Triple-diode solar cell current optimization – An analytical solution based on the Lambert W function

Abstract

A novel mathematical modeling approach for the Triple-Diode Model (TDM) and its parameter estimation is introduced in this paper. For the first time in the literature, this paper presents two analytical solutions for calculating the current in TDM solar cells using the Lambert W function. Additionally, a new metaheuristic algorithm, the Adaptive Evaporation Rate Water Cycle Algorithm (Adaptive ERWCA), is proposed for estimating TDM solar cell parameters. The proposed algorithm is tested using both the new analytical solutions and a well-known iterative approach for the current-voltage characteristics of the TDM solar cells model. Extensive testing is conducted on three well-known solar cells/modules and a panel under various weather conditions. The results demonstrate that the proposed analytical expressions for the current-voltage characteristics are accurate and highly effective for representing TDM solar cell current. The accuracy of the parameter estimates obtained with the application of the proposed algorithm, considering both analytical solutions and the iterative approach, is compared with existing literature results. It is shown that the proposed algorithm outperforms existing algorithms in solar cell parameter estimation across both the analytical and iterative approaches for current-voltage characteristics. Remarkably, for the RTC France solar cell, the SOLAREX MSX 60 solar module, and the PHOTOWATT-PWP 201 solar module, the obtained Root Mean Square Errors (RMSE) are 0.00075141, 0.01157153, and 0.0010578, respectively. These results are currently the best reported in the literature.