A self-started predictor–corrector method for calculating the Lambert W function within the scope of the photovoltaic single diode model

Abstract

The single diode model is one of the most employed to represent the behavior of photovoltaic generators. Nonetheless, the transcendental nature of its characteristic equation requires that some mathematical approach be specifically adopted to allow the determination of its solution. In recent years, the approach via the Lambert W function has gained more and more popularity; however, the calculation of this special function still faces performance issues. That said, the present paper proposes a self-started predictor–corrector method for calculating the Lambert W function in the interval of interest of the single diode model. This method was properly designed to return high-quality solutions at a low and fixed computational cost. In this sense, the moderate complexity of its four equations stands out, as well as its non-conditional and non-iterative nature. The results obtained for appropriate case studies ascertain its elevated level of accuracy. Also, they demonstrate that it is more effective and faster than other state-of-the-art alternatives. Therefore, the paper’s major contribution is this novel method, which proves to be reliable, easy to implement, and useful for making the employment of the single diode model in studies more efficient.