Analytical Calculation of the Optimal Temperature and Expected Voltage of a PEM Fuel Cell Considering the Properties of the Membrane Material

Abstract

The manuscript investigates how temperature affects the behavior of proton exchange membrane (PEM) fuel cells under different operating conditions, considering both closed- and open-cathode designs. The analysis is based on a range of current densities (0.2–1.0 A/cm²) selected to reflect typical operational phases: activation, ohmic, and concentration loss sections. The results show that although higher temperature can improve cell voltage, this effect only lasts up to a certain point, with the most critical component being ohmic losses due to altered membrane hydration. This study presents a detailed computational model capable of determining the optimal operating temperature of PEM fuel cells by accounting for the physical properties of the cell materials, thus extending previous simplified calculation models. The novelty of the model lies in its quantitative consideration of the temperature dependence of not only the Nernst potential but also the activation, ohmic, and concentration losses—specifically through the temperature-dependent hydration behavior of the membrane. A key advantage of the new model is that it enables performance estimation without requiring hardware-based measurements, while maintaining a deviation of less than 5.9% from experimental results. On the basis of the calculations, a distinct optimal temperature can be determined for each current density value, which is not provided by earlier simplified models.