The pressure-dependent operation of polymer electrolyte membrane fuel cell systems is considered, following a general research methodology. Based on previous research a model refinement from a phenomenological mathematical model towards a semi-empirical mathematical model is presented. It is shown that for the fuel cell device under test and the chosen compressor a low-pressure operation in suction mode is more efficient compared to the supercharged operation. This matter of fact permits optimized operating and control strategies for (multifunctional) fuel cell systems for aircraft applications