International Journal of Photoenergy

Volume 2019, Article ID 4692108, 16 pages

https://doi.org/10.1155/2019/4692108

## Adaptive Electromagnetic Field Optimization Algorithm for the Solar Cell Parameter Identification Problem

Department of Industrial Engineering, Bursa Uludag University, Bursa, Turkey

Correspondence should be addressed to Ilker Kucukoglu; rt.ude.gadulu@ulgokucuki

Received 21 January 2019; Revised 18 April 2019; Accepted 28 April 2019; Published 3 June 2019

Academic Editor: Huiqing Wen

Copyright © 2019 Ilker Kucukoglu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Solar cell parameter identification problem (SCPIP) is one of the most studied optimization problems in the field of renewable energy since accurate estimation of model parameters plays an important role to increase their efficiency. The SCPIP is aimed at optimizing the performance of solar cells by estimating the best parameter values of the solar cells that produce an accurate approximation between the current vs. voltage () measurements. To solve the SCPIP efficiently, this paper introduces an adaptive variant of the electromagnetic field optimization (EFO) algorithm, named adaptive EFO (AEFO). The EFO simulates the attraction-repulsion mechanism between particles of electromagnets having different polarities. The main idea behind the EFO is to guide electromagnetic particles towards global optimum by the attraction-repulsion forces and the golden ratio. Distinct from the EFO, the AEFO searches the solution space with an adaptive search procedure. In the adaptive search strategy, the selection probability of a better solution is increased adaptively whereas the selection probability of worse solutions is reduced throughout the search progress. By employing the adaptive strategy, the AEFO is able to maintain the balance between exploration and exploitation more efficiently. Further, new boundary control and randomization procedures for the candidate electromagnets are presented. To identify the performance of the proposed algorithm, two different benchmark problems are taken into account in the computational studies. First, the AEFO is performed on global optimization benchmark functions and compared to the EFO. The efficiency of the AEFO is identified by statistical significance tests. Then, the AEFO is implemented on a well-known SCPIP benchmark problem set formed as a result of real-life physical experiments based on single- and double-diode models. To validate the performance of the AEFO on the SCPIP, extensive experiments are carried out, where the AEFO is tested against the original EFO, AEFO variants, and novel metaheuristic algorithms. Results of the computational studies reveal that the AEFO exhibits superior performance and outperforms other competitor algorithms.

#### 1. Introduction

Renewable energy has experienced a tremendous increase in recent decades because of the depletion of conventional sources oil, coal, or natural gas. Among various kinds of renewable energy sources such as wind, wave, nuclear, and biomass, solar or photovoltaic (PV) energy is the most important source due to its properties such as effectiveness, wide-scale availability, unlimited capacity, and safe-use [1]. Furthermore, PV, which is able to provide power for specific purposes, is an emission-free system with direct conversion from solar energy to electricity [2]. Since solar cell installation has received great attention, numerous researchers have focused to maximize the efficiency of PV systems. In order to control and optimize PV systems, it is required to accurately simulate the characteristics of the PV system before installation. The accuracy of the PV systems mainly depends on the parameters of solar cells, which are generally not provided by the cell manufacturers [3]. Therefore, it is vital to identify the parameters of solar cells or modules based on nonlinear mathematical models. Among a variety of existing models in the literature, the main ones are the single-diode model (SD), the double-diode model (DD), and the PV module model [4–6]. The problem of extracting the parameters of solar cells from the experimental data is called the solar cell parameter identification problem (SCPIP) in literature.

To solve the SCPIP, there exist several solution approaches in the literature, which are mainly divided into two groups: deterministic and heuristic solution approaches. Regarding the deterministic approaches, a number of methods are employed by the researchers, such as nonlinear least squares based on the Newton model [7], iterative curve fitting [8], Lambert W-function [9], and J-V model [10]. However, these deterministic solution approaches are not efficient to solve the SCPIP since they need continuity, convexity, and differentiability conditions for being applicable and involve heavy computations [4, 11]. To cope with the complexity of the SCPIP, heuristic methods are used as an alternative to deterministic solution approaches.

Regarding the popular metaheuristic algorithms, simulated annealing algorithm [12], genetic algorithm [13, 14], particle swarm optimization algorithm [15, 16], differential evolution algorithm [17–20], pattern search [21], artificial bee colony algorithm [22] are widely used for the SCPIP. In addition to these well-known heuristic algorithms, there exist several papers in the literature which consider more recent approaches, such as bacterial foraging algorithm [23, 24], teaching-learning-based optimization algorithm [25–27], biogeography-based optimization algorithm [28], chaos optimization algorithm [29], artificial fish swarm algorithm [30], bird mating optimizer approach [31], artificial immune system [32], evolutionary algorithm [1], cat swarm optimization algorithm [33], moth-flame optimization algorithm [5], JAYA optimization algorithm [34, 35], chaotic whale optimization algorithm [36], imperialist competitive algorithm [37], bee pollinator flower pollination algorithm [38], shuffled complex evolution algorithm [39], memetic algorithm [40], interior search algorithm [41], collaborative swarm intelligence approach [42], and cuckoo search algorithm [43]. On the other hand, it has been proven by No-Free-Lunch theorem [44] that none of these algorithms is able to solve all type of optimization problems. As a result of No-Free-Lunch theorem, it should be denoted that a new algorithm is always likely to exhibit better performance on the SCPIP compared to the existing solution methodologies.

Based on the aforementioned motivation, this study considers electromagnetic field optimization (EFO) algorithm to solve the SCPIP. The EFO is a relatively new and effective algorithm on global optimization problems, and it has been shown that the EFO outperforms other optimization algorithms and effectively balance the exploration and exploitation performance [45]. Conversely, it is also reported that the traditional EFO tends to suffer poor exploitation performance on specific optimization problems [46]. Therefore, this study introduces an adaptive version of electromagnetic field optimization to solve the SCPIP efficiently, which is called the adaptive EFO (AEFO). The proposed AEFO adaptively controls the algorithm parameters and explores the search space effectively, especially in the early stages of the search process, whereas exploitation is emphasized in the latter phases. In addition to the adaptive control of parameters, boundary control and randomization procedures are modified in the algorithm. In computational studies, performance of the proposed algorithm is tested into two parts. First, the AEFO is performed on a recently introduced global optimization benchmark problem set and compared to the EFO solutions to identify the efficiency of the adaptive control mechanism of the proposed algorithm. In the second part, the AEFO is tested on the well-known PV models and compared to the original version of the EFO, artificial bee colony algorithm (ABC), particle swarm optimization (PSO), and differential evolution algorithm (DE) in identical test conditions. The AEFO is further tested against recent metaheuristic algorithms, which are presented to solve the SCPIP. Computational results and statistical tests show that the AEFO significantly achieves superior performance to competitor algorithms.

The main contributions of the proposed study are as follows: (i)To the best of the author’s knowledge, the EFO has not been considered in the literature to solve the SCPIP until now(ii)An adaptive version of the EFO is introduced by enriching the algorithm employing an adaptive search strategy. Additionally, modified boundary check and randomization procedures are used for the candidate solution generation. By these novel modifications, the performance of the traditional EFO is improved(iii)Detailed comparisons between the EFO and the AEFO variants and also between the AEFO and the other recent algorithms are presented. The outperforming performance of the AEFO is proved by statistical significance tests

The remainder of the paper is organized as follows. In Section 2, the SCPIP is described and the mathematical formulation of the problem is given. Section 3 presents the details of the EFO. Section 4 introduces the proposed AEFO for the SCPIP. Computational results are given in Section 5. Finally, a conclusion part with future research perspectives is provided in Section 6.

#### 2. Problem Definition

To describe the characteristics of the solar cells, there exist several models in the literature. In this study, the SD and DD models, which are the most commonly used models since their practical usage for the solar cells, are taken into account [4, 11]. In this section, the SD and DD models are introduced, and the SCPIP based on these models is defined.

##### 2.1. Single-Diode Model

The SD model consists of a current source in parallel with a diode, a shunt resistor to represent the leakage current, and a series resistor to denote the losses of load current. This model has commonly used to describe the static characteristics of solar cells because of its simplicity and accuracy [34]. Figure 1 represents the equivalent circuit for the SD model, where is the terminal voltage, is the series resistance, is the shunt resistance, is the terminal current, is the photo-generated current, is the diode current, and is the shunt resistor current.