Björn Fridholm

Robustness Comparison of Battery State of Charge Observers for Automotive Applications

This paper compares the robustness of three different battery State of Charge (SoC) estimation algorithms: the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF) and the H-infinity filter. Their performance when subject to disturbances such as parameter uncertainties, different sensor noise characteristics and sensitivity to tuning of the filter are examined. Simulations show that the appropriate choice of observer algorithm will depend on battery chemistry as well as on the intended application. For batteries with a strong correlation between SoC and OCV, the UKF is robust to disturbances such as sensor bias. The H-infinity observer shows performance on par with the UKF but the variability of the estimation errors are larger. The EKF is a good all-round choice.

Theoretical bounds on the accuracy of state and parameter estimation for batteries

Today it is standard to use equivalent circuit models to describe the dynamic behavior of Li-ion vehicle batteries. The parameters and states change with operating point and are therefore continuously estimated using bayesian observers, though without knowing to what degree the performance can be improved. Posterior Cramér-Rao Lower Bounds (CRLBs) can be used to theoretically quantify the optimal accuracy of bayesian estimators. In this paper we apply this to a second-order nonlinear equivalent-circuit model of a lithium-ion battery. It is shown, by numerical calculations, how the posterior Cramér-Rao Lower Bounds depend on the amplitude and frequency of the current, and on the slope of the Open Circuit Voltage (OCV) curve. Furthermore, it is investigated how much the accuracy is reduced in combined estimation of the states and the resistance compared to when the resistance is perfectly known. More importantly, it is also shown that the Mean Square Errors (MSE) of an Extended Kalman Filter (EKF) are close to the posterior CRLBs, which means that, under the investigated circumstances, it is not possible to significantly reduce the MSEs by replacing the EKF by any other observer.