Reduced-order electrochemical models with shape functions for fast, accurate prediction of lithium-ion batteries under high C-rates

This paper proposes physical-based, reduced-order electrochemical models that are much faster than the pseudo-2D (P2D) model, while providing high accuracy even under the challenging conditions of high C-rate and strong polarization of lithium ion concentration and potential. In particular, a weak form of equations are developed by using shape functions, which reduces the fully coupled electrochemical and transport equations to ordinary differential equations, and provides self-consistent solutions for the evolution of polynomial coefficients. Results show that the models, named as revised single-particle model (RSPM) and fast-calculating P2D model (FCP2D), give reliable prediction of battery operations, including under dynamic driving profiles. They can calculate battery parameters, such as terminal voltage, over-potential, interfacial current density, lithium-ion concentration distribution, and electrolyte potential distribution with a relative error less than 2%. Applicable for moderately high C-rates (below 2.5C), the RSPM is up to more than 33 times faster than the P2D model. The FCP2D is applicable for high C-rates (above 2.5C) and is about 8 times faster than the P2D model. With their high speed and accuracy, these physics-based models can significantly improve the capability and performance of the battery management system and accelerate battery design optimization.