1
Theoretical study of Hybrid solar cell parameters evaluation from I-V
characteristics
N. NEHAOUA1,2*, I. AMI1,3, F. MEBTOUCHE1,2, H. MEZIANI1,2, S.H. ABAIDIA1,2
1 Faculty of Science, Physics Department, University M’Hamad Bougara Boumerdes, 35000,
ALGERIA
2 Laboratory of Coatings, Materials, and Environment (LRME), Mhamed Bougara Universty of
Boumerdes (UMBB), ALGERIA
3 Theoretical Physics Laboratory, Faculty of Physics, University of Sciences and Technology Houari
Boumedien, ALGERIA.
Abstract. Photovoltaics, which convert directly solar energy into electricity, provide a practical and sustainable
solution to the challenge of meeting the increasing global energy demand. Computer simulation is an important
tool for investigating solar cell device’s behavior and optimizing their performance. This work develops a new
approach to retrieve the five parameters of the single diode equivalent solar cell/module model using the
measured current-voltage data and its derivative (G=dI/dV). A nonlinear least-square technique based on the
Newton-Raphson method under MATLAB Program is applied to determine the five parameters of the hybrid
solar cell including under different temperature.
Keywords: solar energy, parameters extraction, organic-inorganic SCs, I-V characteristics.
Received: July 12, 2021. Revised: May 15, 2022. Accepted: June 12, 2022. Published: July 4, 2022.
1. Introduction
Renewable solar energy is the clean alternative
solution in general and, in particular, on the
generation of electric power using photovoltaic cells
which is the most important energy sources [1].
Solar cells provide more energy than other
conventional sources with the additional advantage
of being lightweight and cost-effective [2-3].
intensive studies are in progress to enhance the
device’s conversion efficiency and long-term
stability, from crystalline silicon solar cells to thin-
film, dye-sensitized (DSSCs), organic, and recently
perovskite solar cells. enormous effort to obtain high
efficiency and minimize all kinds of losses in the
structure [4-6]. Solar cells are usually assessed by
measuring the current-voltage characteristics of the
device under different environmental conditions.
Generally, most solar cells manufacturer provides
panel datasheet that includes information like open-
circuit voltage (Voc), short circuit current (Isc), and
maximum power point (MPP) [7] which is not
enough to build five parameters based on an
accurate power prediction model. the equivalent
model (fig.1) of the single diode (SDM) parameters
is based on the employed circuit, such as
photocurrent current (Iph), saturation current (Is),
diode ideality factor (n), series (Rs) and shunt (Rsh)
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2022.21.16
N. Nehaoua, I. Ami, F. Mebtouche,
H. Meziani, S.H. Abaidia
E-ISSN: 2224-266X
154
Volume 21, 2022
resistances. Consequently, the choice of the solar cell
model and the parameters extraction methods are
based on different principles such as estimation
speed, PV technology, complexity and accuracy [8].
Fig. 1 – Equivalent circuit model of the illuminated solar cell.
The evaluation of these parameters has been the
subject of an investigation by several authors. Some
methods select a part of the current-voltage (I-V)
characteristic [9-10] and others exploit the whole
characteristic [11-12]. A special trans function theory
(STFT) properties are presented for determining the
ideality factor of a real solar cell as reported by
Santakrus et al [13]. Priyank et al [14] method gives
the value of series Rs and shunt resistance Rsh using
illuminated I-V characteristics in the third and fourth
quadrants and the Voc-Isc characteristics of the cell.
Jain and Kapoor have presented an accurate method
using the Lambert W-function [15-16] to study
different parameters of organic solar cells, but it has
been validated only on simulated I–V characteristics.
The authors in [17] have used a slightly modified
version of the Newton–Raphson method to solve a
model reduced to three parameters instead of five, by
using some algebraic manipulations.
The authors in [18] propose a two-step models, the
simulated annealing algorithm and analytical
formulations based on the manufacturer datasheet to
estimate the series resistance and ideality factor and
remaining parameters. Also depending on the PV
module datasheet, the method presented in [19] uses
analytical formulations to calculate the five SDM
parameters using a numerical iterative method as a
function of the environmental conditions, including
the irradiance spectrum.
A novel parameter extraction method for the one-
diode solar cell model is proposed by Wook et al [20]
the method deduces the characteristic curve of an
ideal solar cell without resistance using the I-V
characteristic curve measured. Khalis et al [21]
propose a new method to evaluate the five parameters
of illuminated solar cells and the influence of
temperature.
The presented research work considers the implicit
non-linear equation for computing the SDM model
parameters. A computational intelligence approach is
proposed to solve this implicit equation. The root
mean square algorithm is used for error minimization
and fitting the model equation to the measured I–V
characteristic curves and its derivative. This
approach of fitting the model and extracting the five
parameters is considered to be accurate because of
using a full range I–V characteristics, a strong
mathematical algorithm, and optimised steps for the
parameter’s initial guess values.
2. Theory and analysis
2.1. Solar cell single diode model
Under illumination and normal operating
conditions, the single diode model is however the
most popular model for solar cells [19], the SDM
solar cell is described by the implicit form given [22]
by :
( )
exp 1 s
ph d p ph s s
sh
V IR
I I I I I I V IR
nR
+
= − − = − + − −
(1)
The five parameters that appear in the SDM model
equation to characterize the PV cell and module at a
specific meteorological condition are photocurrent
(Iph), reverse saturation current (Is), ideality factor (n),
series resistance (Rs), and the shunt conductance (Gsh
(=1/Rsh)). Ip is the shunt current and β=q/kT is the
usual inverse thermal voltage.
The explicit form of the SDM can be formulated with
the help of Lambert W-function as shown in eq. (2)
[23]. we plot a new I-V characteristics cure using the
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2022.21.16
N. Nehaoua, I. Ami, F. Mebtouche,
H. Meziani, S.H. Abaidia
E-ISSN: 2224-266X
155
Volume 21, 2022
extracted parameters to compare with the measured
curves.
( )
( )
( )
( )
sh sh ph s
T sh s
R V R I I
nV R R
sh S T s s sh
sh s s T sh s sh s
R Iph I nV R I R V
I W e
R R R nV R R R R
++
+
+
= − −
+ + +
(2)
Where W is the principal branch of Lambert W-
function.
2.2. Development method
In this case, the current-voltage (I-V) relation of
an illuminated solar cell is given by Eq. (1) which is
implicit and cannot be solved analytically. The
proper approach is to apply least squares techniques
by considering the measured data over the entire
experimental I-V curve and a suitable nonlinear
algorithm to minimize the sum of the squared errors.
In this section, we propose a new technique that uses
the measured current-voltage curve and its derivative.
A nonlinear least-squares optimization algorithm
based on the Newton-Raphson model is hence used
to evaluate the solar cell parameters. The problem, we
have, is to minimize the objective function S with
respect to the set of parameters θ:
(3)
Where Ө is the set of unknown parameters Ө= (Iph, Is,
n, Rs, Gsh) and Ii, Vi are the measured current, voltage
and computed conductance
respectively at the ith point among N measured data
points. Note that the differential conductance is
determined numerically for the whole I-V curve
using a method based on the least-squares principle
and a convolution. The conductance G can be written
as:
(4)
Where:
(5)
Consequently, by minimizing the sum of the squares
of the conductance residuals instead of minimizing
the sum of the squares of current residuals as reported
by Easwarakhanthan et al [11]. The Newton-Raphson
method can be used to obtain an approximation to the
exact solution, and it is given by:
(6)
With
=0 (7)
Where i is the index for iteration number. Both of
and are the five elements vectors that hold
the next and the current values of the five parameters.
J(Ө) is the Jacobian matrix that contains the partial
derivatives for each equation corresponding to each
of the five parameters, it will be a 5x5 matrix
computed for the current value of the four
parameters. contains the five partial
differential equations to be calculated for the current
values of the parameters. The developed system of
nonlinear equations can be represented in the
following form:
1 1 1 1 1
12 2 2 2 2
3 3 3 3 3
44 4 4
5 5 5
ph s s sh
ii
ph ph ph s s sh
ss
ss
ph s s sh
sh sh
ph s s sh
ph s s
F F F F F
I I R R n
F F F F F
III I R R n
II
F F F F F
RR
I I R R n
RRFF F F
nn
II R R
F F F F
I I R
+
=−
( )
( )
( )
( )
( )
1
1
2
3
4
4
5
55
, , , ,
, , , ,
, , , ,
, , , ,
, , , ,
ph s s sh
ph s s sh
ph s s sh
ph s s sh
ph s s sh
sh
F I I R R n
F I I R R n
F I I R R n
F I I R R n
FF I I R R n
n
F
Rn
−
(8)
Although Newton’s method converges only locally
and may diverge under an improper choice of
reasonably good starting values for the parameters, it
remains attractive with the number of variables and
their partial derivatives easily. To illustrate the
approach, we have first applied the method to a
computer-calculated curve reproducing the same
solar cell characteristic used by Eswarakhantan et al
[11]. To test the effects of different initial values on
the method, the known exact solutions were
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2022.21.16
N. Nehaoua, I. Ami, F. Mebtouche,
H. Meziani, S.H. Abaidia
E-ISSN: 2224-266X
156
Volume 21, 2022
multiplied by the factors [0.2-1.5] respectively and
after carrying out the calculations; the extracted solar
cell parameters were almost identical to the
theoretical ones.
2.3. Experiments
The method was validated on different types of
photovoltaic devices, organic and inorganic solar
cells under illumination and using experimental I–V
characteristics under different conditions including a
temperature effect on parameters determination.
The first one, is an inorganic solar cell based on a
silicon solar cell under a temperature of 33°C and a
solar module in which 36 polycrystalline silicon solar
cells are connected in series at 45°C.
Second, a polymer solar cells based on TiO2
nanocrystals (anatase and rutile) as electron
extraction layer under a temperature of 298.15 K and
irradiation intensity of 100 mW/cm2, where the
currents are generally 1000 times smaller and have
high series resistances compared to inorganic
(silicon) solar cells.
3. Results and discussion
The experimental current-voltage (I–V) data were
taken from Easwarakhantan et al [11] for the
commercial silicon solar cell/module and from Lijie
Zhu et al [8] for the polymer solar cell. The extracted
parameters obtained using the method proposed here
for the different devices are given in Table 1.
Satisfactory agreement is obtained for most of the
extracted parameters. A comparison with different
methods is also given, and good agreement is
reported. Statistical indicators of accuracy for the
method of this work are shown in Table 2.
The best fits are obtained for the silicon solar cell and
module with a root mean square error of less than 1%
and 2% for the polymer solar cell. In figures 2, 3, and
4, the solid squares are the experimental data for the
different solar cell and the solid line is the fitted curve
derived from Eq. (1) with the parameters shown in
Table 1 for the different solar cell organic and
inorganic solar cell.
In order to test the quality of the fit to the
experimental data, the percentage error is calculated
as follows:
(9)
Where Ii,cal is the current calculated for each Vi, by
solving the implicit Eq.(1) with the determined set of
parameters ( Iph, n, Rs, Gsh, Is). (Ii, Vi) are respectively
the measured current and voltage at the ith point
among N considered measured data points avoiding
the measurements close to the open-circuit condition
where the current is not well-defined [22]. Statistical
analysis of the results has also been performed. The
root means square error (RMSE), the mean bias error
(MBE) and the mean absolute error (MAE) are the
fundamental measures of accuracy. Thus, RMSE,
MBE and MAE are given by:
1/2
2
i
i
i
e
RMSE N
e
MBE N
e
MAE N
=
=
=
(10)
N is the number of measurements data taken into
account.
For comparaison, The root means square error
RMSE1 is calculated using the equation 11, where
Ii,cal is given by the equation (2) as following:
( )
1/2
2
,100
1
1i i cal
i
II
RMSE NI
−
=
(11)
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2022.21.16
N. Nehaoua, I. Ami, F. Mebtouche,
H. Meziani, S.H. Abaidia
E-ISSN: 2224-266X
157
Volume 21, 2022
Table1: Extracted parameters for different solar cell and module
Model type
T(°C)
Iph (A)
Is (mA)
n
Rs (Ω)
Gsh (Ω-1)
Crystalline silicon solar cell
Mono-Si-solar cell
33
40
47
0.7606
0.8235
0.8987
0.2296
0.2369
0.2892
1.4425
1.4835
1.5058
0.0392
0.0351
0.0289
0.0114
0.0208
0.0198
Ref [11]
33
0.7608
0.3223
1.4837
0.0364
0.0186
Poly-Si- module
45
50
55
1.0333
1.0621
1.0966
2.4920
2.6682
2.9831
47.35
47.85
48.26
1.2373
1.086
1.058
0.00144
0.0028
0.0056
Ref [11]
45
1.0318
3.2876
48.450
1.2057
0.00182
Polymer solar cell based on TiO2
TiO2 anatase
25
30
35
15.35
15.60
15.96
1.01 e-6
1.03 e-6
1.04 e-6
1.65
1.78
1.88
1.40
1.35
1.31
0.20e-2
0.19e-2
0.13e-2
Ref [8]
25
15.66
1.08 e-5
1.69
1.45
0.18e-2
TiO2 Rutile
25
30
35
13.95
14.25
14.58
3.77e-6
3.98e-6
3.88e-6
1.92
1.96
2.09
2.05
2.00
1.98
0.16e-2
0.13e-2
0.10e-2
Ref [8]
25
14.64
3.89e-6
1.88
2.18
0.12e-2
Table2: Statistical indicators prediction of accuracy
for the method of this work
Good agreement is observed, especially for the
inorganic solar cells. It is therefore necessary to
emphasize that the proposed method is not based on
the I-V characteristics alone but also on the derivative
of this curve, i.e. the conductance G. Indeed, it has
been demonstrated that it is not sufficient to obtain a
numerical agreement between measured and fitted I-
V data to verify the validity of a theory, but also the
conductance data have to be predicted to show the
physical applicability of the used theory. The
interesting points with the procedure described herein
is the fact that it has been successfully applied to
experimental I–V characteristics of different types of
solar cells from inorganic to organic solar cells with
completely different physical characteristics and
under different temperatures. In contrast to other
methods that have already been developed for this
purpose, the proposed method has no limitation
condition on the voltage. Furthermore, the presented
Model
type
T
(°C)
RMSE
(%)
RMSE1
(%)
MBE
(%)
MAE
(%)
Crystalline silicon solar cell
Mn-Si
33
40
47
0.442
0.522
0.482
0.162
0.193
0.172
-0.016
-0.023
-0.018
0.310
0.365
0.273
Poly-Si
45
50
55
0.227
0.252
0.277
0.193
0.215
0.236
-0.007
-0.008
-0.009
0.183
0.204
0.222
Polymer solar cell based on TiO2 nanocrystal
A-TiO2
25
1.806
1.503
0.638
1.201
R-TiO2
25
1.682
1.325
0.423
1.092
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2022.21.16
N. Nehaoua, I. Ami, F. Mebtouche,
H. Meziani, S.H. Abaidia
E-ISSN: 2224-266X
158
Volume 21, 2022
method, tested for the selected cases, is more reliable
to obtain physically meaningful parameters and is
straightforward to use.
Mono- silicon solar cell
Poly- silicon solar module.
Fig.2-Experimental data (■) and the fitted curve (-) for the commercial silicon solar and module.
TiO2 anatase
TiO2 rutile
Fig.3-Experimental data (■) and the fitted curve (-) for the polymer solar cells
5. Conclusion
This contribution presents and analyses a simple
and powerful method of extracting solar cell
parameters which affect directly the conversion
efficiency, the power conversion, the fill factor, and
the current-voltage shape of the solar cell. These
parameters are the ideality factor, the series
resistance, diode saturation current, and shunt
conductance. This technique is not only based on the
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Voltage (V)
Current (A)
I-V characteristics and fitted curves
experiental data
fitted curve
-2 0 2 4 6 8 10 12 14 16 18
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Voltage (V)
Current (A)
I-V characteristics and fitted curves
experimental data
fitted curve
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2022.21.16
N. Nehaoua, I. Ami, F. Mebtouche,
H. Meziani, S.H. Abaidia
E-ISSN: 2224-266X
159
Volume 21, 2022
current-voltage characteristics but also the derivative
of this curve, the conductance G. by using this
method, the extracted parameters are Is, n, Rs, Gsh, and
Iph. The method has been successfully applied to a
silicon solar cell, a module, and an organic solar cell
under different temperatures. The results obtained are
in good agreement with those published previously.
The method is very simple to use. It allows real-time
characterization of different types of solar cells and
modules in indoor or outdoor conditions.
Reference
[1] G.M Wilson, M Al-Jassim, W.K Metzger, S.W
Glunz, P Verlinden, G Xiong, L.M Mansfield,
B.J Stanbery, K Zhu, Y Yan. J. Phys. D Appl.
Phys. 2020, 53, 493001.
[2] M Yamaguchi, F Dimroth, J F. Geisz, N J. Ekins-
Daukes. J. Appl. Phys. 129, 240901 (2021)
[3] M. Yamaguchi, Phys. Status Solidi C 12, 489
(2015)
[4] A Polman, M Knight, E.C Garnett, B Ehrler, W.C
Sinke. Science 2016, 352, 6283.
[5] A W Y Ho-Baillie, J Zheng, Md A Mahmud, Fa-Jun
Ma, D R McKenzie, M A Green. Applied Physics
Reviews 8, 041307 (2021).
[6] S Kim, V.Q Hoang, C.W Bark. Nanomaterials
2021, 11, 2944. doi.org/10.3390/nano11112944.
[7] F. Rasool, et al., Sol. Energy 153 (2017) 519–530.
[8] O Ourahmoun, wseas transactions on circuits and
systems journal,
DOI: 10.37394/23201.2020.19.20
[9] J P Charles, M Abdelkrim, Y H Muoy, P Mialhe,
Solar cells. 4, 169-178 (1981)
[10] J. P. Charles, M. A. Ismail, and G. Bordure,
Solide- State electron. 28 (8), 807-820 (1985)
[11] T. Easwarakhanthan, J. Bottin, I. Bouhouch, and
C. Boutrit, Int. J. Solar Energy. 4, 1-12 (1986)
[12] Phang, Jacob, C. H. Chan, S. H. Daniel, Solar
cells. 18, 1-12 (1986)
[13] N. Santakrus Singh, Amit Jain, and Avinashi
Kapoor, Solar Energy Materials and Solar Cells.
93, 1423–1426 (2009)
[14] M. Priyanka, and S. Lal, N. Singh, Solar energy
material and solar cells. 91, 137-142 (2007)
[15] A. Jain, A. Kapoor, Solar energy mater, solar
cells. 86, 197-205 (2005)
[16] A. Jain, A. Kapoor, Solar energy mater, solar
cells. 81, 269-277 (2004)
[17] J Appelbaum, A Peled, 2014. Solar Energy
Materials and Solar Cells 122, 164–173.
[18] Utkarsh Jadli, Padmanabh Thakur, Rishabh Dev
Shukla. 2018.. IEEE Journal of Photovoltaics 8
(1), 239–247. ISSN 2156–3381. doi:
10.1109/JPHOTOV.2017.2767602.
[19] Seyedkazem Hosseini, Shamsodin Taheri,
Masoud Farzaneh, Hamed Taheri, Mehdi
Narimani. 2018. IEEE Journal of Photovoltaics
8 (2), 572–580. ISSN 2156–3381.
[20] Wook Kim, Woojin Choi, solar energy. 84,
1008-1019 (2010)
[21] M. Khalis, Y. Hemine, M. Zazoui, Eur. Phys. J.
Appl. Phys. 54, 10102 (2011)
[22] L. Peng, Y. Sun,Z. Meng, Y Wang, Y Xu Journal
of power source 227 (2013) 131-136.
[23] A Vijayakumari, 2020. A non-iterative MPPT of
PV array with online measured short circuit and
open circuit quantities. Journal of King Saud
University Engineering Sciences. ISSN
10183639. doi: 10.1016/j.jksues.2020.04.007.
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2022.21.16
N. Nehaoua, I. Ami, F. Mebtouche,
H. Meziani, S.H. Abaidia
E-ISSN: 2224-266X
160
Volume 21, 2022
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
