## 1 Introduction  
Due to the increasingly severe environmental contamination and energy crises, renewable energy has been in urgent demand for decades. Solar cells convert electricity from inexhaustible solar energy, which is the most promising renewable energy source [1]. Since the 1900s, the PV industry has developed rapidly. It is reported that over 500 G Wp of PV system capacity was installed worldwide in 2018, a number that is projected to increase to 700 G Wp by 2021 [2]. Estimating the actual performance of operating PV systems and managing and optimizing these systems has become an urgent problem that makes it necessary to establish an accurate model to closely emulate characteristics of solar PV systems [3]. The modeling of PV systems is normally composed of two steps: (1) mathematical model formulation and (2) parameters extraction [4]. At present, researchers have posed a variety of equivalent solar cell models, among which the single-diode model (SDM) and double-diode model (DDM) are the widely used in engineering applications [5] The model parameters are the main factor that affects PV model accuracy; examples include photogenerated current \(l_{ph}\), diode reverse saturation current \(l_{d}\), series resistance \(R_{s}\), parallel resistance \(R_{sh}\), and diode ideality factor \(n_{1}\). Parameters are uncertain and cannot be directly obtained, which makes the extraction of parameters for PV models a focus of current research. Moreover, these parameters intuitively reflect the impact of various factors on solar PV model operation. Hence, it is indispensable for simulation, performance evaluation, fault analysis, and control of PV systems to identify parameters accurately [6]. The typical PV mathematical model of SDM and DDM is an implicit transcendental equation, which has the disadvantage that it cannot be solved explicitly using ordinary electronic functions, which brings challenges to the design of parameter estimation methods [7; 8]. Researchers have recently used several methods for parameter identification of PV model, which can be divided into three different methods: analytical methods, deterministic methods, and heuristic methods. When using analytical approaches, some assumptions need to be made in advance, which reduces the accuracy of the solutions [9]. Several methods have been proposed, including Newton-Raphson methods [10; 11], iterative curve fitting [12], Lambert W-functions [13], and more. Although deterministic methods are simple and quick, these methods are sensitive to initial values. In addition, these deterministic methods usually have incidental restrictions such as differentiability and convexity of decision space, which may lead to the search convergence at local optima [14]. Meta-heuristic algorithms essentially belong to the same category as the deterministic method, but they do not need specific computing conditions, and their concept and structure are relatively uncomplicated, which makes them easy to implement [15]. Therefore, heuristic methods have been widely used in solving the problem of PV model parameter extraction [7], such as particle swarm optimization [16; 17], differential evolution [18], simulated annealing [19], genetic algorithms [20], whale optimization algorithm, hybrid firefly algorithm [21], artificial bee colony [22; 23], cat swarm optimization [24], teaching-learning-based optimization [25; 26], asexual reproduction optimization [27] and other algorithms [28; 29]. Although it can achieve relatively superior solutions, deficiencies such as instability and premature convergence still exist. According to the theorem of 'no free lunch' (NFL), there is no general optimal algorithm that can solve all unsolved optimization research in the best way [6]. Therefore, we try to develop a new method which is suitable for a specific domain that shows better effectiveness compared to previous methods [4]. The Multi-Verge Optimizer (MVO), proposed in 2016 [30], is a powerful natural-based heuristic method for global optimization.