Application of Buckingham π theorem for scaling-up oriented fast modelling of Proton Exchange Membrane Fuel Cell impedance

This work focuses on the development of a fast PEMFC impedance model, built starting from both physical and geometrical variables. Buckingham's π theorem is proposed to define non-dimensional parameters that allow suitably describing the relationships linking the physical variables involved in the process under-study to the fundamental dimensions. This approach is a useful solution for those problems, whose first principles-based models are not known, difficult to build or computationally unfeasible. The key contributions of the proposed similarity theory-based modelling approach are presented and discussed. The major advantage resides in its straightforward online applicability, thanks to very low computational burden, while preserving good level of accuracy. This makes the model suitable for several purposes, such as design, control, diagnostics, state of health monitoring and prognostics. Experimental data, collected in different operating conditions, have been analysed to demonstrate the capability of the model to reproduce PEMFC impedance at different loads and temperatures. This results in a reduction of the experimental effort for the FCS lab characterization. Moreover, it is highlighted the possibility to use the model with scaling-up purposes to reproduce the full stack impedance from single-cell one, thus supporting FC design and development from lab-to commercial system-scale.