CPG-SPMT: Control-oriented parameter-grouped single particle model with thermal effects for Lithium-Ion batteries

With the shift to low-carbon energy and advances in storage technologies, high-fidelity electrochemical models of lithium-ion batteries are increasingly needed. This paper presents an open-source implementation of the Control-oriented Parameter-Grouped Single Particle Model with Thermal effects (CPG-SPMT), which achieves a balance between model fidelity and computational efficiency. The model employs a parabolic approximation to discretize solid-phase diffusion using two states per electrode and applies parameter grouping to reduce the number of independent parameters without compromising physical interpretability. A thermal sub-model with Arrhenius-type temperature dependence is integrated to account for heat generation and dissipation effects. The model is expressed in explicit state-space form, supporting applications in observer design and predictive control. Comprehensive validation is conducted using A123 18,650 lithium iron phosphate cell data across eight ambient temperatures (-10 ∘C to 50 ∘C) and three driving profiles (DST, US06, FUDS), yielding 24 operating conditions. The model achieves an average root mean square error (RMSE) of 0.033 V, mean absolute error (MAE) of 0.022 V, and R^2 = 0.9683, demonstrating high prediction accuracy. The full codebase, validation scripts, and dataset are publicly released to facilitate further research in battery modeling, parameter identification, and real-time BMS control implementation.