It is well known that the electrical power generated by a

photovoltaic module can be significantly reduced compared to

the optimal production conditions (maximum power point), but

also compared to the metrological conditions. Indeed, many

factors, such as partial shading can have a considerable impact

on the electrical production of a photovoltaic panel.

The first step to study about an appropriate control method

in photovoltaic systems is to know how to model and simulate

a PV system attached to the converter and power grid. In

general, PV systems present nonlinear Power-Voltage (P-V)

and Current-Voltage (I-V) characteristics which tightly depend

on the receiving irradiance levels and ambient conditions. The

mathematical model of the photovoltaic device is significantly

valuable for studying the maximum power point tracking

algorithms, doing research about the dynamic performance of

converters, and also for simulating photovoltaic components

by using circuit simulators.

This paper is organized as follows: we pursue the

mathematical analysis of the responses of a single module

under uniform irradiance levels. Afterwards, in a more

practical scheme, by analyzing the effects of the partial

shading phenomenon on the output of PV systems, the study is

followed up by the modeling of the module and array under

partial shading conditions. Finally, the simulation of the

outputs for the proposed algorithms under different degrees of

partial shading is presented.

A photovoltaic cell is described by the single diode model,

this model is generalized to a photovoltaic (PV) module by

considering it as a set of identical cells connected in series

and/or in parallel.

The modeling of the elementary cell is based on an

equivalent electrical circuit [2]. In our study we use a model

with a single diode as shown in figure 1.

Fig. 1 PV equivalent circuit model.

Comparative Study Of P&O and PSO Particle Swarm Optimization

MPPT Controllers Under Partial Shading

MAHBOUBA BRAHMI, CHIHEB BEN REGAYA, HICHEM HAMDI, ABDERRAHMEN ZAAFOURI

Research Laboratory LISIER, National High School of Engineers of Tunis ENSIT, University of Tunis, 5 Av.

Taha Hussein, Tunis, 1008,

TUNISIA

Abstract: Maximum power point tracking (MPPT) is a vital and essential requirement for photovoltaic (PV)

systems under normal irradiance and partial shading conditions (PSCs). Although, perturb and observe (P&O)

algorithm does not map the global maximum power point (GMPP), whereas the algorithm for particle swarm

optimization (PSO) tracks it efficiently. This paper explores the rapid determination of GMPP under PSCs using

a proposed particle swarm optimization MPPT technique which operates in conjunction with a boost converter.

To achieve this analysis, MATLAB/SIMIULINK is used. The results of the simulation illustrate the high

tracking performance of the proposed technique under various irradiance patterns.

Keywords: PV, MPPT, DC/DC, P&O, PSO,PARTIAL SHADING.

Received: September 12, 2021. Revised: August 12, 2022. Accepted: September 14, 2022. Published: October 2, 2022.

1. Introduction 2. Modeling of Photovoltaic System

Parameters

2.1 Equivalent Electrical Circuit

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2022.4.7

Mahbouba Brahmi, Chiheb Ben Regaya,

Hichem Hamdi, Abderrahmen Zaafouri

E-ISSN: 2769-2507

45

Volume 4, 2022

An ideal photovoltaic cell under illumination can be defined in

a simple way as an ideal current source that produces a current

IPh in parallel with a diode.

the general equation of this model:

I0: saturation current in Ampere(A);

n : quality factor of the dimensionless diode;

K : Boltzmann constant (1.38066×10-23 J/K= 8.61400×10-

5eV/K);

T: absolute temperature in Kelvin (K);

q : absolute charge of an electron in coulomb

(1.60281×10-19 C)

In the case of an ideal cell in the dark, the solar cell solar cell

follows the behavior of a conventional diode.

(4)

Thus:

(5)

In the case of a real photovoltaic cell, we observe a voltage

loss at the output resistor (RS) as well as leakage currents at

the resistor (RP).

The characteristic equation is deduced from the equivalent

circuit and from Kirchhoff's laws [3]:

(6)

The parallel resistor current is given by the relation:

(7)

The diode current is given by the following relation:

(8)

The photon current is given by the following relation:

(9)

the output characteristic of the PV cell can be deduced by

solving the following implicit form:

I

(10)

Figure 2 shows the output of the PV module, which employs

72 cells connected to provide a power (P) of 290 W at a

terminal voltage (Vpvm) of 35.37 V.

(a)

(b)

Fig. 2 Output characteristics of PV module at normal condition (a) I-

V characteristic; (b) P-V characteristic.

In any outdoor environment, the whole or some parts of the

PV system might be shaded by trees, passing clouds, high

building, etc., which result in non-uniform insolation

conditions. During partial shading, a fraction of the PV cells

which receive uniform irradiance still operate at the optimum

efficiency. Since current flow through every cell in a series

configuration is naturally constant, the shaded cells need to

operate with a reverse bias voltage to provide the same current

as the illumined cells. However; the resulting reverse power

polarity leads to power consumption and a reduction in the

maximum output power of the partially-shaded PV module.

Exposing the shaded cells to an excessive reverse bias voltage

could also cause “hotspots” to appear in them, and creating an

open circuit in the entire PV module. This is often resolved

with the inclusion of a bypass diode to a specific number of

cells in the series circuit.

2.2 Characteristics of the PV System

Under Partial Shading

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2022.4.7

Mahbouba Brahmi, Chiheb Ben Regaya,

Hichem Hamdi, Abderrahmen Zaafouri

E-ISSN: 2769-2507

46

Volume 4, 2022

Fig. 3 Current-voltage curve of a PV array under partial shading

condition.

Fig. 4 Power-voltage curve of a PV array under partial shading

condition.

Concerning the review mentioned in the introduction,

conventional MPPT algorithms cannot distinguish the local

and global maximum point existing on the P-V characteristic

curve; this is contributed to the complexity of tracking the

correct maximum point. In addition, a variation in PV current

and voltage occurs in the system when there is partial shading,

so the conventional MPPT is not able to detect the changes.

The most interesting information obtained from the samples is

that, although the P-V curve has more than one maximum

power point, each power peak, including the local and global

maximum points, exists at multiples of 70% to 85% of the PV

module's open circuit voltage, except for the two rightmost

sections of the curve, where the peak exists between 75% and

95%. We varied the manufacturer's PV module specifications

(SunPower SPR-X20-250-BLK; Trina Solar TSM-170D, and

Jinko Solar JKM310M-72) using Models A and B in Figures 5

and 6, as the studies can distinguish six cases. The P-V

characteristic curves of all cases, including the power peaks,

are shown in Figure 7, and the summarized information is

presented in Table 1.

Figure 7 shows tests with three different PV modules, varying

irradiation and temperature; the power peak, including local

and global, exists in the highlighted researched regions. We

can also observe in Table 1. that the increase of the

temperature brings less measured VOC, which verifies the P-V

characteristics. We can observe that although the location of

the overall power peak varies in each model, the peaks always

exist in the searched region. Thus, it is not necessary to search

the entire regions of the P-V characteristic

curves.

Fig. 5 Pattern A at 25 ◦C.

Fig. 6 Pattern B at 30 ◦C.

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2022.4.7

Mahbouba Brahmi, Chiheb Ben Regaya,

Hichem Hamdi, Abderrahmen Zaafouri

E-ISSN: 2769-2507

47

Volume 4, 2022

Case

PV Module’s

specification

Irradiation

Pattern

VOC per

Module (V)

Case 1

Case 2

SunPower SPR-

X20-250-BLK

A

B

50.93

Case 3

Case 4

Trina Solar

TSM-170D

A

B

43.6

Case 5

Case 6

Jinko Solar

JKM310M-72

A

B

47.1

Table 1. Summarized information of example cases.

a. Case 1

b. Case 2

c. Case 3

d. Case 4

e. Case 5

f. Case 6

Fig. 7. P-V characteristic curves for Cases 1–6.

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2022.4.7

Mahbouba Brahmi, Chiheb Ben Regaya,

Hichem Hamdi, Abderrahmen Zaafouri

E-ISSN: 2769-2507

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Volume 4, 2022

In order to have the best power transfer between the

photovoltaic generator and the load, we have modeled the

whole conversion chain with MatlabSimulink. The following

figure represents the block diagram of our photovoltaic

system.

Fig. 8 block diagram of the photovoltaic system

To evaluate the robustness of the PSO algorithm in finding the

GMPP under partial shading, the PV field was exposed to a

non-uniform irradiance at start. The PV string 1 receives an

irradiance of 800W / m² and the others receive 1000W / m²,

the temperature is maintained constant at 25°C. The results

obtained are presented in Figure 9.

Fig. 9 simulation results of the PSO-MPPT

and P&O-MPPT under Partial Shading.

Fig. 10 output voltage of the PSO-MPPT

and P&O-MPPT under Partial Shading

It is clearly observed that the PSO-MPPT is not trapped by the

LMPP of the characteristic P-V and converged precisely to the

GMPP.

We can also note that power oscillations do not exist at all,

resulting in a constant output power of the PV field and

avoiding energy waste due to oscillations, while the MPPT

perturbation and observation controller presents very

important undulations.

We have also tested PSO-MPPT and P&O with many

many other shading models. The results indicate that PSO-

MPPT cannot accurately track the GMPP accurately when the

shading pattern applied to the PVG is complicated.

In other words, when the P-V characteristic curve has power

peaks greater than two, PSO-MPPT will not be able to

accurately track the GMPP.

In this work, a model of PV system composed

of 4 PV panels connected in series and a DC-DC converter are

developed. Around the DC-DC converter, two MPPT

controls: P&O and PSO are presented.

The PV system simulation was made for a non-uniform

irradiance in order to make a comparison

between the MPPT control based on the P&O algorithm and

the PSO MPPT control and to determine the best control in

terms of performance and robustness.

The simulation results showed that the PSO algorithm can

guarantee a good performance compared to the classical P&O

control when the shading pattern applied to the PVG is not

complicated.

3. Siiimulation Result

4. Conclusion

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2022.4.7

Mahbouba Brahmi, Chiheb Ben Regaya,

Hichem Hamdi, Abderrahmen Zaafouri

E-ISSN: 2769-2507

49

Volume 4, 2022

[1] M. Brahmi, B. R. Chiheb, H. Hamdi and Z.

Abderrahmen (2022), “Comparative Study of P&O

and PSO Particle Swarm Optimization MPPT

Controllers for Photovoltaic Systems”, 2022 8th

International Conference on Control, Decision and

Information Technologies (CoDIT).

[2] H. Hamdi, B. R. Chiheb and Z. Abderrahmen (2019),

“Performance improvement of a photovoltaic system

with a radial basis function network based on particle

swarms optimization”, 2019 International Conference

on Signal, Control and Communication (SCC).

[3] Hamdi, H., Regaya, C. B., & Abderrahmen, Z.

(December 2019). A sliding-neural network control of

induction-motor-pump supplied by photovoltaic

generator.

[4] Hichem, H., Chiheb, B. R., & Abderrahmen, Z. (2019).

Performance improvement of a photovoltaic system

with a radial basis function network based on particle

swarms optimization.

[5] Hichem, H., Chiheb, B. R., & Abderrahmen, Z. (May

2019). Real-time study of a photovoltaic system with

boost converter using the PSO-RBF neural network

algorithms in a MyRio controller (Vol. 183).

[6] Jones, A. R. (01 January 2022). Design and

Implementation of Photovoltaic Powered SEPIC DC-

DC Converter Using Particle Swarm Optimization

(PSO) Technique.

[7] Roy, S. S. (07 December 2021). A PSO Based MPPT

Controller for Solar PV System at Variable

Atmospheric Conditions (Vol. volume 1373).

[8] TaraEmail, B. B., & Suresh, H. L. (21 August 2021).

Comparative Analysis of MPPT Techniques in Grid-

Connected and Stand-alone PV System.

Brahmi Mahbouba is a PhD student and member in Laboratory

of Industrial Systems Engineering and Renewable Energy

(LISIER). Her main research interests are renewable energy

optimization and real time control.

Ben Regaya Chiheb, currently work as an Associate Professor

in Higher Institute of Applied Sciences and Technology of

Kairouan, Tunisia and member in Laboratory of Industrial

Systems Engineering and Renewable Energy (LISIER). His

main research interests are robust estimation and robust

filtering, adaptive control, real time control and renewable

energy optimization.

Hamdi Hichem currently works at the Electrical

engineering, École Nationale Supérieure d'Ingénieurs de Tunis

(ENSIT). Dr. Hichem is member in Laboratory of Industrial

Systems Engineering and Renewable Energy (LISIER). His

current project is 'Real-time study of a photovoltaic System

and wind energy'.

Zaafouri Abderrahmen received a B.Sc. in electrical

engineering from the High Normal School of Technical

Education of Tunis (ENSET) in 1993. In 1995, Prof. Zaafouri

obtained the Master’s degree in automatic control at the same

university, and the Ph.D degree from the National Engineering

School of Tunis in 2000; he joined the High School of

Sciences and Techniques of Tunis (ESSTT) at Tunis

University as an assistant professor. Now, he is a member in

Laboratory of Industrial Systems Engineering and Renewable

Energy (LISIER). His main research interests are approaches

to robust control of uncertain systems: performances study.

Contribution of individual authors to the

creation of a scientific article (ghostwriting

policy)

Mahbouba Brahmi conceived the FMSPSO-MPPT

algorithm.

Mahbouba Brahmi, Chiheb Ben Regaya and Hichem

Hamdi carried out the simulation using MATLAB-

Simulink.

Mahbouba Brahmi and Abderrahmen Zaafouri

performed the analysis.

Mahbouba Brahmi, Chiheb Ben Regaya, Hichem Hamdi

and Abderrahmen Zaafouri wrote the paper.

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_US

References

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2022.4.7

Mahbouba Brahmi, Chiheb Ben Regaya,

Hichem Hamdi, Abderrahmen Zaafouri

E-ISSN: 2769-2507

50

Volume 4, 2022