F. Javier Toledo (Operations Research Center, University Miguel Hernández of Elche), Vicente Galiano (Computers Engineering Department, Miguel Hernández University of Elche), María Victoria Herranz (Operations Research Center, University Miguel Hernández of Elche), Jose M. Blanes (Industrial Electronics Group, Miguel Hernández University of Elche) and Efstratios Batzelis (Electronics and Computer Science, University of Southampton, Southampton, UK)


In this paper we describe and compare the methods for the calculation of all the key points of the photovoltaic single-diode model. These include the short-circuit point, the open-circuit point, the maximum power point, the mean slope point, the maximum curvature point, and the jerk point. The main contribution of this paper is a new algorithm to obtain the maximum power point which is based on reducing its computation to solve a single-variable equation. Its unique solution leads to an explicit expression of the point by using a recent parametrization of the single-diode model current–voltage curve. In the numerical resolution of the previous equation, we will use as starting point the mean slope point which has been proved to be close to the maximum power point. Previously, we will provide for the first time in the literature an exact and explicit expression of the mean slope point. The new algorithm proposed reaches the accuracy of the best known numerical methods, but it is much faster, almost reaching the execution times of explicit formulas.