Extraction of photovoltaic generator parameters through combination of an analytical and iterative approach

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 5, October 2022, pp. 4529~4537
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i5.pp4529-4537  4529
Journal homepage: http://ijece.iaescore.com
Extraction of photovoltaic generator parameters through
combination of an analytical and iterative approach
Abdelaaziz Benahmida1
, Noureddine Maouhoub1
, Kawtar Tifidat1
, Hassan Sahsah2
1
Laboratory of Electronics, Signal Processing and Physical Modeling, Department of Physics, Faculty of Sciences, Ibn Zohr University,
Agadir, Morocco
2
Laboratory of Metrology and Information Processing, Department of Physics, Faculty of Sciences, Ibn Zohr University,
Agadir, Morocco
Article Info ABSTRACT
Article history:
Received Dec 31, 2020
Revised May 21, 2022
Accepted Jun 6, 2022
In the present work, we propose an improved method based on a
combination of an analytical and iterative approach to extract the
photovoltaic (PV) module parameters using the measured current-voltage
characteristics and the simple diode model. First, we calculate the series
resistance using a set of analytical formulas for the base values of the three
current-voltage curves. Then, the three other parameters are analytically
expressed as functions of serial resistance and ideality factor based on the
linear least-squares method. Finally, the ideality factor is calculated applying
an iterative algorithm to minimize the normalized root mean square error
(NRMSE) value. The proposed method was validated with a real
experimental set of two PV generators, which showed the best fit to the I-V
curve. Moreover, the proposed method needs only the initial value of the
ideality factor.
Keywords:
Current-voltage curve
Least square method
One diode equivalent circuit
Photovoltaic generator
This is an open access article under the CC BY-SA license.
Corresponding Author:
Noureddine Maouhoub
Department of Physics, Faculty of Sciences, Ibn Zohr University
BP 8106 Agadir, Morocco
Email: n.maouhoub@uiz.ac.ma
1. INTRODUCTION
Photovoltaic systems are used widely in employment, either solely or in confluence with other
electrical power sources. Applications powered by photovoltaic (PV) systems include communication
equipment, somehow powered telecommunications installations, remote monitoring, lighting, water
pumping, and battery charging. The modeling of PV arrays and modules plays an essential role in the
performance and productivity of PV systems. The extraction of solar cell or PV module parameters is critical
for determining the performance of various jobs and carrying out their design and quality control.
Several techniques and approaches have been offered to obtain the five physical parameters using
the one diode model. These approaches are grouped into three classes: analytical, numerical, and
evolutionary approaches [1]–[23]. Villalva et al. [5], which is among the most cited diving factories in this
area, proposed a simple algorithm to extract the five parameters. This algorithm uses the series resistance as a
duplication parameter to minimize the error between the calculated and measured peak power values. The
disadvantage of this method is that it’s accurate near the maximum power point but inaccurate in other
regions and uses a fixed value of ideality factor equal to 1.3. Cubas et al. [11] has proposed a coherent
approach using four analytical expressions with some approximation to extract the four parameter values and
an ideality factor equal to 1.3. Ma et al. [17] have presented an extraction algorithm based on bio-inspired.
Furthermore, a study of two technics using an iterative algorithm and the Lambert function has been

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 5, October 2022: 4529-4537
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suggested in work [18] to determine the five parameters of the PV modules under varying environmental
conditions.
New, Achouby et al. [21] provided an exact numerical approach to find the five physical
parameters. This method is based on varying the ideality parameter and resolving a nonlinear system of four
equations. This method requires appropriate initial guess for four physical parameters. Zaimi et al. [22]
presented a method based on a combination of well-founded and numerical approaches. This technique needs
two coherent initial values of series resistance and ideality factor. Stornelli et al. [23] suggested a new,
five-parameter method. This simplified method allows one to find the optimal value of the ideality parameter
and the shunt resistance.
In this investigation, we present another technique based on a combination of iterative and analytical
approaches to extract physical parameters of a single diode model of a PV generator. In the first step, we use
a well-founded expression to calculate the series resistance Rs. In the spare step, we derive three analytic
equations giving the parallel resistor Rsh, the saturation current Is, and the photo-current Iph as functions of
series resistance Rs and ideality factor n using the linear least squares method. In the final step, we use the
ideality factor as a parameter iteration to minimize the normalized root mean square error (NRMSE). This
procedure has the advantage of using only one foremost value of an ideality parameter and allows us to
reduce the number of unknowns to one.
2. PROPOSED METHOD
2.1. PV module modelling
A PV module consists of several solar cells in series or parallel that transform solar irradiation into
electrical current. To describe the PV module behavior, we use in our work the one diode model with five
parameters; this model is the most used in the literature. The electrical equivalent circuit of the model is
depicted in Figure 1.
Figure 1. Equivalent circuit for one diode PV cell model
The mathematical behavior of the PV panel connecting the output current and voltage and the five
parameters is given by (1).
𝐼 = 𝐼𝑝ℎ − 𝐼𝑠 (𝑒𝑥𝑝 (
𝑉+𝑅𝑠.𝐼
𝑛.𝑁𝑠.𝑉𝑡ℎ
) − 1) −
𝑉+𝑅𝑠.𝐼
𝑅𝑠ℎ
(1)
Where Iph is the photoelectric current, Is is the current of saturation on the diode, Rsh is the parallel resistance,
n is the ideality factor, Rs is the series resistance, Ns is the number of solar cell connected in series
(Ns=1 for the solar cell), Vth is the thermal voltage given by: 𝑉𝑡ℎ =
𝑘𝐵.𝑇
𝑞
. Where q is the electronic charge, kB
is the Boltzman’s constant and T is the temperature in Kelvin. The equation (1) is implicit and requires
numerical resolution. The explicit expression of this equation using the Lambert function is given by (2):
𝐼 = −
𝐼𝑠+𝐼𝑝ℎ
1+𝑅𝑠.𝐺𝑠ℎ
+
𝐺𝑠ℎ
1+𝑅𝑠.𝐺𝑠ℎ
𝑉 +
𝑅𝑠
𝐿𝑎𝑚𝑏𝑒𝑟𝑡𝑊 (
𝐼𝑠.𝑅𝑠
𝑛.𝑁𝑠.𝑉𝑡ℎ.(1+𝑅𝑠.𝐺𝑠ℎ)
𝑒𝑥𝑝 (
𝑉+𝑅𝑠.(𝐼𝑠+𝐼𝑝ℎ)
𝑛.𝑁𝑠.𝑉𝑡ℎ.(1+𝑅𝑠.𝐺𝑠ℎ)
)) (2)
where Gsh is the parallel conductance given by 1/Rsh.
2.2. Extraction method
2.2.1. Analytical expression of Rs
The evaluation of the (1) at the three remarkable points of I-V curve (V=Voc, I=0), (V=0, I=Isc) and
(V=Vmp, I=Imp) points, respectively, provide the equations:

Int J Elec & Comp Eng ISSN: 2088-8708 
Extraction of photovoltaic generator parameters through combination of an … (Abdelaaziz Benahmida)
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0 = 𝐼𝑝ℎ − 𝐼𝑠 (𝑒𝑥𝑝 (
𝑉𝑜𝑐
) − 1) −
𝑉𝑜𝑐
𝑅𝑠ℎ
(3)
𝐼𝑠𝑐 = 𝐼𝑝ℎ − 𝐼𝑠 (𝑒𝑥𝑝 (
𝑅𝑠𝐼𝑠𝑐
) − 1) −
𝑅𝑠𝐼𝑠𝑐
𝑅𝑠ℎ
(4)
𝐼𝑚𝑝 = 𝐼𝑝ℎ − 𝐼𝑠 (𝑒𝑥𝑝 (
𝑉𝑚𝑝+𝑅𝑠𝐼𝑚𝑝
) − 1) −
𝑉𝑚𝑝+𝑅𝑠𝐼𝑚𝑝
𝑅𝑠ℎ
(5)
According to [11] and using the three previous equations, Rs can be expressed analytically:
𝑅𝑠 =
𝛼𝑉𝑚𝑝+𝛽(𝑉𝑜𝑐−𝑉𝑚𝑝)
(𝛼+𝛽)𝐼𝑚𝑝
(6)
α and β are given by:
𝛼 = (𝑉
𝑚𝑝 + (𝐼𝑚𝑝 − 𝐼𝑠𝑐)𝑅𝑠ℎ0) 𝑙𝑛 (
𝑉𝑚𝑝+(𝐼𝑚𝑝−𝐼𝑠𝑐)𝑅𝑠ℎ0
𝑉𝑜𝑐−𝐼𝑠𝑐𝑅𝑠ℎ0
) ; 𝛽 = 𝑉
𝑚𝑝 − 𝑅𝑠ℎ0𝐼𝑚𝑝 (7)
Rsh0 is the slope at the short circuit point:
𝑅𝑠ℎ0 = −
𝑑𝑉
𝑑𝐼
|
𝐼=𝐼𝑠𝑐
(8)
2.2.2. Calculation of Is, Iph and Gsh
In order to calculate the three parameters Iph, Is and Rsh as function of Rs and n, we use a linear least
square method to minimize the follow error expression:
𝐹 = ∑ (𝐼𝑖,𝑐𝑎(𝑉𝑖,𝑒𝑥) − 𝐼𝑖,𝑒𝑥)
2
=
𝑁
𝑖=1
∑
(𝐼𝑝ℎ − 𝐼𝑆 (𝑒𝑥𝑝 (
𝑉𝑖,𝑒𝑥+𝑅𝑆.𝐼𝑖,𝑒𝑥
𝑛.𝑉𝑡ℎ
) − 1) − 𝐺𝑠ℎ(𝑉𝑖,𝑒𝑥 + 𝑅𝑆. 𝐼𝑖,𝑒𝑥) − 𝐼𝑖,𝑒𝑥)
𝑁
𝑖=1 ² (9)
Ii,ex and Ii,ca are the measured and the theoretical current. Vi,ex is the experimental voltage of the PV module
and N is the number of experimental points. The minimization of the F function requires the system
resolution (10):
{
𝜕𝐹
𝜕𝐼𝑝ℎ
= 2 ∑
𝜕𝐼𝑖,𝑐𝑎
𝜕𝐼𝑝ℎ
(𝐼𝑖,𝑐𝑎 − 𝐼𝑖,𝑒𝑥
𝑁
𝑖=1 ) = 0
𝜕𝐹
𝜕𝐼𝑠
= 2 ∑
𝜕𝐼𝑠
𝑁
𝑖=1 ) = 0
𝜕𝐹
𝜕𝐺𝑠ℎ
= 2 ∑
𝜕𝐺𝑠ℎ
𝑁
𝑖=1 ) = 0
(10)
After some mathematical operations, the previous system of equations become [19]:
{
𝐼𝑝ℎ𝑁 − 𝐼𝑠 ∑ 𝐸𝑋𝑃𝑖 − 𝐺𝑠ℎ ∑ 𝑉𝑠ℎ,𝑖
𝑁
𝑖=1
𝑁
𝑖=1 = ∑ 𝐼𝑖,𝑒𝑥
𝑁
𝑖=1
−𝐼𝑝ℎ ∑ 𝐸𝑋𝑃𝑖 + 𝐼𝑠 ∑ 𝐸𝑋𝑃𝑖
2
𝑁
𝑖=1 +
𝑁
𝑖=1 𝐺𝑠ℎ ∑ 𝑉𝑠ℎ,𝑖
𝐸𝑋𝑃𝑖
𝑁
𝑖=1 = − ∑ 𝐼𝑖,𝑒𝑥
𝑁
𝑖=1 𝐸𝑋𝑃𝑖
−𝐼𝑝ℎ ∑ 𝑉𝑠ℎ,𝑖
𝑁
𝑖=1 + 𝐼𝑠 ∑ 𝑉𝑠ℎ,𝑖
𝐸𝑋𝑃𝑖 + 𝐺𝑠ℎ ∑ 𝑉𝑠ℎ,𝑖
2
𝑁
𝑖=1
𝑁
𝑖=1 = − ∑ 𝐼𝑖,𝑒𝑥𝑉𝑠ℎ,𝑖
𝑁
𝑖=1
(11)
where EXPi and Vsh,i are given by (12):
𝐸𝑋𝑃𝑖 = 𝑒𝑥𝑝 (
𝑉𝑖,𝑒𝑥+𝑅𝑆.𝐼𝑖,𝑒𝑥
𝑛.𝑁𝑆.𝑉𝑡ℎ
) − 1; 𝑉𝑠ℎ,𝑖 = 𝑉𝑖,𝑒𝑥 + 𝑅𝑆. 𝐼𝑖,𝑒𝑥 (12)
2.2.3. Algorithm of ideality factor extraction
In this algorithm, we use ideality factor n as variation parameter which varies between 1 and 2 for
silicon material and solve the linear system of (10) using MATLAB to find Iph, Is and Rsh values. Then, we
select n that minimize the NRMSE value:

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𝑁𝑅𝑀𝑆𝐸 =
[
1
𝑁
∑ (𝐼𝑖−𝐼𝑖,𝑚)
2
𝑁
𝑖=1 ]
1
2
1
𝑁
∑ 𝐼𝑖,𝑚
𝑁
𝑖=1
(13)
In Figure 2, we have detailed the extraction strategy of the five parameters using our proposed technique. The
main steps are given by the following flowchart.
Figure 2. Proposed flowchart method
3. RESULTS AND DISCUSSION
We confirm the suggested approach through two experimental test cases: the RTC solar cell at 33 °C
and 1000 W/m² [1] and the multicrystalline panel KC200GT operating at standard test conditions (STC)
(T=25 °C and G=1000 W/m2), the experimental current-voltage curve are extracted from manufacturer’s
datasheet [24]. In order to evaluate the accuracy of our method, we use the NRMSE using (13) and the
absolute error given by (14):
𝐴𝐸 = |𝐼𝑖,𝑒𝑥 𝑝 − 𝐼𝑖,𝑐𝑎𝑙| (14)
In Table 1, we summarized the remarkable points values and Rsh0 for the solar cell and the PV panel.
Table 1. Remarkable point’s values and Rsh0
RTC solar cell KC200GT PV panel
Imp (A) 0.67 7.61
Vmp (V) 0.46 26.3
Isc (A) 0.76 8.21
Voc (V) 0.57 32.9
Rsh0 (Ω) 58.656 597
Tables 2 and 3 present the obtained values of the five parameters using the our technic for the solar
cell and PV module respectively. For comprehensive comparison, the proposed algorithm is evaluated
against previously techniques. According to this two tables, our method has the lowest NRMSE value. In
Figures 3(a) and 3(b), we plot the NRMSE values versus ideality factor n, for the two experimental cases.
According to these figures, the optimal value of n which minimizes the NRMSE is equal to 1.55 for solar cell
and equal to 1.1 for PV module.

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Figures 4(a) and 4(b) present the measured and the simulated current-voltage I (V) curves obtained
by using the Lambert-function model, for the two cases studies, solar cell and KC200GT. As it can be seen
for both cases, the simulated characteristics are in excellent accordance with the experimental data. The
benefits of the proposed method are that need only one initial guess.
Table 2. Solar cell parameters at 33 °C and 1000 W/m²
Parameters Method [3] Method [6] Method [25] Proposed method
Rs(Ω) 0.037 0.036 0.0355 0.033
n 1.45 1.48 1.4905 1.55
Iph(A) 0.7611 0.7607 0.7611 0.7606
Is(A) 2.422.10-7 3.267.10-7 3.514.10-7 6.271.10-7
Rsh(Ω) 42 60.24 45.0472 66.36
NRMSE 0.078 0.068 0.0072 0.0026
Table 3. PV module parameters at STC conditions
Parameters Method [11] Method [5] Method [19] Method [23] Proposed method
Rs(Ω) 0.23 0.221 0.233 0.2185 0.23
n 1.3 1.3 1.0758 1.1 1.1
Iph(A) 8.213 8.214 8.211 8.196 8.211
Is(A) 9.76.10-8 9.825.10-8 2.12.10-9 3.27.10-9 3.143.10-9
Rsh(Ω) 597.38 415.405 132.88 164.2 154.64
NRMSE 0.0571 0.0564 0.0086 0.0087 0.0069
(a) (b)
Figure 3. NRMSE vs. n for (a) solar cell and (b) KC200GT
(a) (b)
Figure 4. Measured and simulated characteristics I (V) for (a) solar cell and (b) KC200GT

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In order to evaluate the impact of temperature cell T and irradiance level G on the five parameters
and the I-V characteristic, we use the following expressions [19].
𝑛(𝑇, 𝐺) = 𝑛𝑆𝑇𝐶 (15)
𝑅𝑠(𝑇, 𝐺) = 𝑅𝑠,𝑆𝑇𝐶 (16)
𝑅𝑠ℎ(𝑇, 𝐺) = 𝑅𝑠ℎ,𝑆𝑇𝐶 (17)
𝐼𝑝ℎ(𝑇, 𝐺) =
𝐺
𝐺𝑆𝑇𝐶
. (𝐼𝑝ℎ,𝑆𝑇𝐶 + 𝐾𝑖. (𝑇 − 𝑇𝑆𝑇𝐶)) (18)
𝐼𝑠(𝑇, 𝐺) =
𝐼𝑝ℎ(𝑇,𝐺)−𝐺𝑠ℎ.𝑉𝑜𝑐(𝑇,𝐺)
𝑒𝑥𝑝(
𝑉𝑜𝑐(𝑇,𝐺)
𝑁𝑠.𝑛.𝑉𝑡ℎ(𝑇)
)−1
(19)
Where, GSTC and TSTC are the overall radiation ant temperature under STC conditions and Voc is given by the
following analytical model [21]:
𝑉
𝑜𝑐(𝑇, 𝐺) = 𝑉𝑜𝑐,𝑆𝑇𝐶 + 𝐾𝑉. (𝑇 − 𝑇𝑆𝑇𝐶) + 𝑛. 𝑁𝑠. 𝑉𝑡ℎ(𝑇). 𝑙𝑛 (
𝐺
𝐺𝑆𝑇𝐶
) (20)
Where, KV is the temperature coefficient of Voc and Voc, STC is the open-circuit voltage in STC conditions.
Figure 5(a) displays the measured and the simulated I-V characteristic for the KC200GT panel. As
can be clearly seen, the simulated curve of the aforementioned PV module is in very close accord with the
measured data at T=25 °C and at various irradiation levels. In Figure 5(b), we display variations of absolute
error curve for a temparture 25 °C and different irradiation levels. In the voltage variation interval [0, Vmp],
the theoretical and experimental I=f(V) curves are in good agreement and the absolute current error tends to
cancel. When, at a voltage variation n the interval [Vmp, Voc], the current decreases rapidly and the AE
increases slightly but still remains below 0.15 for the irradiadiance 1000 W/m² and 0.3 for the iradainces
800 W/m², 600 W/m², 400 W/m² and 200 W/m². The current has an exponential characteristic in the zone
[Vmp,Voc] at an almost constant voltage.
(a) (b)
Figure 5. Accuracy of the proposed method (a) measured and simulated I(V) characteristics and
(b) absolute error AE(V), for KC200GT panel under varying irradiance
In Figure 6(a), we display the measured and the simulated I-V characteristic, for the KC200GT
panel for fixed irradiation 1000 W/m² and at the temperature values 25 °C, 50 °C and 75 °C. We also display,
in Figure 6(b), the curves AE=f(V). It is clearly that the simulated values of the model are in harmony with
the measured data. In the voltage variation interval [0, Vmp], the theoretical and experimental I=f(V) curves
are in good agreement and the absolute current error tends to cancel. When, at a voltage variation in the
interval [Vmp, Voc], the current decreases rapidly and the AE increases slightly but still remains below 0.2 for

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the temperature 25 °C and 0.8 for the temperatures 50 °C and 75 °C. In the [Vmp,Voc] area the voltage is
almost constant while the current is exponential and is sensitive to a few simple variations.
(a)
(b)
Figure 6. Accuracy of the proposed method (a) measured and simulated I(V) characteristics and (b) absolute
error AE(V), for KC200GT panel under varying temperature
4. CONCLUSION
This article proposed an efficient hybrid method to determine the five PV module parameters using
the measured current-voltage characteristics and the simple diode model. This method is based on the
analytical calculation of the series resistance using three specific points of the experimental current-voltage
curves. The saturation current, the photo current and the parallel resistance are expressed depending on the
ideality factor by solving of a system of three linear equations using the linear least squares approach. The
ideality factor value is determined iteratively to minimize the NRMSE value. The results obtained for two
experimental cases studies of solar cell and PV panel show a good agreement and low error between the
measured and the simulated data.
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BIOGRAPHIES OF AUTHORS
Abdelaaziz Benahmida received a degree in Electromechanical Engineering
from the National School of Mineral Industry (ENIM), in Rabat, Morocco, in 2004. In 2021 he
achieved a Bachelor’s degree in Economic Sciences and Management. Currently, Ph.D student
in Electronics and Renewable Energy at the Department of Physics, Laboratory of Electronics,
Signal Processing and Physical Modeling, Faculty of Science, University Ibn Zohr, Agadir,
Morocco. His research focuses on electrical characterization of photovoltaic generators,
modeling and optimization of solar systems. He can be contacted at the following email
address: abdelaaziz.benahmida@edu.uiz.ac.ma.

4537
Noureddine Maouhoub is currently a Professor at Faculty of Sciences,
Department of Physics, Ibn Zohr University in Agadir, Morocco. He obtained his Ph. D degree
in Electronics and Microelectronics from Chouaib Doukkali University, Faculty of Sciences-
El Jadida, Morocco. He received the Master degree in Electronics, Automatics and Signal
Processing from the same University. His current area of interest is Photovoltaic System,
Characterization and optimization of PV Generators and Characterization and modeling of
MOSFET transistor. He can be contacted at email: n.maouhoub@uiz.ac.ma.
Kawtar Tifidat received her Lic degree in Electronics and Systems of
Communication from Ibn Zohr University. Hold a Master’s degree in Systems and
Telecommunication from the Faculty of Sciences, Ibn Zohr University, Agadir, Morocco.
Currently, a Ph.D. student in Electronics and Renewable Energies at the Department of
Physics, Laboratory of Electronics, Signal Processing and Physical Modeling, Faculty of
Sciences, Ibn Zohr University, Agadir, Morocco. Her main research interests include
modeling, simulating, designing, and optimization of photovoltaic systems. She can be
contacted at email: kawtar.tifidat@edu.uiz.ac.ma.
Hassan Sahsah is currently a Professor at Faculty of Sciences, Department of
Physics, Ibn Zohr University in Agadir. He obtained his Ph. D degree in Opto-Electronics and
instrumentation from Jean Monnet University, Faculty of Sciences-Saint Etienne, in 1994. His
research interest includes Photovoltaic System and Opto-Electronics. He can be contacted at
email: h.sahsah@uiz.ac.ma.

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