## 1 Introduction  
The use of renewable energy sources is rapidly developing, and the application of solar energy focusing on photovoltaic systems is becoming increasingly popular [1,2]. The major challenge in photovoltaics system is posed by the instability, nonlinearity and complexity of the current-voltage and power-voltage characteristics equation. The relation between photovoltaic current and voltage is both implicit and nonlinear [3, 4, 5, 6] and it depends on several factors such as module temperature, solar radiation and its distribution, spectrum, cable losses, dust accumulation, shading and soiling [7, 8]. Therefore, it is vital to produce a more accurate mathematical model that can better reveal the actual behavior and represent the relationship between current and voltage. In this context, many mathematical models have been developed in the literature to describe the electric, dynamic and thermal behavior of photovoltaic cell/module with a different level of complexity. In particular, the solar cell can be modelled as a static model for DC/DC (direct current), or as a dynamic model for DC/AC (alternating current) with capacitance and parallel dynamic resistance, with diode and photocurrent as proposed in [9; 10; 11]. They can be classified globally into two categories: implicit and explicit models [12; 13]. The former [5; 14; 15; 16] need iterative numerical methods to solve the nonlinear current-voltage equation. On the other hand, the latter models are based on simple analytical expressions [4; 17; 18; 19; 20; 21; 22]. Different physical models were compared on photovoltaic power output prediction in [23] and available models of solar cell are presented in [24]. A different photovoltaic model used for 24-hour-ahead forecasting using neural network is presented in [25], while a comparison between physical and hybrid methods is given in [26] and artificial neural network models are employed in [27]. These models differ mainly by the number of diodes, the presence or absence of a shunt resistor, and by the numerical methods used to determine the unknown parameters. Further, the two diodes model is known as the most accurate model for representing the equivalent electrical circuit. While the single diode model is the most commonly used of the two types; in the simplified four-parameter model neglecting shunt resistance by assuming it as infinite value, and in five-parameter models by maintaining the effect of the shunt resistance. The five and seven parameters models evaluate the photocurrent, the saturation current, the series and shunt resistors and the quality factor of the diode. The eight parameters model adds build-in voltage, thickness, average mobility-lifetime. The exponential non-linearity of current-voltage equations causes many difficulties in prediction and extraction of the electric, dynamic or thermal parameters [28] while, the implicit models are not capable of determining the behavior of the photovoltaic cell/module under many effects. Furthermore, solar cell models have multi-modal objective functions and model parameters vary with operational conditions such as temperature and irradiance. The main problem is to identify the optimal parameter values such as photo-generated current, diode saturation current, series resistance, and diode quality factor. Over the years, various papers have been presented and developed different techniques to identify the optimal values of the electric parameters to describe the behavior of the characteristics. These can be categorized into analytical methods, numerical methods and metaheuristic methods. There are several analytical and numerical (generally gradient-based) methods, as described in Table 1.  
Metaheuristic methods are powerful in local searches, but they tend to get trapped in locally optimal values and depend on the photovoltaic module's manufacturer's data such as open circuit, short circuit, and maximum power points.