State of charge estimation of Lithium-ion battery using an improved fractional-order extended Kalman filter

Accurate estimation of Lithium-ion battery's (LiB) state of charge (SOC) in the battery management system (BMS) is very critical to the performance of battery electric vehicles (BEV) because it indicate how much charge is remaining in the battery. However, due to the nonlinear properties of the LiB and the uncertainty of battery models, estimating the SOC of battery online during vehicle operation is often a major challenge. This paper proposes a model-based estimation method named an improved fractional-order extended Kalman filter (IFO-EKF) to overcome the shortcomings of the electrical equivalent circuit model (EECM) in a regular LiB integer-order model. Firstly, a simplified first-order fractional-order model (FOM) which combines the advantages of both the EECM and the electrochemical impedance spectroscopy (EIS) was developed to accurately interpret battery electrochemical processes using electrical circuit made up of resistors and constant phase element (CPE) having fractional-order characteristics. Secondly, the unknown parameters of the FOM model are identified off-line using quantum particle swarm optimization (QPSO) algorithm. In addition, due to the non-linear dynamic characteristics of LiB, Kalman filter family algorithms used in battery state estimation faces some shortcomings which results in filter divergence caused by the implementation of inappropriate co-variance matrix in the algorithm which leads to inaccuracies and estimation error in the model. The convergence rate of the proposed IFO-EKF algorithm in this study was improved by introducing a Grunwald- Letnikov (G-L) fractional derivative and a time-varying measurement error covariance (R) into the proposed estimation algorithm. Finally, to verify the validity of the proposed model, the HWFET, UDDS and NEDC vehicle dynamics condition tests were used to compare the estimation results of the IFO-EKF against the integer-order extended Kalman filter (IO-EKF) algorithm. The simulation results of the IFO-EKF algorithm proved that it is a better estimation algorithm than the IO-EKF in terms of accuracy.

Automated summary

This paper proposes an improved fractional-order extended Kalman filter (IFO-EKF) algorithm to accurately estimate the state of charge (SOC) of the battery. A simplified fractional-order model combining the advantages of the electrical equivalent circuit model and the electrochemical impedance spectroscopy is developed. The unknown parameters of the model are identified using a quantum particle swarm optimization algorithm. The convergence rate of the proposed algorithm is improved by introducing a fractional derivative and a time-varying measurement error covariance.