Revealing inhomogeneities in electrode lithiation using a real-time discrete electro-chemical model

Transmission line-or mixed conducting network models are a widely used model category for the characterization of porous electrodes in the frequency domain. Their benefits in time domain modeling and simulation are strongly underestimated as the transfer function of the model's impedance cannot be transformed into the time domain analytically. Instead, spatial discretization is required, which leads to a differential-algebraic equation system. This allows for a spatial resolution of the porous electrode and for the investigation of local phenomena. Therefore, the introduced model is considered a discrete electrochemical model. In this study, we efficiently solve the differential-algebraic equation system using a linear-implicit method. The time-domain model of a graphitic anode is parametrized based on frequency domain impedance measurement data. The validity of the parameter transformation is shown in low- and high-dynamic test profiles, for a wide range of the degree of lithiation of the negative electrode. Finally, the parametrized model is used for the prediction of lithium deposition during charging at various C-rates. The comparison with a standard-equivalent circuit model reveals that the discrete electrochemical model is capable of detecting local Li plating due to the spatial resolution and is significantly more sensitive. Hence, real-time capable transmission line models are applicable for sophisticated fast charging controls.