Lambert W-function simplified expressions for photovoltaic current-voltage modelling

Abstract

In this paper, the first work carried out at the IDR/UPM Institute within the frame of the educational innovation project PIRAMIDE is presented. This work is related to photovoltaic behavior modeling simplification. The aim is to derive simplified and easy-to-work-with equations for the Lambert W-function. This mathematical function represents a quite useful tool when modeling solar cells/panels performance (that is, the current-voltage curve) by analytical approaches. However, the Lambert W-function has a complex solving process which might represent an unaffordable mathematical challenge for a great number of professionals/technicians from the photovoltaic industrial sector. Simple approximations for the Lambert W-function on both of its branches (positive and negative), are proposed in this work. The results of the present work show a simple but accurate way of photovoltaic systems modeling, even when working with the implicit equation of the 1-Diode/2-Resistor equivalent circuit model (whose solution is given in the present work by an explicit equation).