Numerical calculation of series and shunt resistances and diode quality factor of a photovoltaic cell using the Lambert W-function

Abstract

A number of methods currently exist to determine the modeling parameters of a solar cell. The authors presented in earlier a work a method to numerically determine the values of series and shunt resistance using the Lambert W-function at maximum power point primarily using data provided by the manufacturer. This method however assumes the diode constant value is known. An experimental investigation revealed that by setting the diode constant to unity as suggested in other work, a growing disparity between model output and experimental values would arise away from the maximum power point. To address this issue, a modification is proposed to the method of Ghani and Duke (2011) which permits the calculation of the diode constant and the corresponding values of series and shunt resistances. The method was experimentally validated by collecting the current-voltage characteristics of a multi-crystalline cell exposed to 800, 900, and 1000 W/m² of outdoor illumination in Hamilton, New Zealand. A comparative analysis of the model generated data using parameters found by the proposed method and two additional methods against experimental data revealed a significant reduction in the root mean square error over the entire current vector was obtained using the proposed method. The method is simple to apply and can be carried out using data provided the manufacturer.