Parameterization of an Electrochemical Battery Model Using Impedance Spectroscopy in a Wide Range of Frequency

The parameterization of the electrochemical pseudo-two-dimensional (P2D) model plays an important role as it determines the acceptance and application range of subsequent simulation studies. Electrochemical impedance spectroscopy (EIS) is commonly applied to characterize batteries and to obtain the exchange current density and the solid diffusion coefficient of a given electrode material. EIS measurements performed with frequencies ranging from 1 MHz down to 10 mHz typically do not cover clearly isolated solid state diffusion processes of lithium ions in positive or negative electrode materials. To extend the frequency range down to 10 μHz, the distribution function of relaxation times (DRT) is a promising analysis method. It can be applied to time-domain measurements where the battery is excited by a current pulse and relaxed for a certain period. By means of curve-fitting techniques, the pulse-relaxation measurement can be transferred in a function suitable for the DRT analysis, which is the basis for constructing additional low-frequency impedance points.

In this work, the EIS measured in the frequency domain and the simulated EIS derived from the time-domain measurement by the DRT method are combined to cover all electrochemical processes of the battery, especially the lithium-ion diffusion in the electrodes. The electrical equivalent circuit model (ECM) consisting of resistors, ZARC elements and Warburg elements in the frequency domain is applied to fit the EIS curve and identify the P2D model parameters. By investigating the intercalation processes using the distribution function of the differential capacity (DDC) technique, particles with different particle sizes are considered and their corresponding solid diffusion coefficients are identified by the established ECM. The consistency between time- and frequency-domain data is elaborated based on a model of a commercial automotive cell.