Advanced modeling and parameter estimation of PEM fuel cells using the g-function and self-adaptive differential evolution algorithm

Proton exchange membrane fuel cells (PEMFCs) have emerged as a promising technology due to their high efficiency, adaptability, and potential for integration into various applications, ranging from portable devices to large-scale power grids. A critical aspect of PEMFC research is the accurate modeling of its electrical characteristics. While traditional modeling approaches focus on the voltage-current relationship, there is a growing need to develop models that define current as a function of output voltage, particularly for control system applications. This study introduces a novel approach to PEMFC modeling using the g-function, a logarithmic transformation of the Lambert W function, which has been successfully applied in solar cell modeling. The g-function overcomes numerical limitations associated with the Lambert W function, ensuring greater stability and accuracy in computational applications. Additionally, this research proposes the self-adaptive differential evolution (SaDE) algorithm, a new metaheuristic optimization technique for estimating PEMFC parameters, addressing the need for robust and efficient parameter determination. To validate the proposed approach, a comprehensive comparative analysis is conducted against existing modeling and parameter estimation methods. Furthermore, sensitivity analysis is performed to assess the impact of parameter variations on model performance. The comparative evaluation across three different PEMFC systems (Ballard Mark V, BCS 500, and NedStack PS6) demonstrates consistent improvements, with RMSE reductions of up to 6.65% and SSE gains as high as 12.87%. These quantitative results highlight not only the enhanced accuracy but also the robustness and transferability of the proposed methodology across different fuel cell types. The results demonstrate that the proposed methodology offers improved numerical stability, enhanced accuracy, and efficient parameter estimation compared to conventional approaches. This study contributes to advancing PEMFC modeling techniques, providing a reliable framework for optimizing fuel cell performance and supporting their integration into sustainable energy systems. Overall, this study contributes a validated and versatile framework for advancing PEMFC modeling and optimization, supporting their integration into sustainable and real-world energy systems.