On the parameters domain of the single-diode model

Abstract

The I-V curves of solar photovoltaic (PV) systems have been widely used as a tool to determine their electrical operation. Usually, I-V curves are described by means of three cardinal points: the short-circuit point ( 0 , I sc ) , the open-circuit point ( V oc , 0 ) , and the maximum power point ( V mp , I mp ) . In this context, to study the I-V curves, the Single-Diode Model (SDM) is often used. In this manuscript, we present a practical approach for determining the parameters domain of the SDM given a set of cardinal points. An in-depth mathematical analysis showed that the cardinal points must satisfy the following inequalities V oc / 2 < V mp < V oc and I sc / 2 < I mp < I sc . Then, it is possible to implicitly represent the SDM by means of one single parameter in a thoroughly chosen coordinate space. Based on these theoretical results, a fast computational algorithm for calculating the SDM parameters limits is proposed. The algorithm has been computer-tested using 40 000 synthetically generated maximum power points which are processed in about one minute of the CPU time on a standard laptop computer. Moreover, as a practical application, the California Energy Commission database is analyzed using the proposed algorithm.