Opposition-based JAYA with population reduction for parameter estimation of photovoltaic solar cells and modules

https://doi.org/10.1016/j.asoc.2021.107218Get rights and content

Highlights

  • Parameter estimation is very important to the optimization of photovoltaic systems.

  • An enhanced JAYA optimization algorithm called EJAYA is developed.

  • The linear population reduction strategy and GOBL mechanism are incorporated in EJAYA.

  • EJAYA is applied to solve the parameter estimation of different PV cells and modules.

  • Our approach obtained highly competitive results compared with related methods.

Abstract

To efficiently increase the conversion of solar energy into electricity, it is vitally important to find the appropriate equivalent circuit parameters to execute the modeling, evaluation, and maximum power point tracking on photovoltaic (PV) systems in high quality and efficiency. In this study, an enhanced JAYA (EJAYA) algorithm is proposed for accurately and efficiently estimating the PV system parameters. In EJAYA, it consists of three main improvements: (i) A modified evolution operator, based on the tendency factor adaption, is introduced to increase the probability of approaching the victory. (ii) The simple deterministic population resizing method is incorporated to control the convergence rate during the search. (iii) EJAYA employs generalized opposition-based learning mechanism to avoid being trapped in local optima. Experimental results tested over several different PV models demonstrate the excellence of EJAYA on accuracy, stability, and convergence speed. Additionally, to further highlight the effectiveness of EJAYA, other different modules from the data sheet are tested at different temperature and irradiance. Consequently, EJAYA is superior to become an alternative for the parameter detection of PV cells and modules at various practical conditions.

Introduction

There exists a severe challenge on the sustainable development of energy resources for this century. Excessive air pollution, ozone depletion, and global warming have made civilizations begin to find alternative energy options to fossil fuels, such as wind, solar, geothermal energy [1], [2]. Among these renewable energies, solar energy is envisaged as one of the most feasible alternative source as it is renewable, clean, and abundant [3]. Since the PV systems are highly nonlinear, selecting an accurate model to closely describe the characteristics of PV cells is extremely important [4]. Despite the fact that various PV models have been developed, two equivalent PV models are widely and commonly adopted in practice, namely single diode and double diode models [5]. Generally, the accuracy and reliability of the current–voltage (I–V) characteristic curves are particularly dependent on the diode model parameters [6]. Additionally, reliable equivalent parameters can also be employed to effectively solve the maximum power point tracking problems [7]. Therefore, it is a crucial task to estimate the appropriate parameter values for these PV models to imitate the performance of real solar cells or modules [8].

To accurate estimate the PV model parameters, many researchers have studied numerous methods in recent years, which can be divided into three major categories, including analytical approaches, deterministic approaches, and meta-heuristic approaches [9]. The basis of analytic approaches is mathematical equations analysis according to the characteristics of the problems, thus these methods are easy to implement but may reduce the solution accuracy due to the necessary hypotheses and the value of artificially specified points [10]. Different from the analytical technique, the deterministic approaches are generally gradient-based methods, such as the Newton–Raphson [11], Lambert W-functions [12], which are sensitive to initial values and prone to be trapped in local optima. To overcome these drawbacks, recently, various meta-heuristic approaches have been employed to solve parameter estimation problems for PV models [6], [13], such as genetic algorithms (GA) [14], particle swarm optimization (PSO) [15], differential evolution (DE) [16], simulated annealing (SA) [17], harmony search (HS) [18], cuckoo search (CS) [19], artificial bee colony (ABC) [20], teaching learning based optimization (TLBO) [21], fireworks algorithm (FA) [22], chaotic whale optimization algorithm (CWO) [23], flower pollination algorithm (FPA) [24], Ant Lion Optimizer (ALO) [25], JAYA [26], improved shuffled complex evolution algorithm (ISCE) [27]. Although the results obtained by many meta-heuristic approaches are pretty satisfactory, there is still great developing space for seeking competitive meta-heuristic algorithms to solve PV parameter estimation, in terms of the convergence speed, accuracy, reliability and the complexity of tuning parameters.

The JAYA algorithm, recently proposed by Rao [28], is a population-based and effective algorithm for optimization problems. JAYA has two eminent superiorities than other meta-heuristic methods. First, unlike most of the meta-heuristic approaches, there is no extra control parameters in JAYA. For example, the scaling factor and crossover probability in DE need to be set, PSO requires the inertia weight and two acceleration coefficients, and CMAES [29] needs to set the step size and other parameters determined by equations. Hence, JAYA can omit the difficulty of adjusting control parameters effectively. Second, only one evolution phase per generation in JAYA makes the algorithm more simple to implement and less computation time to consume, which gives JAYA a latent applicability and development. Due to these promising features, JAYA and some advanced variants have been widely utilized in solving various real-world problems [30], [31].

In this paper, an enhanced JAYA (EJAYA) algorithm is proposed to solve the parameter estimation problems for PV models more accurately, efficiently and reliably. In EJAYA, a modified perturbation operator is proposed, which adjusts the tendency of approaching the best solution and avoiding the worst solution with the adaptive tendency factors. Besides, the linear population reduction strategy and the generalized opposition-based learning mechanism are incorporated together into JAYA. To evaluate the performance of EJAYA in parameter estimation, several different PV models namely the single diode model, the double diode model, and the PV modules are utilized in the experiments. Compared with other parameter estimation approaches, the results indicate that the performance of EJAYA is exceedingly competitive.

The main contributions in this work are as follows.

  • EJAYA is developed to estimate the parameters of different PV models. In EJAYA, a modified evolution operator based on simple adaptive scheme is proposed to lead to better perturbation during the search process.

  • The linear population reduction strategy is employed in EJAYA to make a balanced trade-off between the exploration and the exploitation, thus enhancing the convergence speed of the algorithm.

  • To help EJAYA jump out of the local optimum and improve the performance, the generalized opposition-based learning mechanism is incorporated.

  • Extensive experiments are carried out on different PV models, including standard PV models and other modules under different irradiance and temperature, to investigate the performance of EJAYA.

The remainder of this paper is organized as follows. Section 2 gives the problem formulation of PV models and the objective function to be optimized. The original JAYA algorithm is briefly introduced in Section 3. Then, Section 4 presents the proposed EJAYA algorithm in detail. The experimental results and elaborate analysis are reported in Section 5. Finally, the conclusions of this paper are given in Section 6.

Section snippets

Mathematical model and problem formulation

To model the behaviors of PV system, there are different PV models presented in the literature. Among numerous equivalent circuit models, the single diode and double diode models are widely used for electrical engineering. In this section, the modeling of PV cells and modules are described at first. Then, the objective function for the parameter estimation problem is briefly introduced.

The JAYA algorithm

JAYA is a recently proposed meta-heuristic algorithm [28]. In this section, the core three operations of JAYA are briefly described.

Motivations

Generally, the balance between the exploration and the exploitation determines the performance of the meta-heuristic algorithms. Accordingly, the key point to develop an eminent algorithm is to make a trade-off between the two abilities of the algorithm. As introduced above, JAYA has only one direct evolution strategy to generate trial vectors. Thus, the exploration and exploitation abilities of JAYA cannot be efficiently maintained during the search process. To remedy this drawback, an

Experimental results and analysis

In this section, the performance of the proposed EJAYA is evaluated for parameter estimation of three common PV models (SDM, DDM and SMM) using several standard I–V data sets firstly, with respect to the accuracy, the convergence and the robustness. Then, the influence of the initial population size NP and the effectiveness of different components in EJAYA is verified and analyzed as well. Finally, the practicality and reliability of EJAYA for both SMM and DMM, is further tested using the I–V

Conclusions

In this paper, an enhanced JAYA algorithm namely EJAYA is proposed to efficiently and accurately solve the model parameter estimation problem for various PV cells and modules. This application of the proposed EJAYA is to build precise PV models for cells and modules. In practice, the accuracy of PV models may extremely affect the dynamic analysis and simulation of PV systems. On the other hand, the PV models and the estimated parameters play a significant role on the maximum power point

CRediT authorship contribution statement

Xi Yang: Resources, Project administration, Software, Data curation, Writing - original draft, Writing - review & editing. Wenyin Gong: Funding acquisition, Supervision, Conceptualization, Methodology, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was partly supported by the National Natural Science Foundation of China under Grant Nos. 62076225 and 62073300, the Natural Science Foundation for Distinguished Young Scholars of Hubei, China under Grant No. 2019CFA081, and the Fundamental Research Funds for the Central Universities, China, China University of Geosciences (Wuhan) under Grant no. CUGGC03.

All authors read and approved the manuscript.

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