Differential Equation-Based Mathematical Model for Electrochemical Impedance Analysis of Lithium-Ion Batteries

Abstract

Electrochemical impedance spectroscopy (EIS) is a useful diagnostic method to define dynamic electrochemical characteristics of lithium-ion batteries. This work presents a mathematical model which is a differential equation model (that views charge transfer, double-layer capacitance, and ion diffusion as coupled governing equations in both time and frequency domains). This model is numerically solved by implicit Laplace-domain transformation with the finite-difference scheme in a frequency domain of 10 mHz-100 kHz. Numerical validation has shown great consistency with reference impedance properties with root mean square error (RMSE) value of 0.0058 Ω Ohms, a mean absolute error (MAE) of 0.0043 Ω Ohms and coefficient of determination (R²) value of 0.9986 Ω. Sensitivity analysis reveals that the change in impedance caused by changes in charge-transfer resistance and diffusion coefficients is 12.4% and 15.1% , respectively. The suggested mathematical framework will offer computational efficient and numerically stable battery impedance analysis tool that can be used to estimate the state, perform battery diagnostics and design a better battery management system in electric vehicle and energy storage applications.