Advancements on Lumped Modelling of Membrane Water Content for Real-Time Prognostics and Control of PEMFC

PEMFCs play a key role in the energy transition scenarios thanks to the zero emissions, versatility, and power density. PEMFC performances are improved optimizing water management to ensure proper ion transport: it is well known that a well-balanced water content avoids either electrodes flooding or membrane drying, causing gas starvation at the active sites or low proton conductivity, respectively. In this paper, an analytical formulation for water transport dynamics within the membrane, derived from membrane water balance, is proposed to overcome the limitations of PEM dynamics model largely adopted in the literature. The dynamics is simulated thanks to the introduction of a characteristic time with a closed analytical form, which is general and easily implementable for any application where both low computational time and high accuracy are required. Furthermore, the net water molar fluxes at the membrane boundaries can be easily computed as well for a cell’s simulation. The analytical formulation has a strong dependency on the operative conditions, as well as physical parameters of the membrane itself. From the proposed formulation, for a 200 µm membrane, the characteristic time can vary from 5 s up to 50 s; this example shows how control strategies must consider PEM dynamic behavior.