State-of-Charge Estimation of LiFePO4 Batteries by Voltage–Expansion Force Fusion

Abstract The flat voltage plateau of LiFePO4 batteries limits the accuracy of voltage-based state-of-charge (SOC) estimation. To address this, a method integrating voltage and expansion force is proposed. Experimental data under different preload forces (1000 N, 2000 N) and dynamic conditions (dynamic stress test, federal urban driving schedule, and urban dynamometer driving schedule) show that the expansion force effectively reflects SOC variations. A voltage observation model and a Gaussian process regression (GPR)-based expansion force model with a squared exponential automatic relevance determination kernel are constructed, where GPR automatically optimizes parameters to relate expansion force to current and SOC across operating conditions. Signal fusion is realized via a series-connected double-layer untraceable Kalman filter (DLUKF), achieving root mean square error ≤ 0.66%, mean absolute error ≤ 0.48%, and maximum error (MAX) ≤ 2%, outperforming single-observation methods. With initial errors of ±20%, open-circuit voltage-based correction accelerates DLUKF convergence while keeping MAX within 2%. SOC estimation can be computed within 5 ms/step, meeting battery management system real-time requirements and demonstrating strong practical potential.