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

Abstract

Models of series-parallel (SP) photovoltaic (PV) arrays focus on the system of nonlinear equations that represents the array’s electrical behavior. The solution of the system of nonlinear equations can be posed as an optimization problem and solved with different methods; however, the models do not formulate the optimization problem and do not evaluate different optimization algorithms for its solution. This paper proposes a solution, using global optimization algorithms, of the mathematical model that describes the electrical behavior of a SP 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 the single-diode model. Consequently, for each string a system of nonlinear equations is build applying the Kirchhoff’s 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 that both algorithms solve the optimization problem and allow the reproduction of the generator’s characteristic curves. Moreover, the results also indicate that the optimization problem is correctly defined, which opens the possibility explore other optimization algorithms to reduce the computation time.