Battery depletion time prediction based on T-SPM

Abstract
Dynamic changes in power consumption of mobile devices make it difficult for traditional empirical models to provide accurate State of Charge (SOC) predictions under complex load conditions, leading to serious "range anxiety" problems. Establishing a physically driven dynamic battery model is crucial for optimizing battery management systems (BMS). This article develops a thermally coupled single particle model (T-SPM), which uses Padé approximation method to simplify partial differential equation (PDE) of solid-state lithium ion diffusion into an efficient 5-dimensional ordinary differential equation (ODE) system. It integrates a thermoelectric feedback mechanism based on Arrhenius equation, simulation results show that this reduced order model improves computational efficiency by 1000 times while maintaining physical fidelity, Throughout entire battery life cycle, voltage prediction error remains within 5%, providing a reliable mathematical framework for real-time battery status monitoring.