Electrochemical impedance spectroscopy beyond linearity and stationarity—A critical review

Electrochemical impedance spectroscopy (EIS) is a widely used experimental technique for characterising materials and electrode reactions by observing their frequency-dependent impedance. Classical EIS measurementsrequire the electrochemical process to behave as a linear time-invariant system. However, electrochemicalprocesses do not naturally satisfy this assumption: the relation between voltage and current is inherently nonlinear and evolves over time. Examples include the corrosion of metal substrates and the cycling of Li-ion batteries. As such, classical EIS only offers models linearised at specific operating points. During the last decade, solutions were developed for estimating nonlinear and time-varying impedances, contributing to more general models. In this paper, we review the concept of impedance beyond linearity and stationarity, and detail different methods to estimate this from measured current and voltage data, with emphasis on frequency domain approaches using multisine excitation. In addition to a mathematical discussion, we measure and provide examples demonstrating impedance estimation for a Li-ion battery, beyond linearity and stationarity, both while resting and while charging.