Available online at www.jtusci.info
ISSN: 1658-3655
Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬
Modeling of photovoltaic module and experimental determination of serial resistance Mohammed S. Benghanem 1 & Saleh N. Alamri 2 1&2
Department of Physics, Faculty of Sciences, Taibah University, Al-Madinah
Al-Munawrrah, KSA
Received 29 June 2008; revised 6 August 2008; accepted 9 August 2008
Abstract
An explicit model is presented for accurate simulation of the I-V curve characteristic of photovoltaic
(PV) module. The model is compared with the traditional I-V curve characteristic and to some
experimental results to show the accuracy of the method. The explicit model proposed is found to be
reliable and accurate in situations where this model is a good approximation of cell or module
performance. Also, an experimental method is presented to determine the series resistance and shunt
resistance of the PV cells and PV modules.
Keywords: I-V characterization; Simulation models; Experimental measurement; Series resistance;
Shunt resistance.
Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
95
2. Review of Existing models of solar cell
1. Introduction
The determination of solar cell model
Characteristic
parameters from experimental data is important in
Several models of PV generator have been
the design and evaluation of solar cells.
developed in literature [1-6]. The aim is to get the
The work described in this paper is to characterize
I-V characteristic in order to analyze and evaluate
the photovoltaic (PV) modules in real conditions.
the PV systems performance. The difference
Also, we give a method to determine the serial
between all models is the number of necessary
resistance RS and the shunt resistance RSh of PV
parameters used in the computational. The most
module. The serial resistance is mainly the sum of
models used are:
•
•
•
•
contact resistance on the front and back surfaces
and the resistances of the bulk and the diffused
layer on the top. The shunt resistance represents a
parallel high-conductivity path across the p-n
junction. The shunt resistance can affect the short
circuit current ISC density as well. The PV
performance depends on the values of RSh and RS.
Therefore, RS and RSh both need to be recognized
and understood in order to analyze the cell and
module performance. The most commonly used
method for measuring the series resistance of a
solar cell was first proposed by wolf and
Explicit Model
Solar Cell Model using four parameters
Solar Cell Model using five parameters
Solar Cell Model using two exponential
2.1. Explicit Model
This model needs four input parameters, the
short-circuit current ISC , the open-circuit voltage
VOC , the maximal current Im, and the maximal
voltage Vm [2]. The relation between the load
current I and the output voltage V is given by:
⎡
⎛
⎛ V
I = I SC ⎢1 − C1 ⎜ Exp ⎜⎜
⎜
⎢⎣
⎝ C 2 . V OC
⎝
⎞ ⎞⎤
⎟ − 1⎟ ⎥
⎟ ⎟
⎠ ⎠ ⎥⎦
(1)
Rauschenbach [1]. This involves measuring the
characteristic
of
a
cell
at
two
different
illuminations.
Where
⎛
I
C1 = ⎜⎜1 − m
I
SC
⎝
Several other methods are available in the literature
for the measurement of series and shunt resistances
[2-6]. All these methods are based on single
exponential model of solar cell and assume that RSh
is infinite and presume RS to be independent of the
intensity of illumination, which may not be valid.
In this paper we propose a new approach to
simulate the IV characterization by given a
photovoltaic resistance for any materials properties
of the solar cell. Also, the photovoltaic resistance is
given for silicon cell. We present an experimental
method for determination of RS and RSh of a solar
cell using the I-V characteristic based on explicit
model proposed.
And
⎛ − Vm
⎞
⎟.Exp ⎜
⎜ C .V
⎟
⎝ 2 OC
⎠
Vm
−1
VOC
C2 =
⎛
I
Ln⎜⎜1 − m
I
SC
⎝
⎞
⎟
⎟
⎠
⎞
⎟
⎟
⎠
2.2. Solar Cell model using four parameters
The classical equation describing the I-V curve of a
single solar cell is given by:
⎡
⎛ q
⎞ ⎤
(V + R S .I ) ⎟ − 1⎥
I = I Ph − I 0 .⎢ Exp ⎜
.
.
A
K
T
⎝
⎠ ⎦
⎣
Where I is the load current
(2)
and V the output
voltage, I0 is the diode reverse saturation current,
IPh is the photo-generated current, RS is the series
Modeling of photovoltaic module and experimental determination of serial resistance Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
96
resistance, q is the electric charge, K the Boltzman
current Im at the maximum power point and the
constant, T is the temperature (oK) and A is the
slopes of curve near VOC and ISC.
ideality factor. The four parameters of this model
Thus:
are: IPh, I0, RS, and A.
⎛ dV ⎞
= − RSO
⎜
⎟
⎝ dI ⎠V =Voc
The effect of shunt resistance is not taking a count
in this model. Equation (2) describes the I-V curve
quite well, but the parameters cannot be measured
(4)
⎛ dV ⎞
= − RSh 0
⎜
⎟
⎝ dI ⎠ I = Isc
in a simple manner. Therefore, a fit based on a
smaller number of parameters which can be
(5)
measured easily have been developed [3]. These
include:
-
The open circuit voltage VOC.
-
The short-circuit current ISC.
-
The maximum power Pm.
The following equations are obtained:
A=
2.3. Solar Cell model using five parameters
In this model, the effect of shunt resistance is
considered [4]. Figure 1 shows a solar cell
V m + I m .R S 0 − VOC
⎡
⎢
⎛
⎞
⎛
V
V
Vt ⎢ Ln⎜⎜ I SC − m − I m ⎟⎟ − Ln⎜⎜ I SC − OC
⎢ ⎝
R Sh
R Sh
⎠
⎝
⎢
⎣⎢
Vt =
shunt resistance RSh.
⎛
V
I 0 = ⎜⎜ I SC − OC
RSh
⎝
I
V
IPh
ID,VD
RS = R S 0 −
RSh
Fig.1. Solar cell equivalent circuit including
series resistance and shunt resistance.
The mathematical description of this circuit is
given by the following equation:
⎞⎤
⎟⎥
⎟⎥
⎟⎥
⎟⎟⎥
⎠⎦⎥
(6)
Where:
equivalent circuit including series resistance RS and
RS
⎛
⎜
⎞ ⎜
Im
⎟+⎜
⎟
⎠ ⎜ I − VOC
⎜ SC R
Sh 0
⎝
K .T
q
⎞
⎛ V
⎟⎟.Exp ⎜⎜ − OC
⎠
⎝ A.Vt
⎞
⎟⎟
⎠
(7)
⎛ V ⎞
A.Vt
.Exp ⎜⎜ − OC ⎟⎟
I0
⎝ A.Vt ⎠
⎛
⎛ I .R
⎛
R ⎞
I Ph = I SC .⎜⎜1 + S ⎟⎟ + I 0 .⎜ Exp ⎜⎜ SC S
⎜
R
Sh ⎠
⎝ A.Vt
⎝
⎝
(8)
⎞ ⎞
⎟⎟ − 1⎟
⎟
⎠ ⎠
(9)
(10)
RSh = RSh 0
2.4. Solar cell model using two exponential
The solar cell equivalent circuit including series
⎡
⎛ q
⎞ ⎤ V + R S .I
I = I Ph − I 0 .⎢ Exp ⎜
(V + RS .I ) ⎟ − 1⎥ −
RSh
⎝ A.K .T
⎠ ⎦
⎣
(3)
resistance
RS,
shunt
resistance
RSh,
two
exponential-type ideal junction, a constant photo-
The five parameters of this model are: IPh, I0, RS,
generated current source is represented by Fig. 2.
RSh and A. For a given temperature and solar
The mathematical description of this circuit is
irradiation
given by the following equation [5]:
intensity,
these
parameters
are
determined by using the open-circuit voltage VOC,
the short-circuit current ISC, the voltage Vm and the
Modeling of photovoltaic module and experimental determination of serial resistance Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
RS
97
I
IPh
V
ID1
ID2
RSh
Fig.2. Solar cell equivalent circuit for model with two
exponential.
⎡
⎡
⎛ q
⎞ ⎤
⎛ q
⎞ ⎤ V + R S .I
I = I Ph − I 01 .⎢ Exp ⎜⎜
(V + R S .I ) ⎟⎟ − 1⎥ − I 02 .⎢ Exp ⎜⎜
(V + R S .I ) ⎟⎟ − 1⎥ −
R Sh
⎢⎣
⎢⎣
⎝ A1 .K .T
⎠ ⎥⎦
⎝ A2 .K .T
⎠ ⎥⎦
The parameters of this model IPh, A1, A2, I01, I02, RS
and
RSh
are
determined
by
the
following
X 2V = −
approximations [5]:
IPh= ISC
I Ph
1
I 02 = .
2 ⎛
⎛ e.V ⎞ ⎞
⎜⎜ Exp⎜ − OC ⎟ − 1⎟⎟
⎝ 2.K .T ⎠ ⎠
⎝
(12)
a simplified relation for RS as:
⎡ dV
RS = − ⎢
⎣ dI
(13)
+
X 1V
RSh = −
(14)
e.I 01
⎛ e.V ⎞
.Exp⎜ − OC ⎟
K .T
⎝ K .T ⎠
⎤
1
⎥
+ X 2V ⎦
X 1V
(17)
1
⎡
⎢
⎢
⎢ ⎛ dV
⎢⎜
⎢⎣ ⎜⎝ dI
⎤
⎥
1
⎥
+ X 1i + X 2i ⎥
⎞
⎥
+ RS ⎟⎟
⎥⎦
I = Isc
⎠
(18)
Where:
With:
X 1V = −
+
The shunt resistance RSh is deduced from equation
V= VOC :
V =Voc
V =Voc
(14) with I= ISC
RS is obtained by derivation of equation (11) at
⎤
⎥
1
⎥
1 ⎥
+ X 2V +
RSh ⎥⎦
(16)
1
<< (X1V + X2V), we can obtain
R Sh
If we consider
I Ph
1
I 01 = .
2 ⎛
⎛ e.VOC ⎞ ⎞
⎜⎜ Exp⎜ −
⎟ − 1⎟⎟
⎝ K.T ⎠ ⎠
⎝
⎡
⎢ dV
RS = ⎢
⎢ dI
⎢
⎣
e.I 02
⎛ e.VOC ⎞
.Exp⎜ −
⎟
A.K .T
⎝ A.K .T ⎠
(11)
⎞
⎟⎟
⎠
X 1i =
⎛ I .R
I 01
Exp ⎜⎜ SC S
Vt
⎝ Vt
X 2i =
⎛ I .R
I 02
Exp ⎜⎜ SC S
A.Vt
⎝ A.Vt
(15)
Modeling of photovoltaic module and experimental determination of serial resistance (19)
⎞
⎟⎟
⎠
(20)
Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
3.
Comparison
with
experimental
98
3.2. Four parameters Model
This method is based on single exponential
Characteristic
model of solar cell and assumes that RSh is
3.1. Explicit Model
Fig.3 shows that the model gives a
infinite, an assumption that may not be valid for
best representation of I-V curve, but the
the cell having low RSh values.
limitation of this method is that it doesn't take
Fig.4 shows the I-V curve given by this method.
account of serial resistance RS and shunt
We note a difference between experimental I-V
resistance RSh.
curve and those simulated in non-linear region
near the maximum power point.
Explicit model
Experimental data
3
Current (A)
2.5
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
16
18
20
Voltage (V)
Fig. 3. The I-V characterization using explicit model at 800 W/m2
and 45oC.
Three parameters model
Experimental data
3
Current (A)
2.5
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
16
18
20
Voltage (V)
Fig. 4. I-V characterization using four parameters model at
800 W/m2 and 45oC.
Modeling of photovoltaic module and experimental determination of serial resistance Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
99
Where n is the number of data, Isi is the ith
3.3. Five parameters model
Fig.5 shows the I-V characterization given
simulated current and Imi is the ith measured
by the five parameters model.
current. The RMSE test provides information on
The five parameters model is shown to give
the short-term performance of the simulation
accurate reliable results but gives non-physical
model. The lower value of RMSE means the
values at low illuminations [4].
more accuracy for the model used.
In order to evaluate the accuracy of the models a
The RMSE values of the models were calculated.
statistical tests was used [7], root mean square
Table 1 shows the RMSE values obtained from
error (RMSE). The RMSE is given as follow:
the models presented. The RMSE average
values, which are a measure of the accuracy of
estimation, have been found to be the lowest for
⎛1
⎞
RMSE = ⎜ ∑ ( I si − I mi ) 2 ⎟
⎝ n i =1
⎠
n
1/ 2
Five parameters model (RMSE = 0.022) at
(21)
illumination of 800 W/m2.
Five parameters model
Experimental data
3
Current (A)
2.5
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
16
18
20
Voltage (V)
Fig. 5. I-V characterization using five parameters model at 800 W/m2
and 45oC.
Table.1. RMSE values for each model
Solar irradiation (Wh/m2)
1000
800
Temperature (oC)
25
45
Explicit model
0.039
0.027
Four parameters model
0.047
0.104
Five parameters model
0.095
0.022
RMSE
Modeling of photovoltaic module and experimental determination of serial resistance Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
This
means
the
good
estimation
of
I-V
By using the following simplification:
characterization by using a five parameters model
than the three parameters model and the explicit
model for the illumination of 800 W/m2.
100
e
⎛ V + RPV . I
⎜⎜
VT
⎝
⎞
⎟⎟
⎠
>> 1
and
IPh= ISC
The I-V curve can be expressed as:
4. Explicit model proposed
Measurements of peak-power and internal series
resistance under natural ambient conditions need
I = I SC
⎛ V +VR
− I 0 .⎜ e
⎜
⎝
⎞
⎟
⎟
⎠
(24)
⎞
⎟ − R PV .I
⎟
⎠
(25)
PV
.I
T
mathematical corrections of the measured I-V
characteristic, considering irradiance and cell
temperature.
The purpose of I-V characteristic approximation by
means of equivalent circuit diagrams lies in the
explicit
calculability
of
matching
problems
between solar generators and several loads. The
equivalent circuit diagram for the effective solar
cell characteristic is given by Fig.6.
R PV
I SC − I
=e
I0
V + RPV . I
VT
Then:
⎛I −I
V = VT .Ln ⎜⎜ SC
⎝ I0
Since I0, VT and RPV are unknown, three conditions
are required to enable use of this fit:
I
1.
If I=0, then V=VOC.
2.
At the maximum power point the fit is
IPh
tangent to the hyperbola Pm= V.I
ID , V D
V
Fig. 6. Equivalent circuit diagram for Effective solar
cell characteristic.
The slope S at the open circuit voltage is
3.
to be considered.
The condition (1) yields:
VOC = V
The effective solar cell characteristic is given by
the following model:
⎛ V +VR
I = I ph − I 0 ⎜ e
⎜
⎝
PV . I
T
⎞
− 1⎟
⎟
⎠
VT =
(22)
⎛I
= VT .Ln⎜⎜ SC
⎝ I0
I =0
VOC
⎛I
Ln⎜⎜ SC
⎝ I0
The explicit version is:
⎛ I ph − I + I 0
V = VT .Ln ⎜⎜
I0
⎝
RPV
⎞
⎟⎟ − RPV .I
⎠
I 0 = I SC .e
(23)
is the photovoltaic resistance, not to be
RPV, VT, I0 and IPh.
Or:
⎞
⎟⎟
⎠
VOC
VT
(26)
and then:
(27)
The condition (2) can be expressed as:
V
I =Im
=
confused with the serial resistance RS.
We need to determine the following parameters:
−
⎞
⎟⎟
⎠
∂V
∂I
Pm
Im
=
I =Im
(28)
P
∂ ⎛ Pm ⎞
= − m2
⎜
⎟
∂ I ⎝ I ⎠ I =I
Im
Modeling of photovoltaic module and experimental determination of serial resistance m
(29)
Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
Differentiating equation (29) according to equation
is then given by the approximate function [6]:
(25), we get:
S=
VT
∂V
=−
−R
(I Sc − I ) PV
∂I
VOC
I SC
=−
I =Im
I
.V
V
I
⎛
⎞
⎜⎜ α 1 . p max p max + α 2 . p max + α 3 . p max + α 4 ⎟⎟
I SC .VOC
VOC
I SC
⎝
⎠
With the equation-constants:
For I =Im, we get:
∂V
∂I
101
P
VT
− R PV = − m2
(I SC − I m )
Im
⎛ − 5.411 ⎞
⎜
⎟
⎜ 6.450 ⎟
α =⎜
3.417 ⎟
⎜
⎟
⎜ − 4.422 ⎟
⎝
⎠
(30)
Then:
We note that the equation (36) is independent of
R PV =
Vm
VT
−
I m (I SC − I m )
(31)
material properties of the solar cell.
The RPV is calculated using equation (34) for
By substituting equation (26) in equation (31), we
silicon cell or using equation (36) for any materials
get:
properties of the solar cell. The value of RPV is
RPV
VT =
V
= m −
Im
substituted into equation (22) to find the I-V curve
VOC
(I SC
⎛I
− I m ).Ln ⎜⎜ SC
⎝ I0
⎞
⎟⎟
⎠
(32)
of a single solar cell.
4.1.
VOC
V
= OC
7
16.11
Ln10
Comparison
between
Explicit
model
proposed and experimental data
Fig. 7 shows a good agreement between
experimental I-V curve and those given by the
⎡
⎤
16.11
I = I SC ⎢1 − 10 − 7.Exp
(V + R PV .I ) ⎥
VOC
⎣
⎦
(33)
explicit model proposed for different illuminations.
Explicit model (1000 W/m2)
Explicit model (800 W/m2)
Experimantal data at 1000 W/m2
Experimental data at 800 W/m2
equation (33) yields:
RPV =
Vm
VOC
−
I m 16.11(I SC − I m )
3
dV
dI
=−
I =0
C urrent (A )
The condition (3) yields:
S=
VT
−R
(I Sc ) PV
2.5
2
1.5
1
Then:
0.5
VT = − (S + R PV ).I SC
(35)
Substituting equation (35) into equation (31), we
get:
RPV = − S
3.5
(34)
I SC Vm ⎛
I
⎜⎜1 − SC
+
Im
Im ⎝
Im
⎞
⎟⎟
⎠
(36)
0
0
2
4
6
8
10
12
14
16
18
20
Voltage (V)
Fig. 7. I-V curve characterization for two illuminations.
Fig. 8 shows the I-V curve of the explicit model
proposed with experimental data and comparison
Modeling of photovoltaic module and experimental determination of serial resistance Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
102
with others models studied. The RMSE values
obtained for the explicit model proposed is 0.01 for
the illumination of 800 W/m2 and 0.03 for the
illumination of 1000 W/m2. The experimental I-V
curve is given by the curve tracer (PVPM 2540C)
for PV modules (Fig.9).
Five parameters model
Three parameters model
Explicit model proposed
Experimantal data
Fig. 9. PVPM 2540C: Curve Tracer for PV Modules.
4.2. New Experimental method for calculation of
3
Rs and RSh
Current (A)
2.5
RSh is calculated near the two points P1 and
2
P2 on the illuminated I-V characteristic. P1 is near
1.5
the short-circuit point and thus corresponds to a
1
low value of voltage; P2 is near the maximum
power point and therefore corresponds to a higher
0.5
0
voltage.
0
2
4
6
8
10
12
14
16
18
20
Voltage (V)
Fig. 8a. Simulation and Experimental I-V Curve for
illumination at 800 W/m2.
RS is calculated near the two points P3 and P4 on
the illuminated I-V characteristic. P4 is near the
open-circuit point (V= Voc) and P3 is near the
maximum power point.
The choice of the four working points P1, P2, P3
and P4 is deduced by iteration using the algorithm
Five parameters model
Three parameters model
Explicit model proposed
Experimantal data
given below.
4.2.1. Methodology
The condition (3) gives:
3.5
Current (A)
3
S=
2.5
dV
dI
I =0
2
This condition means to find a slope near the open
1.5
circuit voltage VOC. So, experimentally we chose
1
two working points P4 corresponding to the
0.5
0
coordinates ( I4, V4) and P3 with the coordinates
0
2
4
6
8
10
12
14
16
18
20
Voltage (V)
Fig. 8b. Simulation and Experimental I-V Curve for
2
illumination at 1000 W/m .
(I4, V4). Then, the slope S is given by:
S=
V − V3
dV
= RS = 4
dI
I3 − I 4
Modeling of photovoltaic module and experimental determination of serial resistance (37)
Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
: I4 =0 ( V4 = VOC ) and I3 is given by iteration
⎛ I ph − I i + I 0
Vi = VT .Ln ⎜⎜
I0
⎝
until we find the value of RS equal to the
experimental value RSM
103
measured by the
⎞
⎟⎟ − R S .I i i = 1 to 4.
⎠
The following examples show the accuracy of this
method.
Measuring device and curve tracer for PV modules
and strings (PVPM 2540C) as shown in Fig.10.
3
P2
P1
Current (A)
2.5
2
P3
1.5
1
0.5
0
Fig. 10. RSM measurement of PV module by PVPM
P4
0
4
6
8
10
12
14
16
18
20
Voltage (V)
2540C.
Fig. 11. Experimental working points.
Algorithm
Example
V4 = VOC , I4 = 0 ;
Monocrystalline
PV-Module
Voc =20.51 V
I3 varies from 0 to ISC ;
Vm =16.58 V
From each values of I3, we get V3 ( equ.23) and
Im = 3.01 A
then we calculate RS (equ.37).
Isc = 3.34 A
If the calculated value of RS is not equal to RSM, we
increase the value of I3 until the value of
The I-V characteristic of the PV-module Isophoton
RS
is given by Fig.12. We have found: RS = 0.64
reaches the measured value RSM. We have find that
Ω and RSh = 89.42 Ω.
I3 is equal to 50 % of ISC.
3.5
The shunt resistance RSh is given by the relation:
P1
3
(38)
The optimal choice is given by (Fig.11):
I1 = ISC (V= 0v) for the point P1.
I2= 95 % of ISC for the point P2.
P2
2.5
Current (A)
V2 − V1
I1 − I 2
1:
Isophoton
Vm, Im, ISC and RSM are fixed ;
RSh =
2
2
P3
1.5
1
I3 = 50 % of ISC for the point P3.
I4 = 0 (V = Voc) for the point P4.
The different voltages V1, V2, V3 and V4
corresponding to each working points P1, P2, P3
and P4 are given by using the equ.23:
0.5
0
P4
0
5
10
15
20
25
Voltage (V)
Fig. 12. Experimental working
Monocrystalline PV-Module Isophoton.
Modeling of photovoltaic module and experimental determination of serial resistance points
for
Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
104
Example2: Monocrystalline PV-Module BP585F
The values of series and shunt resistance are given
Voc =22.3 V
in table 2. We note that for the same illumination,
Vm =18 V
the series resistance of the PV module BP585F is
Im = 4.72 A
the lower. The high value of shunt resistance is
Isc = 5 A
given by the PV module Isophoton.
We have found: Rs = 0.50 Ω and Rsh = 77.75 Ω
Fig.13
shows
the
I-V
characteristic
experimental manipulation of the
Table.2. Values of series and shunt resistances for
for
different PV modules
PV-Module
BP585F.
PV modules
Isophoton
BP585F
MSX 40
RS (Ω)
0.64
0.50
3.06
RSh (Ω)
89.42
77.75
63.83
PV module BP585F
5
P1
4.5
P2
4
Current (A)
3.5
5. Conclusion
3
The explicit model proposed for the I-V curve
P3
2.5
2
is shown to give accurate reliable results. This
1.5
model gives parameter values with good precision.
1
Also, the experimental determination of serial
0.5
0
resistance RS and shunt resistance RSh is more
P4
0
5
10
Voltage(V)
15
convenient method. A theoretical expression given
20
Fig. 13. I-V characteristic for the PV-module BP585F.
RPV for any materials properties of the solar cell. If
Example3: I-V curve approximation
using silicon cell the photovoltaic resistance is
Figure 14 shows the I-V curve for some modules
given by equation (34). The value of RPV is
by using the explicit model proposed.
substituted into equation (22) to find the I-V curve
of a single solar cell or PV module.
PV module Isophoton
PV module Solarex
PV module BP585F
3.5
Acknowledgements
3
We wish to thank the Deanship of Scientific
Research Taibah University
2.5
Current (A)
in equation (36) gives the photovoltaic resistance
financially
supported this work, under contracted research
2
project 33/427.
1.5
References
1
0.5
0
who
0
5
10
15
20
25
30
35
40
Voltage (V)
Fig. 14. I-V characterization for different modules
using the explicit model proposed.
[1] M. Wolf and H. Rauschenbach. Advanced
Energy Conversation, 3, 455 (1963).
[2] G. W. HART. Residential photovoltaic system
simulation electrical aspect.
IEEE, pp.281-288, 1982
[3] S. SINGER, B. ROZENSHTEIN and S.
SAURAZI. Characterization of PV array
Modeling of photovoltaic module and experimental determination of serial resistance Benghanem & Alamri / JTUSCI 2: 94-105 (2009)
output using a small number of measured
parameters.
Solar Energy, Vol.32, No5, pp.603-607,
1984.
[4] D. S. H. CHAN, J. R. PHILIPS and J. C. H.
PHANG. A comparative study of extraction
methods for solar cell model parameters.
Solid State Electronics, Vol. 37, pp.123-132,
1995.
[5] J.A. GOW, C.D. MANNING. Development
of a photovoltaic array model for use in
power-electronics simulation studies.
105
IEEE Proc.Electr. Power Appl., Vol. 146,
No.2, pp.193-200, 1999.
[6] C. Bendel and A. Wagner. Photovoltaic
measurement relevant to the energy yield.
WCPEC-3, World Conference on Photovoltaic
Energy Conversion, Osaka, Japan, 2003, Pr.No
7P-B3-09, PP.1-4.
[7] Ma, C.C.Y. and Iqbal, M.
Statistical
comparison of solar radiation correlations
monthly average global and diffuse radiation
on horizontal surfaces. Solar Energy, 1984,
33, 143-148.
Modeling of photovoltaic module and experimental determination of serial resistance