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This paper proposes physical-based, reduced-order electrochemical models thatare much faster than the electrochemical pseudo 2D (P2D) model, while providinghigh accuracy even under the challenging conditions of high C-rate and strongpolarization of lithium ion concentration and potential in a battery cell. Inparticular, an innovative weak form of equations are developed by using shapefunctions, which reduces the fully coupled electrochemical and transportequations to ordinary differential equations, and provides self-consistentsolutions for the evolution of the polynomial coefficients. Results show thatthe models, named as revised single-particle model (RSPM) and fast-calculatingP2D model (FCP2D), give highly reliable prediction of battery operations,including under dynamic driving profiles. They can calculate batteryparameters, such as terminal voltage, over-potential, interfacial currentdensity, lithium-ion concentration distribution, and electrolyte potentialdistribution with a relative error less than 2%. Applicable for moderately highC rates (below 2.5 C), the RSPM is up to more than 33 times faster than the P2Dmodel. The FCP2D is applicable for high C rates (above 2.5 C) and is about 8times faster than the P2D model. With their high speed and accuracy, thesephysics-based models can significantly improve the capability and performanceof the battery management system and accelerate battery design optimization.

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