Dynamic Electrochemical Impedance Spectroscopy of Lithium-ion Batteries: Revealing Underlying Physics through Efficient Joint Time-Frequency Modeling

The value and interpretation of dynamic electrochemical impedance spectroscopy (DEIS) during the charging and discharging of lithium-ion batteries is examined using the Doyle-Fuller-Newman pseudo-two-dimensional (P2D) lithium-ion battery model with parameters for a lithium-cobalt-oxide/graphite cell. Two computational approaches are explored to balance accuracy, speed, and interpretability: (i) A brute force time domain calculation of the full nonlinear equation set subject to direct current (DC) plus superimposed sinusoidal modulation of frequency ω ₁, followed by post-processing with short-time Fourier transforms to track the dynamic impedance signal at the modulation frequency during charge and discharge; (ii) A fast-computing time-separated method that solves the C-rate dependent P2D equations for the DC charge/discharge transients occurring on the slow time-scales, t _b ∼ O(3600 s/C), followed by solutions to linearized frequency domain equations derived for direct computation of the dynamic impedance signal. The time-separated method is rigorously correct in the limit 1/(t _b ω ₁) → 0. Key physics that drives differences between stationary and dynamic EIS signals is easily explored with the time-separated method. C-rate dependent studies show that DEIS signals are selectively sensitive to interfacial processes in ways that may be promising for real-time diagnostics and control of the negative electrode at high states-of-charge (SOC) and the positive electrode at low SOCs.