Implicit modelling of series-parallel photovoltaic arrays using double-diode model and its solution

Abstract

As defined, a solar photovoltaic array is internally a power-limited nonlinear current source. They are commonly used to convert electromagnetic radiation from the sun, into electric power. Accurate models of arrays in series–parallel configuration, represent each sub-module with the double-diode model. Nevertheless, most of those models imply a high computational cost because they require the Lambert W-function to obtain approximated explicit equations for the sub-module’s voltage and current. This paper proposes a model of series–parallel photovoltaic arrays, operating under homogeneous and non-homogeneous irradiance conditions, where each sub-module is represented by the implicit expression derived from the double-diode model. The array is divided into strings and a system of implicit nonlinear equations is obtained for each string with the sub-modules’ voltages and string’s current as unknowns. The corresponding systems of implicit equations are solved by using the Trust-Region Dogleg method to obtain all the electrical variables of the array. The results from the proposed model are compared with those obtained with the equivalent electrical circuit of the array, used as a reference. Simulation data for small, medium, and large arrays show that the proposed method yields data akin to those of the reference method obtaining RMSE values below 0.104 A for current-voltage curves in homogeneous and non-homogeneous conditions. Likewise, the model is validated against several experimental conditions, showing a remarkable agreement with RMSE values below 0.161 A for current-voltage curves in each condition. Therefore, the proposed model can be used to represent accurately series-parallel arrays operating in homogeneous and non-homogeneous conditions.