# Parameter Estimation of the Bishop Photovoltaic Model Using a Genetic Algorithm
## 1 Introduction
Concerning the model parameters, PVSIM incorporates information for different operating points (irradiance and temperature) to interpolate the parameters values for a particular temperature defined by the user. In addition, the user can define a set of parameters; thus, cell-level information should be obtained to estimate those parameters. However, that work does not describe the procedure adopted to find the parameters values incorporated into the tool database. The parameters of a PV cell can be estimated by different approaches, where the most commonly adopted ones are analytical methods and stochastic techniques (such as heuristics and metaheuristics) [22; 23; 24; 25; 26], which are often called optimization techniques. Analytical methods are based on equations that relate the output current and voltage of the system and, despite those approaches determine the parameters of a PV model, those depend on variables under standard test conditions (STC). Thus, if those parameters are not adequately defined, analytical methods are unable to reproduce the variations in PV profiles due to changes in temperature and irradiance. Although these methods are simple, the resulting models have low performance in the reproduction of different real operating conditions [27; 28; 29]. The optimization techniques are classified in two important groups, the deterministic and the stochastic ones. For the deterministic ones, there are solution methods, such as Newton-Raphson [30], Gauss-Seidel [31] and other methods [32], which are related to methods that require a convex, continuous and differentiable expression of an equation or mathematical model; given this context, it is necessary to clarify that the convergence of an algorithm can stay within a local minimum due to the complexity and non-linearity of the Bishop model. On the other hand, the stochastic methodology is divided into two groups, heuristics and metaheuristics. For the parametric estimation, the metaheuristics approach has been more notable; it contains a randomness factor. In this case, aspects related to the procedure for the selection of candidate solutions, setting parameters and objective function impact the reached solution; further, a statistical analysis is required to validate the results [25; 33]. Optimization algorithms are also widely adopted to estimate the parameters that best fit an I-V profile of a PV cell, module, or panel. Those methods can be used to minimize the energy consumption and costs or maximize the profits, production, performance, or energy efficiency. One of the most used techniques for parameter estimation of the SDM is the genetic algorithm (GA). For example, in [34], a GA is used to analyze the behavior of the estimated parameters as irradiation and temperature changes. Similarly, in [35], a comparative analysis of the parameter estimation of the SDM is performed, evaluating the results provided by the Newton-Raphson algorithm against optimization techniques such as GA and particle swarm optimization (PSO). Besides, hybrid techniques which use analytical formulations and numerical algorithms have been proposed to improve computation time or accuracy. In [36], mathematical formulations to translate I-V curves and a moth-flame algorithm are used to take into account the PV cell parameters sensitivity to weather conditions on the SDM. In short, optimization techniques can be applied in many PV applications as long as the equation to be optimized can be expressed in terms of an objective function, i.e., a mathematical model that can be used in an iterative process [25; 37; 38]. However, the use of optimization techniques require trade-offs between accuracy, computation time and computational resources, which are defined by the method programming and objective function. As it can be noticed in the literature review, optimization techniques have been widely used for estimating the parameters of cells or modules mostly using the SDM or the DDM, which do not represent the behavior of the cell in the second quadrant in a proper way.