  This paper proposes physical-based, reduced-order electrochemical models that
are much faster than the electrochemical 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 a battery cell. In
particular, an innovative 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 the polynomial coefficients. Results show that
the models, named as revised single-particle model (RSPM) and fast-calculating
P2D model (FCP2D), give highly 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 2.5 C), the RSPM is up to more than 33 times faster than the P2D
model. The FCP2D is applicable for high C rates (above 2.5 C) 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.
