Hexic Polynomial Approximation for Spherical Diffusion to Accelerate Accurate Lithium-Ion Battery Simulation


 There is a need for proper estimates of various vital internal states of Li-ion batteries in a battery management system like state of charge, state of health, state of power, and available energy for a better lifetime and user experience. These estimates require electrochemical models that are generally coupled partial differential equations (PDEs) which are computationally expensive. This work proposes hexic polynomial-based models to provide better accuracy than the lower order polynomial-based models (parabolic and quartic models) while providing comparable computational efficiency in solving the PDE-based models for solid phase diffusion. While the constant current discharge behavior of a battery can be captured reasonably well using parabolic profile approximation, for a time-varying current (especially having high-frequency components), such lower order approximations lead to significant errors hence a hexic polynomial approximation is proposed. To compare the accuracy of different approximations for battery simulation, a single-particle model with thermal effects and an isothermal pseudo-2D model are simulated in this paper. The voltage response for the time-varying current profile in SPM shows the superiority of the hexic polynomial approximation over other lower-order approximations in providing a balance between computational efficiency and accuracy