A physics-based electrochemical model for lithium-ion battery state-of-charge estimation solved by an optimised projection-based method and moving-window filtering

State-of-charge (SOC) is one of the most critical parameters in battery management systems (BMSs). SOC is defined as the percentage of the remaining charge inside a battery to the full charge, and thus ranges from 0% to 100%. This percentage value provides important information to manufacturers about the performance of the battery and can help end-users identify when the battery must be recharged. Inaccurate estimation of the battery SOC may cause over-charge or over-discharge events with significant implications for system safety and reliability. Therefore, it is crucial to develop methods for improving the estimation accuracy of battery SOC. This paper presents an electrochemical model for lithium-ion battery SOC estimation involving the battery's internal physical and chemical properties such as lithium concentrations. To solve the computationally complex solid-phase diffusion partial differential equations (PDEs) in the model, an efficient method based on projection with optimized basis functions is presented. Then, a novel moving-window filtering (MWF) algorithm is developed to improve the convergence rate of the state filters. The results show that the developed electrochemical model generates 20 times fewer equations compared with finite difference-based methods without losing accuracy. In addition, the proposed projection-based solution method is three times more efficient than the conventional state filtering methods such as Kalman filter.