Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

Abstract

Abstract Accurate parameter estimation is essential for reliable modeling and performance evaluation of Proton Exchange Membrane Fuel Cells (PEMFCs). This paper introduces the application of Tianji’s Horse Racing Optimization (THRO), a recently developed metaheuristic algorithm, to precisely identify the unknown parameters of a widely used PEMFC model. The proposed THRO-based framework is evaluated on six commercial PEMFC stacks, namely NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12, and Ballard Mark V, and its performance is benchmarked against five recent metaheuristic algorithms: Flood Algorithm (FLA), Educational Competition Optimizer (ECO), Kepler Optimization Algorithm (KOA), Fata Morgana Algorithm (FATA), and Spider Wasp Optimizer (SWO). Comprehensive comparative and statistical analyses demonstrate that THRO consistently achieves superior parameter identification accuracy, robustness, and solution stability across all tested PEMFC models. In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, $$1.12 \times 10^{-2}$$ , $$1.16 \times 10^{-2}$$ , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively. Additionally, THRO attains an extremely low standard deviation levels, indicating strong convergence reliability and resistance to premature stagnation. The obtained results confirm the effectiveness, robustness, and generalization capability of THRO for PEMFC parameter extraction, highlighting its potential as a reliable optimization tool for PEMFC parameter extraction and energy system applications.