Nonlinear Identifiability Analysis of the Porous Electrode Theory Model of Lithium-Ion Batteries

Porous electrode theory (PET) is widely used to model battery cycling behavior by describing electrochemical kinetics and transport in solid particles and electrolyte, and modeling thermodynamics by fitting an open-circuit potential. The PET model consists of tightly coupled nonlinear partial differential-algebraic equations in which effective kinetic and transport parameters are fit to battery cycling data, and then the model is used to analyze the effects of variations in design parameters or operating conditions such as charging protocols. In a detailed nonlinear identifiability analysis, we show that most of the effective model parameters in porous electrode theory are not practically identifiable from cycling data for a lithium-ion battery. The only identifiable parameter that can be identified from C/10 discharge data is the effective solid diffusion coefficient, indicating that this battery is in the diffusion-limited regime at this discharge rate. A resistance in series correlation was shown for the practically unidentifiable parameters by mapping out the confidence region. Alternative experiments in addition to discharge cycles are required in order to uniquely determine the full set of parameters.