Optimizing parameter extraction in proton exchange membrane fuel cell models via differential evolution with dynamic crossover strategy

The proton exchange membrane fuel cell (PEMFC) is a cornerstone of green energy technology due to its advantages, including cleanliness, durability, high efficiency, and low noise. To fully harness its potential, the simulation and optimization of real-time PEMFC-based systems are critical. This study introduces an improved differential evolution algorithm, called differential evolution with dynamic crossover (DEDC), to optimize the extraction of seven unknown parameters in PEMFC models. DEDC integrates two adaptive mutation strategies regulated by a dynamic coefficient and a dynamic crossover mechanism to enhance both global and local search capabilities. The algorithm's performance was validated through 22 benchmark functions, demonstrating its superiority over ten state-of-the-art algorithms in most cases. Subsequently, DEDC was applied to estimate PEMFC model parameters, where statistical analysis revealed its exceptional performance. Specifically, for the Ned-Stack PS6 and BCS 500W PEMFC models, DEDC consistently achieved the lowest root mean square error (RMSE) of 3.0112E-01 and 2.549E-02, respectively. Compared to the worst-performing algorithms, DEDC improved the RMSE by 27.1 % for Ned-Stack PS6 and 79.7 % for BCS 500W, demonstrating its significantly enhanced accuracy. Additionally, DEDC exhibited the lowest standard deviation (4.0766E-16 for Ned-Stack PS6 and 1.318E-16 for BCS 500W), resulting in an unprecedented variance reduction of 99.99 %, proving its unmatched stability and reliability. Furthermore, DEDC demonstrated remarkable robustness across different population sizes, maintaining consistent accuracy and stability regardless of parameter settings. This adaptability ensures its effectiveness in various PEMFC modeling scenarios, making it a reliable optimization tool for real-world applications.