Adaptive historical population-based differential evolution for PEM fuel cell parameter estimation

The proton exchange membrane fuel cell (PEMFC) is regarded as a promising option for a sustainable and eco-friendly energy source. Accurate modeling of PEMFCs to identify their polarization curves and thoroughly understand their operational characteristics has captivated numerous researchers. This paper explores the application of innovative meta-heuristic optimization methods to determine the unknown parameters of PEMFC models, particularly focusing on variants of Differential Evolution such as the dynamic Historical Population-based mutation strategy in Differential Evolution (HiP-DE), augmented with a novel diversity metric. The efficacy of these optimization algorithms was evaluated across six different commercial PEMFC stacks: BCS 500-W PEM, Nedstack PS6 PEM, BCS 250-W PEM, HORIZON 500W PEM, H12 12W PEM, and 500W SR-12P tested under a variety of operating conditions, resulting in analyses of twelve distinct PEMFCs. The objective function for the optimization problem was the sum of squared errors (SSE) between the parameter-derived results and the experimentally measured outcomes from the fuel cell stacks. HiP-DE consistently outperformed compared to Adaptive Differential Evolution with Optional External Archive (JADE), Self-adaptive Differential Evolution (SaDE), Lévy-flight Success-History-based Adaptive Differential Evolution (LSHADE), Improved Lévy-flight Success-History based Adaptive Differential Evolution (iLSHADE), Parameters with Adaptive Learning Mechanism in Differential Evolution (PalmDE), Particle Swarm Optimization Differential Evolution (PSO-DE), jSO, Lévy-flight Parameters with Adaptive Learning Mechanism in Differential Evolution (LPalmDE), and Historical Archive-based Depth-information Reinforced Differential Evolution (HARD-DE) algorithms, achieving a minimum SSE of 0.0254927, which was 53.66 to 69.69% lower than algorithms like JADE, SaDE, LSHADE, and HARD-DE. Additionally, HiP-DE achieved a 99.99% improvement in stability (standard deviation), and a runtime reduction of over 97%, demonstrating its computational efficiency. Comparative analyses with other algorithms, such as JADE, LSHADE, and PalmDE, showed that HiP-DE improved solution accuracy, convergence speed, and overall performance in all cases. The I/V and P/V curves derived from HiP-DE closely matched the datasheet curves for all cases examined, reinforcing its suitability for PEMFC parameter identification.