On the root mean square error (RMSE) calculation for parameter estimation of photovoltaic models: A novel exact analytical solution based on Lambert W function

In the literature, one can find a lot of methods and techniques employed to estimate single diode solar photovoltaic (PV) cell parameters. The efficiency of these methods is usually tested by calculating the Root Mean Square Error (RMSE) between the measured and estimated values of the solar PV cell output current. In this work, first, the values of RMSE calculated using 69 different methods published in many journal papers for the well-known RTC France solar PV cell are presented and discussed. Second, a novel exact analytical solution for RMSE calculation based on the Lambert W function is proposed. The results obtained show that the RMSE values were not calculated correctly in most of the methods presented in the literature since the exact expression of the calculated cell output current was not used. Third, the precision of calculation of the methods used for analytical solving of Lambert W equation is presented and discussed. Fourth, the applicability of the proposed solution methodology in accordance with current-voltage characteristics measured in the laboratory for solar modules of Clean Energy Trainer Setup is checked. Identification of its unknown parameters is presented using three optimization techniques. Further, the proposed solution methodology is proven for Solarex MSX–60 PV module, and the most promising 5-parameter single diode parameters are estimated based on minimization of the precise RMSE values calculated. Finally, this work aimed to develop a good base for proper investigation and implementation of optimization algorithms to solve the parameter estimation problem of 5-parameter single diode PV equivalent circuits.