Nonlinear identifiability analysis of Multiphase Porous Electrode Theory-based battery models: A Lithium Iron Phosphate case study

Porous electrode theory (PET) is widely used to model battery dynamics by describing electrochemical kinetics and transport in solid particles and electrolyte. Standard PET models rely on black-box descriptions of the thermodynamics of active materials, typically obtained by fitting an open-circuit potential which does not allow for a consistent description of phase-separating materials. Multiphase PET (MPET) was recently developed to describe batteries using white-or gray-box descriptions of the thermodynamics with additional parameters that need to be estimated from experimental data. This work analyzes the identifiability of parameters in the MPET model, including the standard kinetics and diffusion parameters, as well as MPET-specific parameters for the free energy of active materials. Based on synthetic discharge data, both linearized and nonlinear identifiability analyses are performed for an MPET model of a commercial Lithium Iron Phosphate/Graphite battery, which identify which model parameters are not identifiable and which are identifiable only with large uncertainty. The identifiable parameters control phase separation, reaction kinetics, and electrolyte transport, but not solid diffusion, consistent with rate limitation by intercalation reactions at low rates and by electrolyte diffusion at high rates. The article also proposes approaches for reducing parameter identifiability issues.