Li-ion based batteries are believed to be the most promising battery system for HEV/PHEV/EV applications due to their high energy density, lack of hysteresis and low self-discharge currents. However, designing a battery, along with its Battery Management System (BMS), that can guarantee safe and reliable operation, is a challenge since aging and other mechanisms involving optimal charge and discharge of the battery are not sufficiently well understood. In a previous article [1], we presented a model that has been studied in [2]–[5] to understand the operation of a Li-ion battery. In this article, we continue our work and present an approximation technique that can be applied to a generic battery model. These approximation method is based on projecting solutions to a Hilbert subspace formed by taking the span of an countably infinite set of basis functions. In this article, we apply this method to the key diffusion equation in the battery model, thus providing a fast approximation for the single particle model (SPM) for both variable and constant diffusion case.

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