Fast Simulation of Nonlinear Electrochemical Impedance of Lithium-Ion Batteries
Authors: Teo Linnette , Pathak Manan , Jang Taejin , Murbach Matthew D. , Schwartz D. T. , Subramanian Venkat R. 
Published: February 2020

Electrochemical impedance spectroscopy (EIS) is a widely used technique for monitoring and characterizing lithium-ion batteries. It can be used to obtain significant insights on electrochemical phenomena such as kinetic and mass transport parameters,1 aging effects,2 and the built up of the solid electrolyte interface (SEI).3

Nonlinear electrochemical impedance spectroscopy (NLEIS) is an extension to EIS as it uses a moderately larger amplitude perturbation, such that the battery’s response is in the weakly nonlinear regime. For lithium-ion batteries, higher harmonic responses have been analyzed to study degradation mechanisms such as lithium plating.4
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5 A model-based approach to examining the variation in second and third harmonic responses to changes in parameters such as diffusion coefficient, reaction rate constant, and double layer capacitance demonstrated the ability of using NLEIS as a characterization and identification tool.6 This is further explored by the increased sensitivity of NLEIS, as compared to EIS, to the battery’s state of charge and state of health, particularly changes in charge transfer symmetry for aged batteries.7 It follows that there is a need to develop computationally fast and accurate tools to model both EIS and NLEIS efficiently for analyzing experimental measurements quantitatively through multi-parameter estimation.
A physics-based model to describe the weakly nonlinear response in the frequency domain was introduced as an extension to Doyle’s pseudo two-dimensional (P2D) lithium-ion battery impedance model.8
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9 In a similar manner to previous work done on solving for the linear impedance response,10 we present a hybrid analytical-collocation approach to solve the model for higher harmonics for NLEIS. The spherical diffusion equations for linear and second harmonic responses are solved analytically for solid phase diffusion in the electrode, while the boundary value problem across the electrodes and separator is solved numerically using orthogonal collocation. We compare the accuracy to the numerical solution obtained by solving the original model in COMSOL, and present an executable that takes parameters and frequencies as inputs and returns both the linear and nonlinear impedance responses for a lithium-ion battery.

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