Comprehensive modeling and simulation of photovoltaic system performance by using matlab/simulink: integrating dynamic meteorological parameters for enhanced accuracy

Abstract

Studying the operation of photovoltaic panels in the presence of varying meteorological parameters is a complex undertaking that requires the development of models to understand the physical phenomena associated with different meteorological factors. The main aim of this study is to examine the impact of meteorological factors, such as illuminance, temperature, and wind speed, on the performance of photovoltaic modules. Our goal is to develop precise models that illustrate how these factors affect the output of a photovoltaic system at a specific location. To achieve this, we utilized a rigorously validated mathematical model, previously tested with photovoltaic simulation software such as PVsyst, enabling accurate prediction of photovoltaic installation output. We compared the results of our simulations, conducted with the chosen mathematical model, with those obtained from PVsyst software. Subsequently, we validated the accuracy of our proposed model using real operating conditions simulated by PVsyst. Additionally, we incorporated additional curves, not available in the PVsyst database, accounting for wind speed as a meteorological parameter.

Full text

Vol.:(0123456789)
Journal of Umm Al-Qura University for Applied Sciences
https://doi.org/10.1007/s43994-024-00175-5
ORIGINAL ARTICLE
Comprehensive modeling andsimulation ofphotovoltaic system
performance byusing matlab/simulink: integrating dynamic
meteorological parameters forenhanced accuracy
MohamedNfaoui1· FatimaEzzahraIhfa2· AyoubBougtaib1· AmineElHarfouf1· SanaaHayani‑Mounir1·
MohamedBennai2· KhalilEl‑Hami3
Received: 31 January 2024 / Accepted: 29 June 2024
© The Author(s) 2024
Abstract
Studying the operation of photovoltaic panels in the presence of varying meteorological parameters is a complex undertak-
ing that requires the development of models to understand the physical phenomena associated with different meteorological
factors. The main aim of this study is to examine the impact of meteorological factors, such as illuminance, temperature,
and wind speed, on the performance of photovoltaic modules. Our goal is to develop precise models that illustrate how these
factors affect the output of a photovoltaic system at a specific location. To achieve this, we utilized a rigorously validated
mathematical model, previously tested with photovoltaic simulation software such as PVsyst, enabling accurate prediction
of photovoltaic installation output. We compared the results of our simulations, conducted with the chosen mathematical
model, with those obtained from PVsyst software. Subsequently, we validated the accuracy of our proposed model using
real operating conditions simulated by PVsyst. Additionally, we incorporated additional curves, not available in the PVsyst
database, accounting for wind speed as a meteorological parameter.
Keywords Component· Photovoltaic· Meteorological parameters· Modeling· Simulation· Matlab/Simulink· PVSYST·
I–V and P–V curves
1 Introduction
In the field of photovoltaics, numerous comprehensive stud-
ies have been conducted to examine the modeling of systems
and their responses across diverse usage contexts, and we
cite the articles from these studies [1–9]. This research is of
critical importance as it aims to optimize efficiency, promote
sustainability, and foster the adoption of photovoltaic sys-
tems. This holistic enhancement is pivotal in the transition
towards cleaner, renewable energy sources, including green
hydrogen [10, 11]. Incorporating findings from these inves-
tigations into the design and implementation of PV systems
can enhance the efficient utilization of solar resources [12,
13], meeting increasing energy demands in an environmen-
tally sustainable manner.
Studies in the field of modeling photovoltaic panels using
equivalent mathematical models have led to significant
advances in understanding and optimizing the performance
of these systems. Researchers have developed various math-
ematical models to depict the electrical behavior of photo-
voltaic panels. These models can vary in complexity, rang-
ing from simple four-parameter models to more elaborate
ones with five, six, or even seven parameters. Generally,
models with a greater number of parameters tend to more
accurately represent the real behavior of photovoltaic panels.
However, this can also result in increased model complexity
and requirements for input data.
This study continues the primary objective of several pre-
vious research endeavors aimed at enhancing and simulating
the performance of a crucial component of the photovoltaic
system. This component is the most expensive and highly
* Mohamed Nfaoui
nfaoui.smp@gmail.com
1 Multidisciplinary Laboratory ofResearch andInnovation
(LaMRI), EMAFI Team, Polydisciplinary Faculty,
University ofSultan Moulay Slimane, Khouribga, Morocco
2 Physics andQuantum Technology Team, LPMC, Faculty
ofScience Ben M’sik, Hassan II University, Casablanca,
Morocco
3 Scientific Institute, Mohammed V University inRabat,
Av. Ibn Batouta, BP 703, 10106Rabat, Morocco

Journal of Umm Al-Qura University for Applied Sciences
susceptible to site-specific climatic conditions. Optimiza-
tion methods for the PV generator are particularly valuable
for manufacturers who lack detailed information about the
future deployment locations of their products.
To achieve our objective, we established a simple and
reliable model, with acceptable accuracy to predict the per-
formance of a PV generator under metrological conditions.
This model is validated using data obtained from the PVsyst
software [14–16]. The results obtained from both the PVsyst
software and the mathematical model are compared.
Subsequently, we can also incorporate additional curves
not listed in the PVsyst software database by considering
wind speed as a meteorological parameter. Hence, incorpo-
rating wind speed as a meteorological parameter is crucial
for accurately simulating the performance of solar photo-
voltaic systems, as it can significantly affect solar energy
production.
2 Modeling andsimulation
ofaphotovoltaic solar cell
2.1 Presentation ofthesingle diode model
andresolution oftheelectrical equation:
There are several methods for simulating the equivalent cir-
cuits of a photovoltaic cell, each with its own advantages
and disadvantages. The equivalent circuit model represents
the photovoltaic cell with an electrical circuit comprising
resistances, capacitances, and current or voltage sources.
The parameters of this equivalent circuit can be determined
from experimental measurements or specific manufacturer
data [17–22].
The incorporation of a photovoltaic (PV) model into Mat-
lab/Simulink can be accomplished by utilizing the equations
derived from the equivalent model of the solar cell [23], as
detailed in the subsequent sections. Typically, this model
includes an ideal diode to account for the inherent nonlinear-
ity exhibited by solar cells [24, 25].
Generally, we can represent the equivalent electrical cir-
cuit of a solar cell in the form of a block diagram, incor-
porating four parameters [26, 27], as illustrated in (Fig.1).
The circuit simulation method is inherently more intricate
compared to other numerical methods employed to solve the
electrical equations governing the behavior of photovoltaic
cells. However, its advantage lies in its enhanced accuracy,
as it encompasses the effects of the electrical behavior of the
entire system [28]. However, this method involves represent-
ing the PV cell as a current source in series with an internal
resistance, and simulating the circuit to find the current and
voltage values across the cell for a given condition of light,
temperature and wind speed [29, 30].
The following table (Table1) presents the electrical char-
acteristics of the manufacturer of the Aleo Solar, aleo 150
S modules.
2.2 Solution andsimulation methodology
The simulation methodology presented in Matlab/Sim-
ulink relies on a mathematical model that delineates the
performance characteristics of a photovoltaic cell, as
Fig. 1 Block diagram of a Photovoltaic Mode
Table 1 Electrical characteristics of the aleo solar module, aleo 150s
under standard conditions (irradiance 1000 W/m2, temperature 25°C
and AM1.5)
Manufacturer specifications of the module
Parameter Symbol Value
Aleo Solar 150 S aleo_150_S.PAN aleo150S
Cell type Polycrystalline Silicon Si-poly
Max power point Pmpp (W) 150.6 W
Short-circuit current Isc (A) 4.700 A
Open circuit Voc (V) 43.40V
Maximum power point
voltage
Vmpp (v) 35.40V
Maximum power point
current
Impp(A) 4.300 A
Number of cells NB cells 72 in series
Efficiency/cells area N/A % 11.76%
Temperature coeffficient muIsc (mA/°C or %/°C) 2.4mA/°C
muVoc (mV/°C) −149mV/°C
muPmpp(%/°C) −0.43
Shunt resistance Rsh (ohm) 400 Ω
Series resistance Rs (ohm) 0.389 Ω
Diode quality factor Gamma 1.35

Journal of Umm Al-Qura University for Applied Sciences
detailed in references [31, 32]. It necessitates the manu-
facturer's technical specifications for the (Aleo Solar, Aleo
150 S model), and a meteorological database encompass-
ing climatic conditions as inputs. As a result, this meth-
odology generates both the photovoltaic panel's efficiency
and its characteristic curves (I–V, P–V) as outputs.
This methodology allowed us to model and analyze the
electrical behavior of a photovoltaic cell using a simple
equivalent circuit with a single diode (see the previous
part) and to obtain simulation results via MATLAB for in-
depth analysis. To facilitate understanding of the described
process, we decompose and detail each step as follows:
In the initial step, we establish a photovoltaic cell
model using a simple electrical circuit, primarily consist-
ing of a single diode.
The next step involves formalizing the equations that
govern the behavior of this circuit.
The final step involves implementing the defined equa-
tions in a simulation environment such as Matlab to ana-
lyze the circuit's behavior under various conditions.
The simulation following these steps enables visuali-
zation and analysis of the photovoltaic circuit's behav-
ior before moving on to physical testing, providing an
economical and efficient means for solar cell design and
optimization.
Presented below is a comprehensive flowchart depicting
the circuit simulation method for modelling a photovoltaic
cell (Fig.2).
This approach exploits the assumption of a linear cor-
relation between the cell current at maximum power (
Imp
)
and the cell short-circuit current (
Isc
). This correlation can
be mathematically expressed as:
Imp =K.Isc
, where '
K
' is
referred to as the current factor. The peak power of the mod-
ule is approximately 90% of its short-circuit current [26–28].
Here is the general description of the steps followed, as pre-
sented in the flowchart above:
1. Establish the parameters for the electrical circuit model.
2. Specify the environmental conditions.
3. Develop a digital representation of the electrical circuit.
4. Configure and initiate the circuit simulator.
5. Examine the results obtained from the simulation.
Lastly, the model is validated and fine-tuned, which
entails a comparative analysis of the simulation outcomes
with experimental data (e.g., PVsyst), leading to adjustments
in the electrical circuit model as necessary.
This procedure encapsulates a fundamental method-
ology for modelling a photovoltaic cell through circuit
simulation techniques. The sequential stages encompass
parameter definition, behavioral modelling of the photo-
voltaic cell, construction of the equivalent circuit, configu-
ration of simulations across various operating points, and
ultimately, scrutinizing the results to gain insights into the
cell's performance under varying conditions.
2.3 Implementation ofthephotovoltaic cell
underMatlab/Simulink
In this section, we develop the PV mathematical model,
represented by Eqs.(1) to (7), which is implemented in the
Matlab/Simulink environment. Then, this model is sub-
jected to simulations under various climatic conditions.
Start
Definition of the parameters of the photovoltaic cell
Electrical parameters (Is, Iph, Rs, Rsh, n, ...)
Environmental parameters (irradia nce, temperature and
wind speed...)
Calculate: Is, Iph, Id fo r each operating point.
Model of: series resistance (Rs), parallel resistance (Rsh) and
current variation with meteorological parameters (I, T, Ws).
Find operating current of the module using
I-module =k*Isc
Setting up the simulation for each operating point:
Calculation of the voltage at the terminals of the cell;
Source current calculation (Id);
Calculation of the voltage across the load resistor (Vload)
Data storage for analysis;
is
I= Imp No
Yes
Change
Results analysis
Characteristic curves (I-V, P-V);
Conversion efficiency;
Sensitivity to e nvironmental variations (I, T, Ws);
End
Fig. 2 Algorithm for calculating the I–V characteristics of a photo-
voltaic cell

Journal of Umm Al-Qura University for Applied Sciences
The flowchart below (Fig.3) illustrates the sequence of
the method used, which was implemented in the Matlab/
Simulink simulation block [33, 34]:
In the following part, we summarize the electrical
model of photovoltaic cells encountered in the literature,
is a simple empirical model (Fig.4), the model that exhib-
its the closest resemblance to the behavior of photovoltaic
cells and is presently the most widely adopted, owing to
the high-quality results it yields, is the single diode model
[35, 36].
These resistances will exert a discernible influence on
the current–voltage (I-V) characteristic of the photovoltaic
cell:
• The series resistance represents the internal resistance
within the cell, primarily comprising the resistance of the
semiconductor material employed, the contact resistance
of the collecting grids, and the resistivity of these grids.
• The shunt resistance arises from the leakage current at
the junction and is contingent upon the specific method-
ology employed in its implementation.
The resistances
Rs
and
Rsh
alter the short-circuit current of
the cell in the photocurrent I_ph. This leads to the derivation
of the following equivalent electrical circuit.
According to Kirchhoff's law, the current generated by
the PV cell is given by:
The photovoltaic current (
Iph
) inherently exhibits
insensitivity to voltage (or series resistance
Rs
) and is
observed to be directly proportional to the density of the
incident photon flux (expressed as the generation-recom-
bination rate), as well as to the carrier diffusion length, a
(1)
I=Iph −ID−Ish
Fig. 3 Flowchart of the proposed method integrated into Matlab/Simulink
Fig. 4 Single diode model Fig. 5 Subsystem of Simulink model for the photo-current

Journal of Umm Al-Qura University for Applied Sciences
representative diagram shown in (Fig.5). Moreover,
Iph
demonstrates a linear dependence on incident solar irra-
diation, while being notably influenced by temperature, as
delineated in the following equation:
where,
Isc
is the short circuit current (at STC);
G
is the irradi-
ance incident on the cell surface,
Gn
is the irradiance under
Standard Test Conditions,
T
is the cell temperature in °C,
Tref
is the reference temperature in °C, and the constant
Ki
is
the short circuit current coefficient.
The equation for shunt current
Ish
, addresses a condition
wherein a segment of the current produced by a solar cell
circumvents the designated load, consequently leading to
efficiency losses. This occurrence can arise from manufac-
turing defects, material imperfections, or incorrect connec-
tions. The expression for
Ish
passing through
Rs
is given by:
In this equation;
Rsh
represents the shunt resistance,
Rs
the series resistance,
Np
the number of cells connected in
parallel and
Ns
the number of cells connected within the
module.
The diode current
ID
is comparable in magnitude to
Ish
at
low voltages, but it increases significantly around
VOC
, it is
expressed as:
q
: Electronic charge constant, 1.6 10–19 C.
K
: Boltzmann
constant (1.386503 0.10–23J/K).
T
: Cell temperature, in
Kelvin.
We can depict the current of the shunt current and the
diode current in the diagram above (Fig.6):
The reverse saturation current
Is
, is an intrinsic character-
istic of diode materials and quality. It quantifies the leakage
current resulting from thermally generated minority carri-
ers, even when the diode is under reverse bias. In an ideal
scenario,
Is
would be zero, signifying the complete absence
of leakage current. However, in reality, all diodes exhibit
some level of leakage current due to imperfections in the
semiconductor material.
The equation describing the saturation current of a diode
is as follows:
Irs
: is the saturation current of the diode and it is given by:
(2)
I
ph =[Isc +Ki(T−Tref )]
G
Gn
(3)
I
sh =VD
R
sh
=V+RsI
R
sh
or Ish =
N
p
R
sh (
V
N
s
+IRs
N
p).
(4)
I
D=IS

eqVD
AKT −1

or ID=Is

e

q
nKbT

V
Ns
+IRs
Np

−1

(5)
I
s=Irs(T
T
c
)
3
e[qEG
nKb
(1
Tc−1
T
)]
or,
Isc
: Short-circuit current.
Voc
: Open circuit voltage.
A
:
Ideality factor.
The schematic representation of diode saturation current
in the diagram above (Fig.7):
We integrate Eqs.(4) and (6) into Eq.(1), the character-
istic equation becomes:
The ideality factor of cell A depends on the recombina-
tion mechanisms in the space charge region. The current
generated by the solar cells can be represented as follows in
the diagram (Fig.8):
In the ideal scenario,
Rs
approaches 0, and
Rsh
approaches
infinity. In practical terms, these resistors are employed to
assess the imperfections of the diode, with Rs typically hav-
ing a low value.
(6)
I
rs =
I
sc
[exp
(
qVoc
NskAT )
−1
]
(7)
I
=Iph −Is

eq
(
V+RsI
)
AkT −1

−(
V
+
R
s
I
R
sh
)
Fig. 6 Subsystem of Simulink model for the shunt-current and the
diode-current
Fig. 7 Subsystem of Simulink model for diode saturation current

Journal of Umm Al-Qura University for Applied Sciences
Through a digital method under illumination, the slopes
of the I-V characteristics are calculated at I = 0 in open cir-
cuit and V = 0 in short circuit, providing the inverse values
of the series and shunt resistances, respectively.
3 Simulation results anddiscussion
In order to simulate the intrinsic mechanism of our cel-
lular components, we have developed a model within the
Matlab environment by leveraging the previously stated
equations. Additionally, we integrated the PV module Aleo
Solar, aleo 150 S, as a reference. This approach allowed
us to generate characteristic plots corresponding to key
parameters, namely voltage, current, power, and efficiency.
At the outset of our research, we chose to use a conven-
tional model commonly employed in the modeling of sili-
con-based solar cells, namely the single-diode model. This
methodological choice was followed by a comprehensive
comparison with data generated by the PVSyst simulation
software. In this process, we undertook a preliminary step
involving accurately adjusting the electrical characteris-
tics of our selected photovoltaic module to optimally align
them with the reference parameters present in the PVSyst
software database [15, 37].
Subsequently, we embarked on the theoretical predic-
tion of essential photovoltaic parameters such as open-cir-
cuit voltage (
Voc
), short-circuit current (
Isc
), series resist-
ance (
Rs
), shunt resistance (
Rsh
), and overall efficiency
(η), by integrating relevant meteorological variables. This
modeling was carried out using our proprietary simulation
program developed within the Matlab/Simulink environ-
ment. Following this, we extracted these same parameters
using the reference software PVSyst, enabling us to con-
duct a rigorous comparison between the results obtained
from these two simulation methods.
The simulations conducted enable the generation of
curves (I–V, P–V,
ηPmax
-E and
ηPmax
-T) for the PV module
under varying illuminations, temperatures, and wind speeds.
3.1 Comparative analysis ofresults
betweenMATLAB/simulink andPVsyst
To assess the accuracy of our mathematical model, we
employed an experimental approach involving simulating
the single-diode model using the Matlab/Simulink develop-
ment environment. Subsequently, we compared the results
obtained from this simulation with those generated by the
PVSyst software, widely recognized in the photovoltaic field
for its effectiveness [38]. For this purpose, we simulated
the current–voltage (I–V) characteristic of a solar cell using
our numerical method. Concurrently, we also examined the
I–V curves provided by PVSyst for the Aleo Solar photo-
voltaic module (Aleo 150 S). This rigorous methodological
approach allowed us to verify the consistency of the results
obtained by our model with those from an industry-standard
photovoltaic tool, thereby reinforcing the credibility of our
analytical approach.
The following figures depict the comparative curves
of values simulated by Matlab/Simulink and the results
obtained by the PVsyst software for different ranges of solar
irradiance and temperature. These comparisons were con-
ducted for a single-diode mathematical model of the photo-
voltaic solar cell.
3.2 Influence ofillumination
The current–voltage (I–V) characteristic is directly depend-
ent on the incident radiation. Indeed, an increase in the
luminous flux results in a shift of the (I–V) curve along
the current axis. In other words, the short-circuit current
is proportional to the irradiance. However, the increase in
the short-circuit current is much more significant than that
of the open-circuit voltage. The latter is minimally affected
by the illumination. The power increases significantly with
the illumination.
The figures below show the evolution of the (I–V) and
(P–V) characteristics of a PV module as a function of the
illumination (Figs.9 and 10).
The variations of current and power concerning voltage
for different levels of sunlight at a constant temperature of
45°C are evident in the previous figures, showing clear
peaks on the power curves corresponding to the Maximum
Power Points (
Pmax
).
It is noteworthy that for lower solar irradiance levels,
the power produced by the module under these conditions
is relatively low. For an irradiance of 200 W/m2, the power
is approximately 24.4 W. Similarly, for an irradiance of
600 W/m2, this power increased and reached 80 W. For
Fig. 8 Subsystem of Simulink model for the solar cell current

Journal of Umm Al-Qura University for Applied Sciences
these irradiance values, the margin of error is relatively
low. As the irradiance increased to 1000 W/m2, the power
produced by the module reached 137.5 W.
In this section, we will examine a comparative study of
the (I–V and P–V) characteristics of a solar cell exposed
to illumination. This study will be based on the single-
diode model. Two sets of results will be considered: the
results from numerical simulations and those obtained
using PVSyst. These results will help generate an implicit
equation describing the relationship between current and
voltage, as well as power concerning the voltage across
the solar cell.
According to our simulations, it has been observed that
the characteristics observed in the results from both meth-
odologies, namely Matlab/Simulink and PVSyst, exhibit a
remarkable degree of homogeneity and agreement.
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0510 15 20 25 30 35 40 45
Voltage [V]
0
1
2
3
4
5
6
Current [A]
Cells Temp=45°C
Incident Irrad=200 w/m2
Incident Irrad=400 w/m2
Incident Irrad=600 w/m2
Incident Irrad=800 w/m2
Incident Irrad=1000 w/m2
Fig. 9 I–V Characteristics of a PV Module for Various Sunlight Intensities at Constant Temperature (45°C)
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0510 15 20 25 30 35 40 45
Voltage [V]
0
20
40
60
80
100
120
140
Power [W]
Incident Irrd = 200 W/m2
Incident Irrd = 400 W/m2
Incident Irrd = 600 W/m2
Incident Irrd = 800 W/m2
Incident Irrd = 1000 W/m2
Cells Temp=45 °C
Fig. 10 P–V Characteristics of a PV Module for Various Sunlight Intensities at Constant Temperature (45°C)

Journal of Umm Al-Qura University for Applied Sciences
3.3 Influence ofTemperature
Temperature is a crucial parameter in the operation of pho-
tovoltaic cells because the electrical properties of a semi-
conductor are highly sensitive to temperature. The figures
below represent the (I-V) and (P–V) characteristics of a PV
module as a function of temperature (Figs.11 and 12), under
constant illumination.
The simulation demonstrates that the open-circuit volt-
age of a solar cell decreases with an increase in the cell's
temperature. It's notable that temperature has a negative
impact on the open-circuit voltage (the higher the tempera-
ture, the lower
Voc
becomes, while the short-circuit current
Icc
increases with temperature). On the other hand, the maxi-
mum power of the generator decreases as the temperature
rises. This decrease is considerably less significant than the
drop in voltage. The influence of temperature on
Icc
can be
disregarded in the majority of cases.
The increase in temperature has also affected the margin
of error for the sunlight intensity G = 1000 W/m2, as the
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0510 15 20 25 30 35 40 45
Voltage [V]
0
1
2
3
4
5
Current [A]
Cells Temp=10°c
Cells Temp=25°C
Cells Temp=40°C
Cells Temp=55°C
Cells Temp=70°C
Incident Irrad = 1000 w/m2
Fig. 11 I–V Characteristics of a PV Module for Various Temperature Values at Constant Irradiance (1000 W/m2)
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0510 15 20 25 30 35 40 45
Voltage [A]
0
20
40
60
80
100
120
140
160
180
Power [W]
Cells Temp=10°C
Cells Temp=25°C
Cells Temp=40°C
Cells Temp=55°C
Cells Temp=70°C
IncidentIrrad = 1000 W/m2
Fig. 12 P–V Characteristics of a PV Module for Various Temperature Values at Constant Irradiance (1000 W/m2)

Journal of Umm Al-Qura University for Applied Sciences
module's performance deteriorates with higher temperatures.
Additionally, as sunlight intensity increases (for example,
G = 1000 W/m2, T = 25°C), the produced power becomes
greater, and the margin of error becomes more significant.
3.4 Analysis oftheimpact ofseries andshunt
resistances
The impact of series (
Rs
) and shunt (
Rsh
) resistances in a
photovoltaic model is crucial for understanding and optimiz-
ing module performance. These resistances have a signifi-
cant effect on efficiency, output power, and the stability of
the photovoltaic module. Here is a more in-depth analysis
of their impact:
Series Resistance (
Rs
): The series resistance significantly
influences the slope of the solar cell's electrical characteris-
tic, especially in the operating range where the photodiode
exhibits behavior akin to a voltage generator. A high series
resistance leads to a decrease in the short-circuit current,
which can affect the overall performance of the solar cell.
Furthermore, it also impacts the maximum power that can
be extracted from the solar cell. Specifically, this maximum
power is optimal when the value of the series resistance is
minimal (Figs.13 and 14).
The simulation was conducted considering various values
of series resistance (
Rs
), including 0.2 Ω, 0.4 Ω, 0.6 Ω, 0.8
Ω, and 1 Ω. It was demonstrated that increasing the value
of the series resistance, i.e., higher values of
Rs
, leads to a
significant reduction in the output power of the solar cell.
Shunt Resistance (
Rsh
) The shunt resistance, com-
monly referred to as “Shunt,” arises due to losses from
recombination’s primarily attributable to thickness, surface
phenomena, and the non-ideality of the junction. Conse-
quently, the shunt resistance (
Rsh
) constitutes an undesired
resistance component that creates a partial short-circuit path
around the solar cell (Figs.15 and 16).
The shunt resistance must be appropriately sized to opti-
mize the output power. It's crucial to note that a low-value
shunt resistance results in a significant decrease in current,
consequently causing a notable loss in output power. There-
fore, it is necessary to maintain a sufficiently high shunt
resistance to maximize the energy conversion efficiency in
our photovoltaic module.
3.5 Analysis oftheinfluence ofillumination,
temperature, andinternal resistances
ontheefficiency ofphotovoltaic solar cells
Illumination and temperature are two crucial parameters in
the photovoltaic effect. Indeed, the incident solar radiation
on solar panels generates power. It is considered one of the
main parameters that can modify the characteristic of a PV
generator, hence influencing its efficiency. The following
figures (Figs.17 and 18) will demonstrate the influence of
illumination and temperature on the efficiency of photovol-
taic panels:
As observed in this figure, an increase in illumination
leads to a corresponding increase in efficiency. Therefore,
we can conclude that illumination has a positive influence
on efficiency.
According to the figure, it is noticeable that the efficiency
of a photovoltaic cell decreases as its ambient temperature
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0510 15 20 25 30 35 40 45
Voltage [V]
0
1
2
3
4
5
6
Current [A]
Serie Res=0.200 ohm
Serie Res=0.400 ohm
Serie Res=0.600 ohm
Serie Res=0.800 ohm
Serie Res=1.000 ohm
Cells temp =40°C,
Incident Irrd=1000w/m2
Shunt Res = 400 ohm
Fig. 13 I–V Characteristics of a PV Module for Varying Series Resistance at (T = 40°C, E = 1000W/m2)

Journal of Umm Al-Qura University for Applied Sciences
rises. For crystalline silicon modules, for instance, this
dependence is linear at high illuminations. The efficiency
decreases, relatively, by approximately 0.5% per degree.
Therefore, depending on climates, a difference of 10–30%
can be observed between the efficiency under Standard Test
Conditions (STC) and the actual instantaneous efficiency
observed in real sunlight. Other phenomena also contrib-
ute to the difference observed between laboratory and field
conditions: notably, the cell's efficiency depends on the illu-
mination and its spectrum.
Series and shunt resistances are intrinsic elements
within a photovoltaic solar cell, significantly impacting its
overall efficiency. A thorough understanding of their influ-
ence is crucial for optimizing solar cell performance. This
necessity arises from the fact that the electrical character-
istics of these resistances play a decisive role in limiting
the loss of electric current and enhancing the conversion
efficiency of solar energy into electricity. Consequently,
the study and control of these resistances are essential
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0510 15 20 25 30 35 40 45
Voltage [V]
0
20
40
60
80
100
120
140
160
180
Power [W]
SerieRes =0.200 ohm
SerieRes =0.400 ohm
SerieRes =0.600 ohm
SerieRes =0.800 ohm
SerieRes =1.000 ohm
Cells Temp=40°C
Incident Irrd = 1000 W/m2
Shunt Res=400 ohm
Fig. 14 P–V Characteristics of a PV Module for Varying Series Resistance at (T = 40°C, E = 1000W/m2)
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0510 15 20 25 30 35 40 45
Voltage [V]
0
1
2
3
4
5
6
Current [A]
Shunt Res=200 ohm
Shunt Res=300 ohm
Shunt Res=400 ohm
Shunt Res=500 ohm
Shunt Res=600 ohm
Cells Temp = 40°C
Incident Irrd = 1000W/m2
Serie Res=0.389
Fig. 15 I–V Characteristics of a PV Module for Varying Shunt Resistance at (T = 40°C, E = 1000W/m2)

Journal of Umm Al-Qura University for Applied Sciences
prerequisites for the continuous development and improve-
ment of photovoltaic technologies.
Increased series resistance results in a decrease in the cur-
rent passing through the cell, leading to increased conversion
of incident energy into heat inside the cell, at the expense of
its extraction as electric current (Fig.19).
When the solar cell is exposed to solar irradiation, it gen-
erates an electrical potential difference. However, a fraction
of this voltage is inevitably dissipated due to the presence of
series resistance. It is noteworthy that a higher series resist-
ance leads to greater voltage dissipation, ultimately resulting
in a reduction of the cell's output voltage and consequently
decreasing its overall performance.
The series resistance of a solar cell typically demonstrates
a positive correlation with temperature. Consequently, when
the solar cell heats up due to exposure to solar radiation, its
series resistance simultaneously increases. This increase in
series resistance can induce an additional decrease in the
intrinsic efficiency of the solar cell (Fig.20).
The shunt resistance, also known as leakage resistance,
represents a parameter of paramount importance capable of
exerting a significant influence on the intrinsic performance
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0510 15 20 25 30 35 40 45 50
Voltage [V]
0
20
40
60
80
100
120
140
160
Power [W]
Shunt Res = 200 ohm
Shunt Res = 300 ohm
Shunt Res = 400 ohm
Shunt Res = 500 ohm
Shunt Res = 600 ohm
Cells Temp = 40°C
Incident Irrad=1000 w/m2
Serie Res = 0.389 ohm
Fig. 16 P–V Characteristics of a PV Module for Varying Shunt Resistance at (T = 40°C, E = 1000W/m2)
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0 100 200 300 400 500 600 700 800 900 1000
Incident global Irrad [W/m2]
0
2
4
6
8
10
12
14
Efficiency at Pmax[%]
Cells Temp=10 °C
Cells Temp=25 °C
Cells Temp=40°C
Cells Temp=55 °C
Cells Temp=70 °C
Fig. 17 Variation of efficiency with illumination for different temperature levels

Journal of Umm Al-Qura University for Applied Sciences
of a photovoltaic solar cell. To fully comprehend this influ-
ence, it is imperative to quantify the effect of the shunt
resistance on the overall efficiency of the solar cell.
A shunt resistance provides an alternative path for elec-
trical current, which can result in partial short-circuiting of
the current generated by the solar cell. This leads to power
losses that reduce the efficiency of converting light into elec-
tricity (Figs.21 and 22). Due to these power losses, a shunt
resistance decreases the overall efficiency of the solar cell,
resulting in less conversion of light energy into electricity.
A lower shunt resistance facilitates the flow of unwanted
currents around the cell, thereby reducing its overall effi-
ciency. Conversely, a higher shunt resistance can cause
unwanted current leakage, leading to a decrease in the
cell's output power.
Both series and shunt resistances significantly impact
the efficiency of a photovoltaic solar cell. Reducing these
resistances is essential to maximize the conversion of solar
energy into usable electricity.
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
01020304050607
08
0
Cells Temp [°C]
0
2
4
6
8
10
12
14
Efficiencyat Pmax[%]
Incident Irrad=1000 W/m²
Incident Irrad=800 W/m²
Incident Irrad=600 W/m²
Incident Irrad=400 W/m²
Incident Irrad=200 W/m²
Serie Res =0.389 Ohm
Shunt res=400 Ohm
Fig. 18 Influence of ambient temperature on the efficiency of the PV panel for different levels of illumination
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0100 200300 400500 600700 800900 1000
Incident Global Irrad [W/m2]
0
2
4
6
8
10
12
Efficiencyat Pmax[%]
Serie Res=0.200 Ohm
Serie Res=0.400 Ohm
Serie Res=0.600 Ohm
Serie Res=0.800 Ohm
Serie Res=1.000 Ohm
Cells Temp =40°C
Shunt Res =400 Ohm
Fig. 19 Variation of efficiency with illumination for different levels of series resistance at a constant temperature of 40°C

Journal of Umm Al-Qura University for Applied Sciences
In summary, understanding the influence of these differ-
ent parameters (meteorological and electrical) on photovoltaic
solar cells requires a multidisciplinary approach, combining
modeling, experimental characterization, theoretical analy-
sis, and practical validation. Such an approach will optimize
the performance of solar cells by considering these essential
parameters.
3.6 Validation ofthesingle‑diode mathematical
model
The initial objective of this study is to identify and char-
acterize the essential electrical and meteorological param-
eters governing the operation of a photovoltaic solar cell.
These parameters include series resistance, shunt resistance,
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
01020304050607
08
0
Cells Temp [°C]
0
2
4
6
8
10
12
14
Efficiencyat Pmax[%]
Serie Res =0.200 Ohm
Serie Res =0.400 Ohm
Serie Res =0.600 Ohm
Serie Res =0.800 Ohm
Serie Res =1.000 Ohm
Incident Irrad=1000 W/m2
Shunt Res=400 Ohm
Fig. 20 Variation of efficiency with temperature for different levels of series resistance at a constant illumination of 1000 W/m2
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
0 100 200 300 400 500 600 700 800 900 1000
Incident Global Irrad [W/m2]
0
2
4
6
8
10
12
Efficiencyat Pmax[%]
Shunt Res = 200 Ohm
Shunt Res = 300 Ohm
Shunt Res = 400 Ohm
Shunt Res = 500 Ohm
Shunt Res = 600 Ohm
Cells Temp =40°C
SerieRes =0.389
Fig. 21 Variation of efficiency with illumination for different levels of shunt resistance at a constant temperature of 40°C

Journal of Umm Al-Qura University for Applied Sciences
photocurrent, solar irradiance, and ambient temperature. The
ultimate goal is to develop an appropriate model, specifically
the single-diode model, to comprehensively describe the
behavior of the solar cell. This model will be used to gener-
ate characteristic curves such as I–V curves (current–volt-
age), P–V curves (power-voltage), as well as efficiencies
ηPmax
-E (maximum efficiency as a function of irradiance)
and
ηPmax
–T (maximum efficiency as a function of tempera-
ture). To achieve this objective, simulations were conducted
in the Matlab/Simulink environment, employing common
numerical methods such as the simulation method for the
electrical circuit of a photovoltaic cell.
For all ranges of irradiance and temperatures, the figures
presented demonstrate no difference in precision between the
simulation of the single-diode mathematical model using Mat-
lab/Simulink and the results obtained from the PVsyst software.
Overall, a good agreement is observed between the curves
simulated by Matlab/Simulink and the results obtained from
the PVsyst software.
This allows us to conclude that the single-diode model is
sufficient to describe the behavior of the Aleo Solar mod-
ule, Aleo 150 S. This finding is consistent with existing
literature.
4 Comparison summary ofmathematical
models ofequivalent electrical circuits
foraphotovoltaic cell (advantages
anddisadvantages)
Mathematical models of equivalent electrical circuits for
photovoltaic cells are essential for analyzing and pre-
dicting their behavior under various conditions. Several
models exist, each having its advantages and disadvan-
tages. For instance, the single-diode model is widely
utilized due to its simplicity and effectiveness for quick
simulations. In contrast, the two-diode and three-diode
models provide higher accuracy by accounting for minor-
ity carrier recombinations. However, this comes at the
expense of increased complexity and longer computation
times. Therefore, the choice of model should be based on
the specific requirements of the study and the anticipated
operating conditions. Table2 presents an analysis of the
principal models found in the scientific literature for mod-
eling photovoltaic cells:
The choice of model depends on the specific application,
the required level of accuracy, and the acceptable complex-
ity. For quick analyses and general estimates, the single
diode model is often sufficient. For applications requir-
ing higher accuracy, especially under various conditions,
the two-diode model or capacitive models may be more
appropriate. Empirical models are useful for specific condi-
tions but provide less insight into the underlying physical
mechanisms.
The single-diode model is the simplest approach to con-
struct a solar cell model as it adequately describes the char-
acteristics of most photovoltaic cells. Consequently, it can
be applied in the majority of models, especially when there
are rapid variations in weather conditions.
However, for our application in real meteorological con-
ditions, the use of a single-diode model proves preferable.
This choice is motivated by its ability to consider all the
physical phenomena operating within the photovoltaic cell.
Moreover, it allows the integration of wind speed as a third
meteorological input parameter. This feature provides the
a) Simulated by PVsyst b) Simulated by Matlab/Simulink
01020304050607
08
0
Cells Temp [°C]
0
2
4
6
8
10
12
14
Efficiency at Pmax [%]
Shunt Res=200 Ohm
Shunt Res=300 Ohm
Shunt Res=400 Ohm
Shunt Res=500 Ohm
Shunt Res=600 Ohm
Incident Irrad=1000 W/m2
SerieRes =0.389 Ohm
Fig. 22 Variation of efficiency with temperature for different levels of shunt resistance at a constant illumination of 1000 W/m2

Journal of Umm Al-Qura University for Applied Sciences
Table 2 Comparison of advantages and disadvantages of mathematical models of equivalent electrical circuits for photovoltaic solar cells
Model Description Avantages Inconvénients
Single Diode
[17–22]
The single-diode model is the simplest and most
widely used for photovoltaic cell modeling. It
comprises a diode, a photo-generated current source
(Iph), a series resistor (Rs), and a shunt resistor
(Rsh)
Simplicity: Easy to understand and implement
Limited Parameters: Fewer parameters to estimate,
which simplifies model fitting
Practical Applications: This model is sufficiently
accurate for many practical applications
Ideal Model: Does not account for certain effects such
as surface recombinations and capacitive effects
Two and Three Diodes
[1–3]
The two-diode and three-diode models include addi-
tional diodes to more accurately represent recombi-
nation phenomena within the photovoltaic cell
By incorporating second or third diodes (Id2 and Id3),
these models more faithfully capture the various loss
mechanisms and non-linear phenomena present in
PV cells. This results in greater accuracy compared
to single or dual diode models
Adaptation to Various Conditions: This model is
more adaptable to variations in temperature and
irradiation, capable of simulating complex effects
and varied losses that cannot be captured by simpler
models
Complexity: More parameters to estimate, making fit-
ting more complex
High Complexity: The three-diode model is much more
complex and requires intensive computations, which
can increase simulation time and the computational
resources needed
Computational Time: Longer computations requiring
more computational resources
Empirical
[4–6]
Empirical models employ mathematical expressions
derived directly from experimental data, bypassing
the need for detailed physical modeling
Simplicity of Implementation: This model is often
simpler to adjust for specific data, making it easier
to implement and modify as needed
Precision for Specific Conditions: Can be highly
accurate for the specific experimental conditions
used for calibration
Limited Generalization: Less capable of generalizing to
untested conditions
Limited Physical Interpretation: Provides little insight
into the underlying physical mechanisms
Capacitance
[7–9]
This model incorporates capacitive effects by adding
parallel capacitive components, which allows for a
more accurate representation of the transient dynam-
ics of the photovoltaic cell
Specific Applications: Useful for applications where
rapid dynamics are critical, such as dynamic power
systems
Increased Complexity: A more complex model with
additional parameters to adjust
Specificity: Less useful for static analyses or equilib-
rium conditions

Journal of Umm Al-Qura University for Applied Sciences
model with increased accuracy compared to other mathemat-
ical models of the photovoltaic cell. By incorporating wind
speed as a determining factor, the single-diode model bet-
ter captures the complex interactions and mutual influences
between meteorological and electrical variables, thereby
contributing to a more accurate prediction of photovoltaic
cell performance under real conditions.
5 Optimizing thermal modeling
byincorporating wind speed formodule
operating temperature
The performance of PV modules is deeply influenced by
environmental conditions, among which wind speed plays a
crucial role. Investigating the impact of wind speed on the
operational temperature of photovoltaic modules is a key
area of research to improve the efficiency and reliability of
solar photovoltaic installations [39, 40]. Operating tempera-
ture provides an in-depth understanding of heat dissipation
mechanisms and wind-induced cooling effects. This aca-
demic and scientific endeavour seeks to unravel the intricate
interplay between wind speed and the operational tempera-
ture of photovoltaic modules. By doing so, it sets the stage
for significant advancements in the design and efficiency of
these sustainable energy systems [41, 42].
Academic research in the literature delineates models
similar to the method using NOCT (Nominal Operating
Cell Temperature) to evaluate the operating temperature of
a photovoltaic solar cell [43, 44]. However, these models
take into account the impact of meteorological variables.
More precisely, the thermal condition of the rear side of
photovoltaic modules is defined as a function of ambient
temperature, solar radiation, wind speed, and empirically
established parameters. The resulting mathematical expres-
sions are formulated as follows:
5.1 Standard approach (NOCT standard model)
The simplest explicit equation to describe the steady-state
operation of the temperature of a solar cell or module relates
the cell temperature (Tc) to the ambient temperature and the
incident solar radiation flux [45].
where,
Tc
= is the cell temperature in degrees Celsius [°C].
Ta
= is the ambient temperature in degrees Celsius [°C].
S = is the incident solar irradiance in 1kW/m2 [1kW/m2].
The nominal operating cell temperature (NOCT) [46], as
defined by the International Electrotechnical Commission
(IEC) 61215 standard, delineates its parameters [47]. This
metric is determined through the evaluation of a photovoltaic
module under open-circuit conditions, carefully facilitated
with controlled ventilation, and subjected to an incident irra-
diance intensity of 800 W/m2. The scenario is characterized
by ambient conditions featuring an outdoor temperature of
20°C, along with a wind speed of 1m/s [48, 49].
5.2 Second approach (Skoplaki model)
Skoplaki developed an advanced model that incorporates
wind data into the NOCT-Standard formula [50]. In addition
to considering ambient temperature (
Ta
) and irradiance in
the plane (I), this model also integrates wind speed (
v
) and
specific properties of solar cells, including efficiency (
𝜂
), the
temperature coefficient of maximum power (
𝛽
), the trans-
mission of the covering system (
𝜏
), as well as the absorption
coefficient of the cells (
𝛼
).
The electrical performance of a module is practically
influenced by any temperature variation, including short
circuit current, maximum power point, open circuit volt-
age, form factor and efficiency [51].
Here is the illustration of the Skoplaki model, formulated
as follows:
𝜂STC
and
𝛽STC
denote the efficiency and the temperature coef-
ficient of maximum power under standard test conditions
(STC). The specific values for
𝜂STC
and
𝛽STC
correspond-
ing to the investigated photovoltaic (PV) technologies are
detailed in Table3 [52]. The product of the transmission
(8)
T
c=Ta+
(NOCT −20◦C
0.8 )
.
S
(9)
T
c=Ta+
I
INOCT
.(
TNOCT −Ta,NOCT
).
h
𝜔
,
NOCT
h𝜔(v).
[
1
−
𝜂
STC
𝜏.𝛼
(
1
−𝛽STCTS TC
)]
Table 3 Attributes of examined photovoltaic technologies
Type of the Photovoltaic technology Silicon Cadmium
(M–Si)
glass–polymer
(P–Si)
glass-polymer
(A–Si)
glass-glass
(µc–Si)
glass-polymer
(CdTe)
glass-glass
NOCT (°C) 45 46 46 44 45
Module efficiency
𝜂STC
(%) 18.4 14.1 6.0 9.5 10.7
Temperature coefficient of maximal power
𝛽STC
(%/K)
−0.38 −0.45 −0.19 −0.24 −0.25

Journal of Umm Al-Qura University for Applied Sciences
coefficient (τ) and the absorption coefficient (α) is conven-
tionally approximated as 0.9 (
𝜏.𝛼=0.9
). The wind convec-
tion coefficient, denoted as
h𝜔
, is characterized as a linear
function of wind speed [53].
Skoplaki presents two different parameters of
h𝜔
:
v𝜔
represents the wind speed in the immediate vicinity of the
module, while
vf
corresponds to the wind speed measured at
a height of 10m above the ground.
To facilitate the conversion between the two distinct wind
speeds, we employed the methodology outlined in [54]:
The wind convection coefficient under NOCT conditions,
denoted as
h𝜔,NOCT
, is defined for a wind speed of
v𝜔
=1m/s.
An alternative parameterization for the wind convection
coefficient
h𝜔
, is proposed by Armstrong and Hurley [55],
as well as by Sharples and Charlesworth [56].
We employed the correlation (12) for wind directions per-
pendicular (± 45°) to the module surface and the correlation
(13) for wind directions parallel (± 45°) to the module sur-
face. The cell temperature, computed using Eq.(9) and the
wind convection coefficient parameterized by Sharples (
h𝜔
),
is referred to as Skoplaki in this context.
5.3 Third approach of(Sandia National
Laboratories‑King)
In recent developments, Sandia National Laboratories have
introduced a more simplified empirical approach to thermal
modeling [57]. This model, defined by Eq.(12), has show-
cased its effectiveness across various applications. Notably,
it has found success in the thermal analysis of flat mod-
ules situated in open racks and configurations featuring flat
modules equipped with rear thermal insulation, replicating
integration scenarios within buildings [58]. Furthermore,
it has been expanded to include concentrator modules with
finned heat sinks. This streamlined model has demonstrated
remarkable adaptability, making it highly suitable for engi-
neering and system design purposes. It delivers operational
temperature predictions for photovoltaic modules with an
accuracy approaching ± 5°C.
(10)
h𝜔=8.91 +2.00vf
(11)
h𝜔=5.7 +2.8v𝜔
(12)
h
𝜔
=8.3 +2.2v
𝜔
For wind direction perpendicular to module surface.
(13)
h
𝜔
=6.5 +3.3v
𝜔
For wind direction parallel to module surface.
The temperature of the solar cell inside the module is then
calculated using a measured back surface temperature and
a predetermined temperature difference between the back
surface and the cell.
The relationship elucidated in Eq.(13) is based on the
postulation of a mechanism involving one-dimensional ther-
mal conduction through the materials behind the photovol-
taic cell [58, 59]. This conduction is observed across various
layers, including the encapsulant and polymer for flat mod-
ules, and the ceramic dielectric along with the aluminium
heat sink for concentrator modules.
Tm
= Temperature of the module's rear face measured
[°C]. E = Solar irradiance measured on the module [W/m2].
E0
= Reference solar irradiance (1000 W/m2). ΔT = The
resulting temperature difference, which is the temperature
gap between the photovoltaic cell and the rear surface of the
module, is assessed under an irradiance condition of 1000
W/m2. In the context of an open-rack installation, this dis-
parity typically ranges from 2 to 3°C for flat-plate modules.
However, in cases where flat-plate modules have a thermally
insulated rear surface, it is reasonable to approximate this
temperature difference as negligible.
where,
a
= Empirically determined coefficient establishing
the upper limit of module temperature at low wind speed
and high solar irradiance.
b
= Empirically determined coef-
ficient establishing the rate at which module temperature
decreases as wind speed increases.
WS
= Wind speed meas-
ured at standard height of 10m [m/s].
Ta
= Ambient air
temperature [°C].
The conventional methodology in meteorology for meas-
uring wind speed and direction involves placing the measur-
ing instrument (anemometer) at an altitude of 10m within
an area characterized by minimal reduction of buildings
or structures that could impede the movement of air, the
recorded data pertaining to wind speed and direction, acces-
sible in meteorological databases, were captured under these
circumstances. However, it is important to note that, at the
post-installation stage of the system, a thorough analysis of
the data may lead to optimization of the thermal model. This
optimization could be achieved by determining new coef-
ficients (a, b) that correct for site-specific influences as well
as discrepancies between anemometric devices and standard
meteorological protocols.
The Table 4 presents coefficients determined
through empirical approaches, which reflect various
(12)
T
c=Tm+
E
E
0
.ΔT
(13)
Tm
=E.
(
e
a+b.WS)
+T
a

Journal of Umm Al-Qura University for Applied Sciences
characteristics inherent to several variants of modules
and assembly schemes. The situations presented in the
table can be considered as reference cases for flat pho-
tovoltaic modules commonly associated with various
manufacturers.
However, it is important to note that the thermal behav-
ior of concentrated photovoltaic modules may exhibit sub-
stantial variations in correlation with the specific mod-
ule configuration. Therefore, it becomes imperative to
empirically establish concentration coefficients specific
to each module design. As an illustration, an example
related to a linear focusing concentration module dating
back to 1994 is presented in the previous table [59, 60].
5.4 Assessment oftheimpact ofwind
speed ontheoperating temperature
ofthephotovoltaic cell
The wind speed exerts a substantial influence on the heat
dissipation phenomenon within photovoltaic (PV) cells,
and consequently, on their operational efficiency. When
solar cells are exposed to solar irradiation, they generate
heat, a potentially detrimental factor to their intrinsic perfor-
mance. Therefore, proper management of cell temperature
is of crucial importance for optimizing cell performance. In
this context, wind speed can function as a heat dissipation
mechanism, thereby contributing to enhancing the cooling
of photovoltaic cells and, consequently, their overall energy
efficiency.
The two graphs below highlight a preliminary linear
relationship between the operating cell temperature and the
ambient temperature, whether derived from experimental
observations or theoretical models.
The objective of this section is to present the outcomes
resulting from the inclusion of wind speed as a meteoro-
logical parameter in influencing the characteristic curves
of the photovoltaic module (V–I, P–V, η); instead of solely
concentrating on the comparison between the mathematical
models we have chosen. Therefore, our study is based on the
implementation of the third approach from the Sandia Insti-
tute, chosen for its reliability, with integrated environmental
parameters that remain sufficiently appropriate, applicable,
and easy to program.
In the first figure, we present the measurement data col-
lected within the Cadarache solar platform [61, 62]. All
of these experimental measurements were carried out in
Table 4 Empirically determined coefficients used to predict the
temperature of the module's rear surface as a function of irradiance,
ambient temperature, and wind speed
Module Type Mount a b
ΔT
(°C)
Glass/cell/glass Open rack −3.47 −0.0594 3
Glass/cell/glass Close roof mount −2.98 −0.0471 1
Glass/cell/polymer
sheet
Open rack −3.56 −0.0750 3
Glass/cell/polymer
sheet
Insulated back −2.81 −0.0455 0
Polymer/thin-film/
steel
Open rack −3.58 −0.113 3
22X Linear concen-
trator
Tracker −3.23 −0.130 13
a) Measured cell temperature (°C) b) Modeling cell temperature (°C)
Fig. 23 The relationship between cell operating temperatures and ambient temperature

Journal of Umm Al-Qura University for Applied Sciences
accordance with NOCT (Nominal Operating Cell Tem-
perature) conditions. In addition, we present the results
obtained using a Matlab code that we have specially devel-
oped. This code calculates and graphically represents the
correlation between ambient temperature and the operating
cell temperature within a photovoltaic module (Figs.23,
24).
Wind speed has a direct influence on the operating tem-
perature of photovoltaic modules. An increase in wind speed
near the photovoltaic modules leads to heightened convec-
tive exchanges between the modules and their external
environment. This, in turn, results in a reduction in the oper-
ating temperature of the cells.
The variation of the temperature difference (T–Ta) (G)
functionally depends on the wind speed. When maintaining
constant lighting (G = 800 W/m2), the relationship between
the cell temperature T and the ambient temperature Ta
becomes a relatively complex function if we integrate the
wind speed. Convective phenomena play a major role in this
relationship [63].
We can further explore the impact of wind speed on the
electrical characteristics of photovoltaic panels and their
a) Measured Wind Speed(m/s) vs Temperature
Difference (T -Ta)
b) Modeling of Wind Speed(m/s) vs Temperature
Difference (T -Ta)
Fig. 24 The relationship between (T–Ta) and the wind speed for an irradiation of 800 W/m2
0510 15 20 25 30 35 40 45
Voltage [V]
0
1
2
3
4
5
6
Current [A]
Ws =1m/s
Incident Irrad=1000 W/m²
Temp=25°C
Ws =9m/s
Ws =7m/s
Ws =5m/s
Ws =3m/s
a) The influence of wind speed on the curve (V-I)
of the PV cell.
b) Influence of wind speed on the (P-V) curve of
the P
V
cell.
0510 15 20 25 30 35 40 45
Voltage [V]
0
20
40
60
80
100
120
140
160
180
Power [W]
Incident Irrad=1000 W/m²
Temp =25°C
Ws=1m/s
Ws=3m/s
Ws=7m/s
Ws=9m/s
Ws= 5m/s
Fig. 25 Characteristics (P–V) and (I–V) of a PV module for different values of wind speed at constant Illuminance of 1000 W/m2 and Tempera-
ture of 25°C

Journal of Umm Al-Qura University for Applied Sciences
energy output, as this is a crucial factor to consider. Wind
speed influences the voltage curve, whether it be the (P–V)
or (I–V) curve, causing a shift towards a higher maximum
power point.
The figures above (Fig.25) depict the (P–V) and (I–V)
characteristics of the solar cell under the influence of vary-
ing wind speeds. Upon examining the curves under different
conditions with increased wind speeds, we observe a rise in
the open-circuit voltage value of the solar cell. This illus-
trates a positive impact of wind speed on the (P–V) charac-
teristics of a photovoltaic solar cell.
Photovoltaic solar panels typically experience a decrease
in efficiency as they heat up. Wind-induced cooling can help
maintain an optimal temperature, thereby improving the
efficiency of converting sunlight into electricity. However,
according to our simulation results, we observed that when
the wind speed exceeds 5m/s, the (P–V) and (I–V) charac-
teristics do not show any significant improvement. On the
contrary, high wind speeds can start to cause problems with
the structural integrity of the installation supports.
The two following curves (Fig.26) illustrate a parameter
of crucial importance in assessing the quality of a photovol-
taic panel, namely the efficiency of a photovoltaic (PV) solar
cell. To do this, we integrated the impact of wind speed on
photovoltaic efficiency, by offering two distinct presentation
modes:
• Efficiency as a function of incident irradiation for differ-
ent wind speeds at a constant temperature of 40°C.
• Efficiency as a function of ambient temperature for differ-
ent wind speeds at a constant illuminance of 1000 W/m2.
In a context characterized by moderate wind speeds,
generally between 1 and 5m/s, It should be noted that the
interaction between wind and photovoltaic cells can have a
significant impact on their output and efficiency. More pre-
cisely, the effect of the wind can be considered as a remark-
able variable insofar as it induces thermal and thermody-
namic phenomena within the solar cell. Indeed, the presence
of a light breeze has the capacity to promote adequate cool-
ing of the solar cell, which, consequently, results in a meas-
urable improvement in its photovoltaic performance. This
improvement can be explained by a reduction in thermal
losses and better heat dissipation, thus allowing the solar
cell to operate at optimal temperatures, thereby increasing
its electrical efficiency.
This methodological approach enables a precise evalu-
ation of the impact of wind speed on the efficiency of PV
solar cells, considering variations in temperature and inci-
dent irradiation. The data obtained through this process will
be essential for a comprehensive characterization of the per-
formance of photovoltaic panels under varying conditions.
6 The nextstep ofour research
andperspective
In our scientific research, particularly in studies examining
the impact of meteorological parameters on the performance
of photovoltaic (PV) cells, it is essential to outline the next
steps and future perspectives, which we have already begun
to explore. This practice not only enhances the depth and
scope of the study but also provides a clear direction for
ongoing and future research endeavors.
The next phase of this study involves expanding our
model to incorporate more complex configurations and
additional environmental variables. Specifically, we plan to
focus on the following aspects, which we have already begun
0 100 200 300 400 500 600 700 800 900 1000
Global incident irrad [W/m²]
0
2
4
6
8
10
12
Efficiency at Pmax [%]
Ws =5m/s
Ws =3m/s
Ws =1m/s
Cells Temp =40°C
01020304050607
08
0
Cells Temperature [°C]
0
2
4
6
8
10
12
14
Efficiency at Pmax [%]
Ws =3m/sWs=5m/s
Ws=1m/s
Incedent Irrad = 1000 W/m²
a) PV efficiency as a function of
illuminance at different wind speeds.
b) Efficiency as a function of ambient
temperature at various wind speeds.
Fig. 26 Variation of efficiency as a function of temperature and as a function of illumination for different wind speed values

Journal of Umm Al-Qura University for Applied Sciences
to study and can delve deeper into during our discussions to
obtain new results:
• Levels of Shading: We will integrate models that account
for partial shading of solar panels due to obstacles such
as trees, buildings, and other structures. This will allow
us to simulate the impact of shading patterns over differ-
ent times of the day and seasons, improving our under-
standing of how shading affects overall energy produc-
tion, we have already initiated studies on the effects of
shading, with the results presented in article [64].
• Detailed Temperature Profiles: Temperature variations
can affect the efficiency of photovoltaic cells. We will
include more detailed temperature profiles in our simula-
tions, considering not only ambient temperature but also
factors such as wind speed, panel heating during opera-
tion, and the cooling effect of airflow over the panel sur-
faces. This will help in predicting the thermal behavior
of the panels more accurately [65].
• Predicting Photovoltaic System Performance: By incor-
porating these additional variables into our model, we
aim to enhance our ability to predict the performance of
photovoltaic systems with greater accuracy [66].
• Simulating Real-World Conditions: Our expanded model
will be capable of simulating a wide range of real-world
conditions, providing a comprehensive understanding of
how various environmental factors interact to influence
photovoltaic performance [67].
• Optimizing System Design: With more precise predic-
tions, we can offer detailed guidelines for optimizing the
design and placement of solar panels to maximize their
efficiency and energy output. This will be particularly
valuable for tailoring installations to specific geographic
locations and climatic conditions [68].
• Improving Reliability: By understanding how different
factors affect photovoltaic performance, we can develop
strategies to mitigate adverse effects, thereby enhancing
the reliability and longevity of solar installations [69].
• Validation with Experimental Data: To ensure the robust-
ness and applicability of our advanced models, we will
validate them with experimental data collected from real-
world photovoltaic installations. This will involve compar-
ing our simulation results with actual performance data to
fine-tune the models and verify their accuracy [70].
By addressing these points in our next phase of research,
we aim to provide a more comprehensive and reliable tool
for the design and optimization of photovoltaic systems,
ultimately contributing to the advancement of solar energy
technology.
7 Conclusion
The intrinsic performance of a photovoltaic generator is
markedly influenced by critical environmental param-
eters, notably solar irradiation, wind speed, and module
temperature.
In this study, we conducted a comprehensive analysis and
modeling of the Aleo Solar photovoltaic module to gain a
deeper understanding of its electrical performance under the
influence of diverse climatic parameters. The single-diode
model was employed to simulate the module's operation
under varying environmental conditions, encompassing
solar irradiation, ambient temperature, and wind speed. Our
simulation results were meticulously compared with data
extracted from the PVsyst software database, focusing spe-
cifically on the technical specifications of the manufacturer's
cell (Aleo Solar, Aleo 150 S model). The module simulation,
grounded in mathematical equations and executed within the
Matlab/Simulink environment utilizing meteorological data,
unveiled that the current–voltage and power-voltage charac-
teristic curves are profoundly impacted due to variations in
climatic condition parameters.
The continuation of this article is based on the integra-
tion of wind speed as a third meteorological parameter in
the electrical model of a photovoltaic cell with a diode. The
goal is to optimize PV module performance using controls
and techniques to minimize the negative impact of weather
parameters.
Excellent alignment was observed between the data gen-
erated by the PVsyst software and the simulated data from
the electrical model of a single-diode photovoltaic cell, dem-
onstrating the high quality of the proposed model.
Author Contributions Category 1: Mohamed Nfaoui, Fatima Ezzahra
Ihfa, Ayoub Bougtaib, Sanaa Hayani-Mounir, Mohamed Bennai, Khalil
El-hami: Conception and design of study. Mohamed Nfaoui, Fatima
Ezzahra Ihfa, Ayoub Bougtaib: Acquisition of data. Mohamed Nfaoui,
Sanaa Hayani-Mounir, Mohamed Bennai, Khalil El-hami: Analysis
and/or interpretation of data. Category 2: Mohamed Nfaoui, Fatima
Ezzahra Ihfa, Ayoub Bougtaib: Drafting the manuscript. Mohamed
Nfaoui, Sanaa Hayani-Mounir, Fatima Ezzahra Ihfa, Ayoub Boug-
taib, Mohamed Bennai and Khalil El-hami: revising the manuscript
critically for important intellectual content. Category 3: Mohamed
Nfaoui, Fatima Ezzahra Ihfa, Ayoub Bougtaib, Sanaa Hayani-Mounir,
Mohamed Bennai and Khalil El-hami: Approval of the version of the
manuscript to be published. Mohamed Nfaoui and Amine El harfouf:
Correction and preparation of the final version of the manuscript.
Funding No funding was received for conducting this study.
Data availability Data available on request from the authors: The data
that support the findings of this study are available from the corre-
sponding author upon reasonable request. Data available in article or
supplementary material: The data that supports the findings of this
study are available within the article (all references cited in this article).
Data sharing not applicable – no new data generated: Data sharing is

Journal of Umm Al-Qura University for Applied Sciences
not applicable to this article as no new data were created or analyzed in
this study. Data generated at a central, large-scale facility: No primary
data have been generated on a specific large-scale facility. Derivative
data supporting the findings of this study are available from the cor-
responding author upon reasonable request. Embargo on data due to
commercial restrictions: There is no data blocking due to any com-
mercial restrictions. Data available on request due to privacy/ethical
restrictions. There are no privacy/ethical restrictions when requesting
available data. Data subject to third party restrictions: The data is not
subject to any third party restrictions.
Declarations
Conflict of interest The authors have no conflicts of interest to declare
that are relevant to the content of this article. All authors have partici-
pated in (a) conception and design, or analysis and interpretation of
the data; (b) drafting the article or revising it critically for important
intellectual content; and (c) approval of the final version. This manu-
script has not been submitted to, nor is under review at, another journal
or other publishing venue. The authors have no affiliation with any
organization with a direct or indirect financial interest in the subject
matter discussed in the manuscript.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article are
included in the article's Creative Commons licence, unless indicated
otherwise in a credit line to the material. If material is not included in
the article's Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will
need to obtain permission directly from the copyright holder. To view a
copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
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