SOC estimation of high capacity NMC lithium-ion battery using ensemble Kalman Bucy filter

Abstract

Nickel manganese cobalt oxide (NMC) lithium-ion batteries are widely used in electric vehicles due to their high energy density and long lifespan. Accurate state of charge (SOC) estimation is crucial for improving battery performance and efficiency. This paper models the battery using a 2-RC equivalent circuit and evaluates three SOC estimation methods: particle filter (PF), Ensemble Kalman-Bucy filter (EnKBF), and deterministic ensemble Kalman-Bucy filter (DEnKBF). The results show that DEnKBF achieves a mean absolute error (MAE) of 1.6 × 10⁻³ and a root mean square error (RMSE) of 1.8 × 10⁻³, while EnKBF achieves a slightly lower MAE of 1.5 × 10⁻³ with the same RMSE. In contrast, PF demonstrates higher errors, with a MAE of 4.3 × 10⁻³ and an RMSE of 4.8 × 10⁻³, indicating lower accuracy. Furthermore, the performance of EnKBF and DEnKBF improves at higher temperatures, with DEnKBF achieving a MAE of 6.9 × 10⁻⁴ and an RMSE of 1.2 × 10^–3 at 50 °C, compared to 2.23 × 10⁻³ and 2.41 × 10⁻³, respectively, at − 5 °C. Similarly, EnKBF achieves a MAE of 9.3 × 10⁻⁴ and an RMSE of 1.06 × 10⁻³ at 50 °C, improving from 3.66 × 10⁻³ to 3.86 × 10⁻³ at − 5 °C. Computationally, DEnKBF and EnKBF exhibit efficient performance with execution times of approximately 0.0126 ms and 0.0136 ms per cycle, respectively, compared to the PF method, which requires 0.0482 ms per cycle. This work introduces the novelty of using the ensemble Kalman-Bucy filter (EnKBF) and deterministic ensemble Kalman-Bucy filter (DEnKBF) for SOC estimation, achieving superior accuracy and efficiency over the particle filter (PF). These methods offer a robust and practical solution for real-time battery management in electric vehicles.