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Building a complete cell impedance model and quickly calculating its frequency response are essential for battery design, optimization, and online management. Based on the widely accepted pseudo-two-dimensional (P2D) model, we build a complete full-order partial-dierential-equation (PDE) model for porous-electrode lithium-ion cells that includes a configurable electrical double-layer model at the solid-electrolyte interface (SEI). With the help of a numeric method, cell impedance and frequency responses of the cell’s electrochemical variables at different locations inside the cell are obtained and analyzed. Moreover, in order to achieve the fast calculation of impedance and frequency responses, we derive transfer functions of the internal electrochemical variables, which give a set of exact closed-form equations for cell impedance and internal-variable frequency responses. The Nyquist plot results calculated by the closed-form equations are exactly consistent with the results of numeric simulations using the full-order model, which verifies the accuracy of the transfer functions and the effectiveness of the simplified method.

An Exact Closed-Form Impedance Model for Porous-Electrode Lithium-Ion Cells