Comparative prediction of single and double diode parameters for solar cell models with firefly algorithm

Due to the non-linearity of current-voltage of solar cell model, the conventional methods are incapable to extract the parameters of solar cell with high accuracy. The implicit nonlinear equation describing the single and double diodes solar cell in five and seven parameters is rewritten as optimization problems with constraint functions and it is solved by using a firefly algorithm optimization. The firefly algorithm is a nature-inspired stochastic optimization algorithm, and able to solve modern global optimization for nonlinear and complex system, based on the flashing patterns and behavior of firefly's swarm. Moreover, this paper develops a unique solar cell modelling approach that incorporates search and optimization techniques for the determination of equivalent circuit parameters of RTC France Company mono-crystalline silicon solar cell single and double diodes at 33°C and 1000W/m² from experimental current-voltage. The statistical errors are used to verify the accuracy of the results. Finally, accuracy of the extracted parameters is verified by comparing the current-voltage curve generated from simulation with those provided by determined experimentally and with different recent algorithms.

I. Introduction

The solar cell model in current-voltage and voltage-power has been described by complex and nonlinear analytical equations, depends on several factors such as the temperature, solar radiation and its distribution, soiling, cable losses. In the research literature, there are several mathematical models that describe the operation and electrical behavior of solar cells; many studies are focused on the modelling of solar cell and developing several electric models with a different level of complexity; in [1] different physical models are compared on photovoltaic power output prediction and [2] an available models of solar cell are presented. These models differ mainly by the number of diodes, the presence or the absence of a shunt resistor, and by the numerical methods used to determine the unknown parameters. The exponential nonlinearity of the current-voltage equation causes many difficulties in identification and extraction of the parameters [3]. Over the year, various parameters extraction techniques have been proposed to identify the optimal values of the unknown parameters, which can be categorized into analytical methods, numerical methods or numerical combined with analytical. The analytical methods used in [4]–[7]; in [8] presents a Lambert W-function based exact representation for double diode model, and then compares their fitness and parameter extraction performance. The analytical-numerical given in [9] and [10] this method based in the datasheet data such as the open circuit, short circuit, and the maximum power points. The analytical and the analytical-numerical methods require continuity, convexity and differentiability conditions for being applicable, and due to the non-linearity of current-voltage curve, the analytical optimization techniques can be unable to effectively solve the parameter identification problem. Therefore, the great potentials on solving modern global optimization for nonlinear and complex system are given by the metaheuristic optimization algorithms [11]–[15] and [16].