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Proton Exchange Membrane Fuel Cells (PEMFC) are energy efficient and environmentally friendly alternatives to conventional energy conversion systems in many yet emerging applications. In order to enable prediction of their performance and durability, it is crucial to gain a deeper understanding of the relevant operation phenomena, e.g., electrochemistry, transport phenomena, thermodynamics as well as the mechanisms leading to the degradation of cell components. Achieving the goal of providing predictive tools to model PEMFC performance, durability and degradation is a challenging task requiring the development of detailed and realistic models reaching from the atomic/molecular scale over the meso scale of structures and materials up to components, stack and system level. In addition an appropriate way of coupling the different scales is required. This review provides a comprehensive overview of the state of the art in modeling of PEMFC, covering all relevant scales from atomistic up to system level as well as the coupling between these scales. Furthermore, it focuses on the modeling of PEMFC degradation mechanisms and on the coupling between performance and degradation models.

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SUMMARYThe performance of a polymer electrolyte membrane fuel cell (PEFC) power stack is assessed in terms of polarization measurements under laboratory conditions by applying a harmonized testing procedure. Harmonization at the level of testing procedures allows for an objective and trustworthy comparison of performance data. The harmonization of the procedure took place among the 55 partners of the Fuel Cell Testing and Standardization Network (FCTESTNET). Selected testing procedures are currently validated through experimental campaigns in the successor project (Fuel Cell Testing, Safety and Quality Assurance, FCTES QA ) involving research laboratories from Europe, US, China, and Korea.This study reports the results of a test of the campaign for the performance assessment of a PEFC power stack carried out at JRC by applying the harmonized procedure for validation. Following the procedure, the test inputs and outputs are subjected to stability checks a priori and during the actual polarization measurement steps of the test. The assessment of the stack performance is based on a statistical approach of the test outputs, which includes the calculation of averages, measurement range, (relative) standard deviation and standard error as well as of a stability parameter. The study demonstrates the necessity of harmonized testing procedures and of a harmonized methodology of presenting the test results in a commonly agreed format to provide a comprehensive performance assessment for PEFC stacks.

Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers‐Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two‐sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non‐linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences.