Model-Free Energy Efficiency Optimization of Proton Exchange Membrane Fuel Cell Based on Extremum Seeking

The optimization of operating points (OPs) is crucial for maximizing the energy efficiency of proton exchange membrane fuel cells (PEMFCs). However, existing strategies primarily focus on a single variable—the oxygen excess ratio (OER)—neglecting the potential of synergistic optimization with the pressure ratio (PR) and stack temperature. This limitation, coupled with the reliance on complex models or cumbersome cost functions, hinders further efficiency gains. This article presents a model-free, multivariate extremum seeking (ES) scheme that addresses these challenges by jointly optimizing OER, PR, and stack temperature. It further introduces a simplified cost function that removes the need for hydrogen consumption measurements and empirical weighting factors. The proposed multivariate ES framework is rigorously proven to achieve local exponential stability. Hardware-in-the-loop (HiL) experiments demonstrate that, after ES-based training under a series of constant-current loads, the optimized OPs scheduled as functions of the stack current achieve energy efficiency improvements ranging from 6.81% to 14.53% over two widely adopted techniques. Furthermore, the optimized OER and PR exhibit clear fitted correlations with the stack current, while the stack temperature converges near its initial value, revealing its secondary impact on parasitic power. The results confirm that the concurrent optimization of multiple OPs unlocks substantial efficiency reserves inaccessible to conventional single-variable approaches.