Proton Exchange Membrane (PEM) fuel cells represent a promising clean energy technology due to their high efficiency, environmental sustainability, and wide applicability in transportation and stationary power systems. Accurate parameter extraction from PEM fuel cell models is critical for reliable performance prediction, control, and optimization. However, this task is challenging because of the nonlinear, multimodal, and highly coupled characteristics of fuel cell models. To address this challenge, this paper proposes an Enhanced Elk Herd Optimizer (EEHO), incorporating a novel best-bull–guided differential reproduction mechanism to improve search accuracy, convergence speed, and robustness. The proposed enhancement enables a portion of offspring solutions to be generated by perturbing the global best solution using scaled differences between randomly selected herd members. This mechanism strengthens exploitation around promising regions while maintaining population diversity and preventing premature convergence. The EEHO is applied to extract seven unknown parameters of PEM fuel cell models by minimizing the sum of squared errors between experimental and simulated voltage data. The effectiveness of the proposed method is validated using two commercial PEM fuel cell stacks, namely a 250 W stack and a BCS 500 W stack. Extensive comparative evaluations against the conventional Elk Herd Optimizer and several well-established methods demonstrate that the EEHO achieves superior performance in terms of accuracy, convergence speed, robustness, and statistical consistency. The proposed algorithm attains lower error values, faster convergence, and more stable performance across multiple independent runs. Furthermore, the extracted parameters produce highly accurate voltage and power characteristics, closely matching experimental observations. The results confirm that the proposed EEHO provides an efficient, reliable, and robust optimization framework for PEM fuel cell parameter extraction and offers strong potential for broader applications in energy system modeling, intelligent optimization, and renewable energy optimization problems. Quantitatively, the proposed EEHO achieved a significant reduction in the averages of the Sum of Squared Errors (SSE) of up to 24.96% and 23.29% compared with the conventional EHO for the 250 W stack and a BCS 500 W stack, respectively, demonstrating its superior accuracy in parameter estimation. To further validate the robustness and generalization capability of the proposed EEHO, two additional commercial PEM fuel cell datasets, of Ballard Mark V and Modular SR-12, are investigated and compared against several state-of-the-art optimization algorithms. The results, supported by Wilcoxon and Friedman statistical tests and boxplot analyses, confirm that EEHO consistently achieves superior accuracy, stability, and convergence reliability across different operating conditions.
Almutairi et al. (2026) studied this question.