Montecarlo based quantitative Kramers-Kronig test for PEMFC impedance spectrum validation

Abstract

Electrochemical Impedance Spectroscopy (EIS) is a very powerful tool to study the behaviour of electrochemical systems. At present, it is widely used in the fuel cell field in order to study challenging cutting edge issues as membrane drying or gas diffusion layer flooding amongst others. The proper analysis of impedance data requires the fulfilment of four fundamental conditions: causality, linearity, stability and finiteness. The non compliance with any of these conditions may lead to biased, or even misguided, conclusions. Therefore it is critical to verify the compliance of these conditions before accepting any analysis performed on an experimental spectrum. This is even more important in a fuel cell experimental spectrum analysis, since fuel cells are markedly non stationary systems. The aim of this work is to establish an impedance spectrum quantitative validation technique to validate the whole experimental spectrum and to identify the individual points within a spectrum that do not comply any of the four conditions, in order to remove these inconsistent points from the analysis. The designed validation method consists in a Kramers Kronig (KK) validation test, by equivalent electrical circuit fitting, coupled with a Montecarlo error propagation method. In a first step, the experimental spectrum is fitted to a particular electrical equivalent circuit, which satisfies the KK relations. Then, in a second step, a statistical Montecarlo method is used in order to propagate the model fitting parameter uncertainty through the model. Using this approach, a consistency region is built for a given confidence level: the experimental points inside this region are considered consistent for the given confidence level, whereas the outside points are rejected. The method was used on PEMFC experimental impedance spectra; and it successfully managed to identify inconsistent points, associated to no stationarities.