer of semiconductors. The electromagnetic
radiation of solar energy can be directly converted to
electricity through photovoltaic effect [7].
When exposed to sunlight, photons with energy greater
than the band-gap energy of the semiconductor are
absorbed and create some electron-hole pair proportional to
the incident irradiation. Under the influence of the internal
electric fields of the p-n junction, these carriers are swept
apart and create a photocurrent which is directly
proportional to solar irradiation [8]. Naturally, PV system
exhibits a nonlinear current-voltage (I-V) and powervoltage (P-V) characteristics which vary with the radiant
intensity and cell temperature. The dependence of power
generated by a PV array with changing atmospheric
conditions can readily be seen in the I-V and the P-V
characteristics of PV arrays as shown in figure 1.
493
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 3, March 2013)
II-1. Ideal Photovoltaic model
To develop an accurate equivalent circuit for a PV cell,
it is necessary to understand the physical configuration of
the elements of the cell as well as the electrical
characteristics of each element. The ideal equivalent circuit
of a PV cell is a current source in parallel with a singlediode. The configuration of the simulated ideal solar cell
with single-diode is shown in figure 2 [9].
20
18
1000 W/m2
16
T= 28°C
14
Array Current (A)
800 W/m2
T=56°C
12
2
600 W/m
10
I
8
400 W/m2
6
ID
4
200 W/m2
2
0
0
5
10
15
20
25
30
35
40
45
V
D
IPV
G
50
Output-Voltage (V)
a) I-V characteristics at various irradiance and temperatures
(T = 28°C & 56°C)
Fig.2: Ideal PV cell with single-diode
The equation for the output current is given by:
350
I  I PV  I D
300
1000 W/m2

 V
I D  I 0 exp 
 AV
T


Where
250
Array Power (Watt)
800 W/m2
T=28°C
600 W/m2
200
Then equation (1) becomes:
T=56°C
400 W/m2
150

 V
I  I PV  I 0 exp 
 AV
T


200 W/m2
100



  1


(2)
I PV is the current generated by the incidence of light;
50
0



  1 (1)


0
5
10
15
20
25
30
35
I0
40
is
Output-Voltage (V)
VT 
b) P-V characteristics at various irradiance and temperatures
(T = 28°C & 56°C)
the
diode
reverse
bias
saturation
current;
Ns * k * T is the thermal voltage of a PV module
q
having Ns cells connected in series; q is the electron
charge; k is the Boltzmann constant; T is the temperature of
the p-n junction and A the diode ideality factor.
A PV cell can at least be characterized by the short
circuit current (ISC); the open circuit voltage (VOC) and the
ideality factor A. The output of current source is directly
proportional to the light falling on the cell. For the same
irradiance and p-n junction temperature conditions, the
short circuit current (ISC) is the greatest value of the current
generated by the cell [10].
The short current is given by:
Fig.1: Simulated characteristics of photovoltaic array.
The nonlinear nature of PV systems is apparent from
fig.1. We note that the array current and power depend on
the array terminal operating voltage. Fig.1 illustrates the
dependence of I-V characteristics on temperature and
irradiance for a sample module. The trends evident in these
plots are similar for other PV module, namely, the strong
effect of irradiance on short circuit current and of
temperature on open circuit voltage, and the weaker effect
of irradiance on open circuit voltage and of temperature on
short circuit current.
For V=0, ISC = I = IPV (3)
494
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Likewise, for the same irradiance and p-n junction
temperature conditions, the open circuit voltage (VOC) is
the greatest value of the voltage at the cell terminals and it
can be written as:


I
V  VOC  A * VT ln 1  SC 
I0 



I
V  VOC  A * VT ln 1  SC 
I0 



 V  I * RS

P  V  I SC  I 0 exp 

 A *VT


For I = 0




  1 



(4)
(5)
RS
V
D
G
Fig.3: PV circuit model with single-diode and series resistance
For the same irradiation and temperature conditions, the
inclusion of a series resistance in the model implies [11]
the use of a recurrent equation to determine the output
current in function of the terminal voltage. The I-V
characteristics of the solar cell are given by [12]:
I  I PV

 V  I * RS
 I 0 exp 
 A *V
T





  1


I
ID
I SC  I  I PV
  for V = 0
  1
 
ISH
RS
(6)
IPV
D
RSH
V
G
A simple iterative technique initially tried only
converged for positive current [13]. The Newton Raphson’s
method converges more rapidly and for both positive and
negative currents [14]. In this case, the short circuit current
ISC is given by:

 I * RS
 I 0 exp  PV
 A *VT

(9)
II.3.1. Photovoltaic model with single-diode, series and
parallel resistances
Photovoltaic cell models have long been a source for the
description of photovoltaic cell behavior. The most
common model used to predict energy production in
photovoltaic cell modeling is the single diode lumped
circuit model [15]. In the single diode model, there is a
current source parallel to a diode. The current source
represents light-generated current IPV that varies linearly
with solar irradiation. This is the simplest and most widely
used model as it offers a good compromise between
simplicity and accuracy [16, 17]. Figure 4 shows the single
diode equivalent circuit model of PV cell which is
commonly used in many studies and provides sufficient
accuracy for most applications.
I
IPV



  1 



II.3. Photovoltaic model with series and parallel
resistances
The PV model devices are basically represented in two
different models with series and parallel resistances:
Single-diode model with series and parallel resistances and
double diode model with series and parallel resistances
II.2. Photovoltaic model with single-diode and series
resistance
More accuracy and complexity can be introduced to the
previous model by adding a series resistance. The circuit
diagram of this model is shown in figure 3.
ID
(8)
And the output power is given by:
And at the same conditions, the output power is given
by:



V

P  V  I SC  I 0 exp 
 A *V

T



for I = 0
Fig.4: PV circuit model with a single-diode, series and parallel
resistances
As mentioned previously, equation (6) doesn’t
adequately represent the behavior of the cell when
subjected to environmental variations, especially at low
voltage [14].
A more practical model can be seen in figure 4, where
RS represents the equivalent series resistance and RSH the
parallel resistance. According to [18] and based on the
equivalent circuit of a photovoltaic panel, its characteristic
equation is deduced.
(7)
Normally the series resistance is small and negligible in
computing (eq.7). Hence, it uses equation (2) as a good
approximation of equation (7).The open circuit voltage VOC
can be written as:
495
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Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 3, March 2013)
  V  I * RS
I  I PV  I 0 exp 
  A *VT
   V  I * RS
  1  
   RSH



I 01 is the reverse saturation current due to
diffusion; I 02 is the reverse saturation current due to
recombination in the space charge layer. A1  1 is the
diode D1 ideality factor and A2  1.2 is the diode D2
Where
(10)
This model yields more accurate result than the PV
model with series resistances RS but at the expense of
longer computational time.
ideality factor. All others parameters are explained
previously.
The light-generated current of the module depends
linearly on solar irradiation and is also influenced by
temperature [15, 21] according to equation (15):
II.3.2. Photovoltaic model with two diode, series and
parallel resistances
In this model, an extra diode is attached in parallel to the
circuit of single-diode model (fig.4).This diode is included
to provide a more accurate I-V characteristic curve that
considers for the difference in flow of circuit at low current
values due to charge combination in the semiconductor’s
depletion [19, 20].
I PV  I PV ,n  K i * T *
IPV
ID1
ID2
ISH
(15)
I PV ,n is the light-generated current of the
Where
I
G
Gn
module at Standard Test Conditions (STC).
The diode saturation current I 0 dependence on
RS
RSH
temperature can be expressed by [16]:
V
3
 q * Eg
T 
I 0  I 0,n *  n  * exp 
T 
 A* K
G
Fig.5: PV circuit model with two-diode, series and parallel resistances
Where
The accuracy of these models is more than the singlediode model but there are some difficulties to solve the
equation. For simplicity, the single diode model of fig.4 is
preferred and is used in this work. The basic equation (6) of
two-diode model of the PV cell is given by the following
equation:
I  I PV  I D1  I D 2
where I
D1


  1





  1


 1.12 eV for the polycrystalline Silicon at 25°C)
I 0,n the nominal saturation current
expressed by equation (17) at Standard Test Condition
(STC) [16].
I 0,n 
(12)
I SC,n

 VOC ,n
exp 
 A *V
T ,n



(17)


  1




Now, the single diode model of PV device can be
improved by modifying the above equations
(13)
I 0,n 
After the combination of equation (12) and (13) and the
inclusion of additional parameters RS and RSH, equation
(11) becomes:
  V  RS * I  
  V  RS * I    V  RS * I 

  1  I 02 * exp 
  1  
I  I PV  I 01 * exp 
  A1 * VT  
  A2 * VT    RSH 
(16)
E g is the band-gap energy of the semiconductor
[12, 16, 22] and
(11)

 V
 I 01 * exp 
 A1 *VT



V
I D 2  I 02 * exp 
 A *V
2
T


( Eg
 1
1 

 
 Tn T 

 VOC ,n  K v * T
exp 

A * VT ,n



Where
(14)


  1




I SC,n is the short circuit current ; VOC ,n the
open circuit voltage ;
irradiance and
Conditions.
496
(18)
I SC, n  K i * T
VT ,n the thermal voltage ; Gn the
Tn the temperature , all at Standard Test
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Therefore, the series resistance RS, which represents
structural resistances of photovoltaic panel [16, 20], has a
strong effect in the voltage-source region. In turn, the shunt
resistance RSH that accounts for current leakage in [10] the
p-n junction, is of great importance in the current-source
region and the maximum power point appears to be
compromise of the hybrid behavior of the cell between both
voltage and current-source region.
K i and K v are short circuit temperature coefficient
and open circuit temperature coefficient respectively. Since
the saturation current has strong temperature dependence;
equation (18) results in a linear variation of I 0,n with
respect to temperature T. The model’s validity with the
new equation has been tested experimentally [16].
III. DETERMINATION OF MODEL PARAMETERS
IV. METHOD TO DETERMINE THE UNKNOWN
PARAMETERS
All model parameters can be determined by examining
the manufacturer’s specification of photovoltaic products.
The performance characteristics of a PV module depend on
its basic materials, manufacturing technology and operating
conditions. The most important points widely used for
describing the cell electrical performance are: the short
circuit point where the current is at maximum (short circuit
current ISC) and the voltage over the module is zero; the
open circuit point where the current is zero and the voltage
is at maximum (open circuit voltage VOC); the Maximum
power point where the product of current and voltage has
its maximum. The power delivered by a PV cell attains a
maximum value at the points (Imp, Vmp).
The aforementioned equations (10) and (14) are implicit
and nonlinear; therefore, it is difficult to arrive at an
analytical solution for a set of model parameters at a
specific temperature and irradiance. Models that use
constant parameters have been proposed [22]. The five
parameters (IPV, I0, A, RS and RSH ) model as seen in
equation (10) assumes that the dark current of a PV system
can be described by a single exponential dependence
modified by a diode quality factor A. The values of the
five parameters in the equation (10) must be determined to
reproduce the I-V curve of a PV system. This requires five
equations containing five unknowns that should be solved
simultaneously to obtain the values of the parameters [19,
20]. G .Walker [7] has further simplified this model by
removing the shunt resistance RSH to obtain a model as the
four parameters model. This model reliably predicts the
performance of single crystal and polycrystalline PV
systems. The four parameters model assumes that the slope
of the I-V curve is flat at the short circuit condition
2
Output Current(A)
X: 0
Y: 1.95
X: 24.24
Y: 1.83
1.5
X: 0
Y: 0.75
1
X: 22.38
Y: 0.7038
X: 0
Y: 0.375
0.5
 dI 
0


 dV V 0
X: 20.97
Y: 0.3519
X: 26.63
Y: 0
0
0
5
10
15
20 X: 24.8 25
Output Voltage(V) Y: 0
(19)
However, this assumption is not valid for amorphous PV
systems. The short circuit I-V is finite and negative, so the
four parameters model can’t reproduce exactly the I-V
characteristics of amorphous silicon. As mentioned
previously, there are key points on the I-V curve of a
photovoltaic cell. For the five parameters model, the first
equation is derived from open circuit condition where I =0
and V = VOC. Equation (10) becomes
30
X: 28.67
Y: 0
Fig.6: A typical I-V plot for a three solar cells. The open-circuit
voltage and short-circuit current are labeled by VOC and ISC
respectively. The point of maximum power is denoted by (Vmp, Imp).
Typically, three points (ISC, 0), (VOC, 0) and (Vmp, Imp)
are provided by the manufacturer’s datasheet at Standard
Test Conditions. An accurate estimation of these points for
other conditions is the main goal of every modeling
technique. From the aforementioned models, it is obvious
that the PV cell acts as a current-source near the short
circuit point and as a voltage-source in the vicinity of the
open-circuit point.

 V
0  I PV  I 0 ¨*exp  OC
 A *VT

  VOC
  1 
  RSH
(20)
The second equation occurs at short circuit condition
where
I = ISC and V =0. Then equation (10) becomes
497
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 I *R
I SC  I PV  I 0 * exp  SC S
  A * VT
  I SC * RS
  1 
RSH
 
After substituting in equation (23) the following
equation is obtained:
(21)

The measured current voltage pair at the maximum
power point can be substituted into equation (10) to obtain
the third equation where I = Impp and V= Vmpp
  Vmpp  I mpp * RS   Vmpp  I mpp * RS
  1 
I mpp  I PV  I 0 * exp 
A *VT
RSH
 
 
The five parameters (IPV, I0, A, RS and RSH) can be
obtained simultaneously solving these equations in
MATLAB using iterative method like Newton Raphson’s
method to solve system of nonlinear equations. For
notational convenience, the following can be defined:
These three equations are obtained using the key points.
In order to get another two equations, we can differentiate
equation (10) with respect to V; thus we get:
RS 0 
I 0
1
 I 0 * 
VT
 dI
* 1 
 dV
  V
* RS  exp  OC
I 0
  A *VT
 1  dI
  * 1 
 R p  dV
RSH 0 

* RS 
I 0

  V  1  dI

* RS  exp  OC   * 1 
* RS 
A
*
V
R
dV
V 0

V 0
  T  p 
A
We get
I mpp
dI

dV
Vmpp
I ISC
Vmpp  I mpp * RSO  VOC

 
Vmpp


V
VT * ln  I SC 
 I mpp   ln  I SC  OC
R
RSH
 
SHO






I mpp


 
V
 I  OC 
SC
RSHO 
The rest of the initial of the parameters can be found
from the following equations [11, 24]
(25)
RSH  RSH 0
(33)

VOC
I0  
 I SC  R
SH

An addition equation can be derived using the fact that
on the P-V characteristic of a PV system at the maximum
power point, the derivative of power with voltage is zero
V V
(31)
(32)
(26)
mp p
d I * V 
dI
 dP 

I
*V  0


dV
dV
 dV  I  I mp p
dV
dI
(24)
The power transferred from the P-V device at any point
is given by:
P  I *V
(30)
V VOC
Based on the work [21, 22], R S0 and RSHO can be
obtained experimentally from the I-V curve. Thus the
initial can be calculated by calculating the diode ideality
factor [23]:
Again at the short circuit point on the I-V curve I = ISC
and V = 0, dI  dI
after substituting in equation
dV
dV V 0
(23), we obtain:
 1  dI
dI
  I 0 *  * 1 
dV V 0
VT  dV
dV
dI
(23)
Again at the open circuit point on the I-V curve, V =
VOC and I = 0, therefore dI  dI
after substituting
dV
dV I 0
in equation (23) we obtain the following results:
dI
dV
Vmpp
 1  I mpp


Vmpp  I mpp * RS   1  I mpp
1 
  I 0 *  1 
* RS  * exp 
* RS 
 




 A *VT
  R SH  Vmpp


VT  Vmpp
(29)
(22)
 1  dI
dI
  V  I * RS  1  dI

 
  I 0 *  1  * RS  exp 
1  * RS 
dV
V
dV
A
*
V
R
dV
 

T
 SH 
 T
I mpp
RS  RS 0 


VOC 

  A *V 

 exp 
T 



VOC
A * VT
exp 
  A *V
I0
T


RS
I PV  I SC * 
1  R
SH

(27)




(35)


 I SC * RS


 A *V
  I 0  exp 
T



To compute the five parameters I PV ,
(28)
(34)




  1


(36)
I 0 , RS , A and
RSH which are necessary to apply equation (10), the above
equations (32)-(36) have been used.
498
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Finally, the equation of I-V characteristics is solved
using the Newton Raphson’s method.
VI. RESULTS AND DISCUSSION
In order to validate the modeling and simulation method
presented above for PV module, the calculated values and
experimental values are compared for a commercial
polycrystalline silicon cells from Solarex MSX60 module,
composed of one parallel string of 36 solar cells. The
electrical characteristics of Solarex MX60 module for G
=1000W/m2 and T=25°C, at Standard Test Condition can
be seen on table 1.
V. NUMERICAL METHOD FOR PV CELL MODELING
In many Physics, Chemistry and Engineering problems,
expression where linear and exponential responses are
combined appear. For instance, the implicit transcendental
equation (10) of the PV cell five parameters model I-V
characteristic can’t be solved explicitly for its output
current or voltage using the common elementary functions.
This has prompted many attempts using iterative or
analytical approximations of such systems [25]. The
Newton Raphson’s method, which is widely used for
obtaining roots of implicit transcendental equations, is
popular in iterative computational applications because of
its simplicity and fast convergence [23, 26]. Newton
Raphson iteration is a numerical technique used for finding
approximations to real roots of the equation f ( I )  0
given in the form of an iterative equation:
I n 1
f (I )
 In  ' n
f (I n )
Where
n
denotes
Table.1
Solarex MSX-60 specifications (1kW/m², 25°C)
n th
Short-circuit current (Isc)
3.8 A
Open-circuit voltage (Voc)
21.1 V
Temperature coefficient of (0.065±0.01)% /°C
short-circuit current (KI)
Approximate effect
temperature on power
Nominal operating
temperature (NOCT)
 V  I * RS
(38)
 
 I0  0
RSH

 V  I * RS 
I 0 * RS
R

 S
* exp 

A *VT
A
*
V
R
T
SH


60 W
Temperature coefficient of -(80±10)mV/°C
open-circuit voltage ( KV)
iteration
reaches an acceptably small value. Using equation (37), the
output current of a PV cell can be calculated by modifying
the I-V relation of five parameter model in equation (10) as
follows:
f ' (I )  1 
Typical peak power (Pmpp)
Current at peak power (Imp) 3.5 A
and f ' ( I )  d  f ( I ). This iterative process can be
dI
concluded when the difference between I n 1 and I n
 V  I * RS
f ( I )  I  I PV  I 0 * exp 
 A *VT
Specifications
Voltage at peak power (Vmp) 17.1 V
(37)
the
Characteristics
of -(0.5±0.015) %/ °C
cell 47±2°C
Table.2:
The calculated data of the parameters for Solarex MSX-60 at 25°C,
AM1.5, and 1kW/m².
(39)
Parameters
Calculated Values
I0
1.859 x 10-7 A
IPV
3.8119 A
RS
0.180 Ω
RSH
360.002 Ω
A
1.360
By using the above equations, the following output
current is computed iteratively
 V  I n * RS  V  I n * RS

I n  I PV  I 0 * exp 
 I0
( 40)
A *VT 
RSH

I n1  I n 
 V  I n * R S  RS
I *R
 
1  0 S * exp 
A *VT
 A *VT  RSH
499
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4
3
Experimental Values
Calculated Values
2
1
0
(Vmp, Imp)
X: 0
Y: 3.8
0
5
10
15
20
Output Voltage(V)
3
Output Current(A)
Output Current(A)
4
25
2
1
30
0
10
15
20 X: 21.1
25
30
Output Voltage(V)
Y: 0
Fig.8: I-V Curve simulated at Standard Test Conditions
(T=25°C, G=1000 W/m2)
2
Fig .7: I-V curve for MSX60 at 25°C, AM1.5, and 1000 W/m
comparison between experimental values and calculated values.
Fig.7 reveals consistency between experimental results
and predicted results. It is obvious that the calculated
values are in good agreement with the experimental values
provided by panel manufacturers. Fig.8 shows the I-V
characteristics at Standard Test Conditions where the three
most important points, maximum power point (V mp, Imp),
short circuit current (0,Isc) and the open circuit point (Voc,0)
data are shown after the computation of all the five
parameters model with numerical method. The model
curves exactly match with the experimental values at the
three points provided by data sheet in table 1.
Fig.9 illustrates the dependence of I-V characteristics on
temperature and irradiance for a solarex MSX-60 module.
The fig.10 shows the P-V characteristics of the PV module
with varying irradiance at constant temperature. From the
graph when the irradiance increases, the output current and
voltage also increases. This result shows the net increase in
power output with irradiance at constant temperatures.
Furthermore, it is known that for a certain PV array, the
voltage –power characteristics are fixed for each insolation
without intersection, as shown in fig.10. Therefore, for any
given PV voltage and power, the corresponding insolation
can be estimated. Also, in fig.11 and fig.12, the P-V and IV characteristics under constant irradiance (G=1000 W/m2)
with varying temperature are presented, respectively. From
these figures, when the operating temperature increases, the
output current increases dramatically while the output
voltage decreases marginally, which results in a net
reduction in power with a rise in temperature.
0
5
4
1000 W/m2
800 W/m2
3.5
600 W/m2
400 W/m2
Output Current(A)
3
200 W/m2
2.5
2
1.5
1
0.5
0
0
5
10
15
20
25
Output Voltage(V)
Fig.9: Curve I-V at T=25 °C for various irradiance levels
60
1000 W/m2
800 W/m2
50
Output Power(W)
600 W/m2
400 W/m2
40
200 W/m2
30
20
10
0
0
5
10
15
Output Voltage(V)
20
Fig.10: Curve V-P at T=25 °C for different irradiances
500
25
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REFERENCES
Output Power (W)
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VII. CONCLUSIONS
An accurate PV cell to module electrical model using
five parameters is presented and calculated using
MATLAB software. The open circuit I-V and P-V curves,
we obtained from the simulation of PV module designed in
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