Newton-Raphson method versus Lambert W function for photovoltaic parameter estimation

This paper compares the performances of the Lambert $W$ function (LWF) and the Newton-Raphson method (NRM) to estimate the parameters of the photovoltaic (PV) models. Lambert $W$ function explicitly represents the PV model under consideration and NRM allows to overcome the implicit nature of the PV model by determining the output current iteratively. LWF and NRM are classified as indirect approaches, and are used to calculate the output current, instead of the most used approach in the literature so far, which is a direct approach to solve the output current (DirectSolve), when metaheuristics are applied. Here, the single-diode model (SDM) was considered, and the estimation of its PV parameters was performed by the gaining-sharing knowledge (GSK) optimization algorithm. The analysis used standard datasets and experimentally measured datasets under different operating conditions. The results obtained from indirect and direct approaches were compared, showing identical accuracy and reliability when considering LWF or NRM. However, from a computational point of view, LWF was slightly more efficient than NRM (0.11% according to the mean number of evaluations). DirectSolve was on average about 35% less accurate than indirect approaches. The comparisons showed that LWF and NRM present a very competitive performance in the PV parameter estimation, differing only slightly in computational costs.