An innovative approach for mathematical modeling and parameter estimation of PEM fuel cells based on iterative Lambert W function

In the literature, identifying the parameters of proton exchange membrane fuel cells (PEMFCs) relies on minimizing the difference between measured and simulated voltage values for different current values. In this regard, expressions representing the PEMFC voltage as a current function are usually used. Unlike literature approaches, in this work, a new mathematical expression of PEMFC current as a voltage function is derived and solved using the iterative Lambert W function for the first time in literature. The root-mean-square error (RMSE) and sum-ofsquares error (SSE) between the measured and estimated current and voltage values are calculated, analyzed, and discussed using the parameters obtained from many optimization methods for two PEMFCs - Ballard-Mark-V 5 kW and BCS 500 W. An improved evaporation rate water cycle algorithm (ERWCA), named Chaotic ERWCA (ChERWCA), is employed to solve the new PEMFC parameter estimation problem based on minimizing SSE between the measured and estimated current values obtained using the new mathematical model. Moreover, SSE and RMSE of voltage and current measures were calculated for different recent methods presented in the literature. The results validate the effectiveness of the new mathematical model and show that the solutions obtained using ChERWCA outperformed those obtained by other methods presented for these fuel cells in the literature. The improvement of voltage SSE using the new mathematical formulation of the PEMFC model and the proposed algorithm is about 0.1% compared to the best result reported in the literature. Finally, this work lays the foundation for developing a novel mathematical model to investigate the operation of PEMFCs in modern power systems.