Battery internal state estimation using a mixed Kalman cubature filter

Batteries are extensively used as small to medium range energy storage devices in smart grids. The estimation of the internal states of the batteries such as state-of-charge (SoC) is critical to provide consistent and efficient energy storage capabilities for the grids. In general, the electrochemical batteries are represented by non-linear mathematical models. Hence, the non-linear filters such as the extended Kalman filter (EKF), cubature Kalman filter (CKF) and particle filters are widely used for the battery state estimation. However, the non-linear filters are complex compared to the linear filters such as the Kalman filter. The non-linear battery model considered in this paper has an inherent linear sub structure. Hence, we propose a mixed Kalman cubature filter to exploit the inherent linearity to achieve better estimation results with a decreased complexity. The proposed filter uses the Kalman filter and the 3rd degree spherical radial cubature rule to calculate the first and second order moments of the linear and non-linear components, respectively, and subsequently, to estimate the SoC of the batteries. The experimental results show that the proposed filter performs better than the EKF and CKF. Further, the computational complexity of the proposed filter is less than the computational complexity of the CKF. Under the chosen conditions, the proposed filter achieves the average mean square error of approximately 1.1% where as the CKF and EKF achieves 1.3% and 1.5%, respectively with the maximum SoC.