An Analytical Modelling Framework for Estimating the Distribution of Relaxation Times in Battery Impedance Using the Randles Model with Blocked-Diffusion Impedance

Abstract The Randles circuit comprising the blocked-diffusion Warburg impedance with frequency dispersion (BDWf) is commonly used to characterise electrochemical processes in the impedance response of battery electrodes. This study develops an analytical formulation of the distribution of relaxation times (DRT) for a Randles circuit incorporating blocked-diffusion impedance with frequency dispersion. Unlike conventional DRT approaches based on ill-posed numerical inversion of the Fredholm integral equation (e.g. Tikhonov regularisation), the proposed formulation provides a closed-form analytical mapping between equivalent circuit parameters and the DRT response. This establishes a direct and physically interpretable relationship between impedance model parameters and distributed time constants. The modelling framework first estimates the parameters of the Randles-BDWf model from measured battery impedance data, and subsequently computes the DRT response using the derived analytical function. The framework enables the deconvolution of time constants associated with charge-transfer kinetics and finite-length diffusion processes in heterogeneous battery electrodes. The proposed approach is applied to impedance measurements from a Li-ion battery at different states of charge and temperatures, demonstrating its ability to capture variations in electrochemical processes. The framework provides a physically consistent alternative to numerical DRT methods, improving interpretability and robustness in the analysis of battery impedance data.