Parameter identification of commercial proton exchange membrane fuel cells using phototropic growth algorithm

Proton exchange membrane fuel cells (PEMFCs) are recognized as a cornerstone technology for sustainable energy systems thanks to their minimal environmental footprint and high energy conversion efficiency. However, the accurate parameter extraction of semi-empirical PEMFC models is a significant challenge due to their non-linear and complex characteristics. To address this critical challenge, this study rigorously implements the Phototropic Growth Algorithm (PGA) for achieving robust and precise PEMFC parameter estimation. The algorithm is responsible for minimizing the sum of squared error (SSE) between the experimentally measured and the predicted stack voltage by optimal adjustment of seven unknown model parameters ( ε 1 , ε 2 , ε 3 , ε 4 , Ψ , R c , μ ) for Temasek 1 kW, Horizon H-12, and Ballard Mark V. The performance of the PGA is compared with up-to-date intelligent problem-solving methods, including Triangulation Topology Aggregation Optimizer (TTAO), Bezier Search Differential Evolution (BeSD), Animated Oat Optimization (AOO), and Crested Porcupine Optimizer (CPO). According to the simulation results, PGA provided the lowest SSE of 0.78425463 for Temasek 1 kW, 0.09652164 for Horizon H-12, and 0.81391170 for Ballard Mark V PEMFC stacks. The SSE results demonstrated a perfect fit between the predicted data by PGA and the experimentally measured data. The Friedman test shows that PGA is the most successful method, with an average score of 1.46. In the Wilcoxon test, PGA was statistically superior in 11 out of 12 comparisons, with a success rate of 91.66 %. Given that all results are together, the present research advances the field of PEMFC technology by providing a statistically validated and high-accuracy optimization tool for precise modelling.