Parameters estimation of solar photovoltaic models via a self-adaptive ensemble-based differential evolution

Highlights

• A novel SEDE algorithm is proposed to estimate the parameters of different PV models.

• The ensemble of multiple mutation strategies and parameters settings are developed.

• A self-adaptive scheme is designed to guide the strategy selection process for balancing the diversity and convergence rate.

• Experimental results indicate the superior performance of the proposed algorithm.

Abstract

Photovoltaic (PV) system as a vital element in the utilize of solar energy, its optimization, control, and simulation are significant. The performance of the PV system is mainly influenced by its model parameters that are varying and unavailable, thus identifying these model parameters is always desired. However, accurate and robust parameters estimation of PV models brings great challenges to the existing methods, since the complicated characteristics when estimating the parameters. Hence, to efficiently provide accurate parameters for the PV model, this study develops a self-adaptive ensemble-based differential evolution algorithm. Three different mutation strategies with different properties are combined into two groups for updating each individual. Furthermore, in order to make the best of different mutation strategies, a self-adaptive scheme is suggested to equilibrate population diversity and convergence, by adjusting the proportion of the mutation strategies used in the population. To evaluate the performance of SEDE, it is used to obtain the parameters of three PV models and compared with other well-established algorithms. Systematic comparison results indicate that SEDE is capable of estimating the model parameters with higher efficiency.

Introduction

Electricity has entered millions of households and people's lives. In general, electricity is converted from coal, but with the burning of coal, a large number of greenhouse gases cause serious pollution to the environment (Chen et al., 2020, Pourmousa et al., 2019). In addition, coal is non-renewable and its conversion efficiency is not very high. Therefore, it is always necessary to find a clean, pollution-free, and efficient alternative energy source for generating electricity (Kannan and Vakeesan, 2016). To achieve this aim, numerous alternative energy sources have been found, such as wind, solar, water, and tidal energy (Long et al., 2020). Among them, wind, water, and tidal energy put strict requirements on the site, and the construction cost of hydropower plants and windmills is extremely high. On the contrary, solar energy exists everywhere. Through photovoltaic (PV) power generation systems, the electricity generated can be transmitted to millions of households (Chen et al., 2019, Zhang et al., 2020). In order to make the PV system have a higher conversion efficiency under various weather and temperature (Yang et al., 2019), performing simulation, optimization, and control on the corresponding PV model is vital and helpful.

For PV models, there exist several commonly used models, for example, the single diode (SD) and double diode (DD) models (Kler et al., 2019). It is expected to find the models’ parameter values that approach the experimental data to maximize the performance of PV models under specific conditions. Accurate parameters are always desired for obtaining high performance of PV models. Hence, searching for parameters of the PV model can be regarded as an optimization problem solved by a powerful optimization method. Recently, as the population-based search engines, the heuristic method has made great achievements in extracting parameters of PV models. They are differential evolution (DE) (Li et al., 2019), artificial fish swarm algorithm (AFSA) (Han et al., 2014), JAYA algorithm (Yu et al., 2019), genetic algorithm (GA) (Zagrouba et al., 2010), imperialist competitive algorithm (ICA) (Fathy and Rezk, 2017), bacterial foraging algorithm (BFA) (Rajasekar et al., 2013), artificial immune system (AIS) (Jacob et al., 2015), cat swarm optimization (CSO) (Guo et al., 2016), particle swarm optimization (PSO) (Liang et al., 2020a), whale optimization algorithm (WOA) (Oliva et al., 2017), grasshopper optimization algorithm (GOA) (Elazab et al., 2020), cuckoo search algorithm (CSA) (Kang et al., 2018), grey wolf optimization (GWO) (Nayak et al., 2019), wind-driven optimization (WDO) (Mathew et al., 2018), backtracking search algorithm (BSA) (Yu et al., 2018), teaching–learning-based optimization (TLBO) (Yu et al., 2017a), and flower pollination algorithm (FPA) (Xu and Wang, 2017). The reasons why heuristic algorithms can be widely employed in practical applications include: 1) they only need to define the parameter search range and an objective function of the problem and do not need to know the specific information of the problem (Liang et al., 2020b), thus they can be easily implemented; 2) they are not sensitive to the initial solution of the problem, which is their advantage over other mathematical methods (Jordehi, 2016); 3) they adopt a model in which multiple individuals evolve simultaneously in the search domain, in this case, the optimal solution is not easily fall into a local optimum. Meanwhile, this allows them to better deal with the problems with multimodal property and discrete search domain (Das et al., 2016).

Inspired by the observation that the abovementioned algorithms still cannot obtain very accurate parameter values within a limited computation burden, this paper develops a new self-adaptive ensemble-based differential evolution (SEDE) to acquire more accurate parameters. Specially, SEDE employs multiple mutation strategies to compensate for the limitations of a single strategy. Meanwhile, these strategies form two overlapping groups, the first group (group₁) is dedicated to making the population search more spaces to avoid losing excellent solutions while the second group (group₂) aims at making individuals conduct a local search for accelerating the convergence rate. Meanwhile, each strategy is matched with one parameter combination from the parameters pool to produce promising solutions. Moreover, considering that the requirements for the population diversity and convergence are different in different evolution stages, a reasonable strategy selection is established on the basis of the proposed self-adaptive scheme.

To sum up, the main contributions of this paper are:

• A new self-adaptive ensemble-based differential evolution (SEDE) is proposed to identify the accurate parameters of varied PV models. In SEDE, the ensemble of multiple different strategies and parameters is employed to compensate for the limitations of a single strategy and fixed-parameter settings in the basic DE.

• A self-adaptive scheme without increasing the computing complexity significantly is designed to meet the requirements of the population in different evolution stages by adjusting the relationship between diversity and convergence.

• The proposed SEDE is tested on different PV models, and experimental results show that SEDE has better or competitive performance in comparison with other fifteen state-of-the-art algorithms.

The remainder of this paper is arranged as follows. The PV models, as well as the problem formulation, are reviewed in Section 2. The basic DE algorithm is described in Section 3, which is followed by Section 4 to introduce the proposed algorithm SEDE. Section 5 presents the simulation results. Conclusion and future studies are given in Section 6.