Experimental investigation and modeling of membrane resistance and hysteresis in a short stack PEMFC under uniform membrane hydration

Maintaining optimal membrane hydration is critical for the performance and durability of proton exchange membrane fuel cell (PEMFC) stacks. While membrane hydration cannot be directly measured, the high-frequency resistance (HFR) obtained from electrochemical impedance spectroscopy (EIS) has been shown to be strongly correlated with membrane hydration. Recent advances in onboard embedded diagnostics have made online estimation of PEMFC membrane hydration based on HFR increasingly feasible, enabling real-time implementation in deployed systems. However, this requires that HFR be systematically mapped to well-defined reference states corresponding to known and spatially uniform membrane hydration levels. To this end an experimental investigation was conducted on a short-stack PEMFC operated under non-reactive H 2 /N 2 conditions to establish this relationship. HFR measurements were obtained over a wide range of relative humidity (RH) levels (30–120%) and stack temperatures (50–80 °C), including both increasing and decreasing RH profiles. The results show that HFR decreases significantly with increasing RH, with up to an 87% reduction between dry and fully humidified conditions. A pronounced hysteresis of up to ∼ 10% was observed between increasing and decreasing RH cycles, particularly in the 40–80% RH range, indicating a strong dependence on hydration history. The hysteresis behavior observed in the HFR–RH relationship is primarily driven by variations in RH, while the influence of temperature hysteresis loop area is comparatively less significant within the investigated operating range. Finally, a physics-informed mathematical model, inspired by the membrane conductivity relation 1 , was developed to correlate HFR with membrane water activity and temperature based on empirical formulations of water uptake and ionic conductivity. To account for hysteresis effects, a sigmoid-based function was incorporated into the primary correlation to capture the path-dependent hydration behavior. The resulting model predicts HFR as a function of RH, stack temperature, and the direction of the most recent RH sequence (increasing (+) or decreasing (−)). The model demonstrated high predictive capability when validated against independent experimental datasets, achieving a root mean square error (RMSE) of 0.59 mΩ and a coefficient of determination (R 2 ) of 0.98.