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Estimation of photovoltaic module model’s parameters using an improved electromagnetic-like algorithm

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This paper offers an electromagnetism-like (IEM) algorithm to estimate the five parameters of a single-diode PV module’s model. IEM uses local search and improves movement step to increase the convergence to optimal solutions. The key of improvement is performed by adding a nonlinear equation to adjust the length of the particle in each iteration. Moreover, the total force formula is simplified to speed up the exploration for an optimal solution. Analyses are carried out by experimental data points at various operational conditions to show the stability and reliability of the proposed methods. The results of the proposed IEM algorithm show a better convergence speed and high accuracy compared with other models in the literature, which involves various statistical errors. The values of average root mean square error, mean bias error, standard deviation, average absolute error, and average test statistic of the proposed method are 589%, 0.51%, 0.19%, 46%, and 0.53, respectively. As a conclusion, the IEM algorithm presents better performance than other methods in the literature in terms of accuracy and convergence.

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\(d\) :

Ideality factor of diode

m :

Number of initial particles

\(\delta\) :

Local search operator

\(S1 - S7\) :

Operational condition (solar radiation and cell temperature)

\(I\) :

Current conducted by the PV module (A)

\(I_{\text{o}}\) :

Saturation current of the diode (A)

\(I_{\text{e}}\) :

Experimental current conducted by the PV module (A)

\(I_{\text{P}}\) :

Proposed current of the PV module (A)

\(I_{\text{Ph}}\) :

Photocurrent (A)

\(q\) :

Charge particle

\(V_{\text{e}}\) :

Experimental voltage conducted by the PV module (V)

\(F\) :

Total force vector

n :

Total dimension of the particle

N :

Length of dataset

\(\lambda\) :

Randomly distributed between 0 and 1

\(V_{\text{T}}\) :

Diode thermal voltage (V)

\(V\) :

Voltage conducted by PV module (V)

\(X\) :

Population set

\(X^{i}\) :

Vector whose components limited between \(L_{k}\) or \(U_{k}\) bound

\(L_{k}\) :

Lower bound

\(U_{k}\) :

Upper bound

\(R_{\text{p}}\) :

Shunt resistance \(\left(\Omega \right)\)

\(R_{\text{s}}\) :

Series resistance \(\left(\Omega \right)\)

\(R^{2}\) :

Determination coefficient

\(f\left( {X^{\text{best}} } \right)\) :

Objective value of each particle

\(\epsilon\) :

Switching control parameters (\(\epsilon \in \left[ {0,1} \right])\)

\(F^{i}\) :

Total force calculation


Maximum number of local iterations


Maximum number of local search iterations


Electromagnetism-like algorithm


Slandered test condition


Standard deviation of RMSE




Constant of Boltzmann (1.380603e−23 J/K)


Absolute error


Root mean square error


Mean bias error


National institute of standards and technology


Newton Raphson


Penalty based differential evolution


Improved adaptive DE


Salp swarm optimization


Central processing unit


Epsilon parameters


Particle swarm optimization


Differential evolution


Artificial bee colony


Improved electromagnetism-like algorithm


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Correspondence to Hussein Mohammed Ridha.

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Pseudo code of the IEM algorithm.

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Ridha, H.M., Gomes, C. & Hizam, H. Estimation of photovoltaic module model’s parameters using an improved electromagnetic-like algorithm. Neural Comput & Applic 32, 12627–12642 (2020).

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