Solution of series-parallel photovoltaic arrays model using global optimization algorithms

This article proposes a solution, using global optimization algorithms, of the mathematical model that de- scribes the electrical behavior of a series-parallel photovoltaic generator, operating under uniform and partial shading conditions. Such a model is constructed by dividing the generator into strings and representing each module in the string with its circuital equivalent, denominated single-diode model. Consequently, for each string a system of nonlinear equations is build applying the Kirchhoff’s current and voltage laws, where the unknowns are the modules’ voltages. The solution of the resulting nonlinear equation system is posed as an optimization problem, where the objective function is defined as the sum of the squared of each nonlinear equation. Minimum and maximum values of each voltage are defined from the datasheet information of the modules and bypass diodes. As a demonstrative example, we arbitrarily select two well-known algorithms to solve this problem: Genetic Algorithms and Particle Swarm Optimization. Simulation results show the validity of our proposal, since both algorithms achieved the exact solution in a relatively short computation time. Moreover, the proposed solution is conceptually simple and easily programmabl.