Stability Analysis of EKF-Based SOC Observer for Lithium-Ion Battery

The state of charge (SOC) plays a critical role in battery management systems. This paper discusses the stability of the nonlinear SOC observer based on the extended Kalman filter. The model characterizing the lithium-ion battery nonlinearity is the basis of the stability analysis. After balancing the accuracy and the complexity of the models, the Thevenin battery model and the logarithmic fitting OCV (open circuit voltage) model are employed. The stability of the SOC observer is theoretically analyzed from two aspects: model parameters and system nonlinearity. Furthermore, the impact of system noises and nonlinear characteristics on the estimation is explored in a numerical way. For the estimation of SOC, the nonlinearity is mainly reflected in the OCV-SOC function. It is found out that the gradient variation of the OCV-SOC curve is not conducive to the estimation, especially when the gradient is small and the voltage noise is large. In order to improve the estimation performance, the role of matrices Q and R as the design parameters of the SOC observer is discussed. The results indicate that the observer is able to exhibit good stability and performance under appropriate settings.