Current Profile Optimization for Combined State of Charge and State of Health Estimation of Lithium Ion Battery Based on Cramer–Rao Bound Analysis

Online State of Charge (SoC) and State of Health (SoH) estimations are essential for efficient, safe, and reliable operation of Lithium ion batteries. Based on the first-order equivalent-circuit model (ECM), a multi-scale extended Kalman filter is adopted in this paper to estimate ECM parameters and battery SoC using dual time scales. The nature of the battery excitations significantly influences the estimation performance. When the input-output data, i.e., the input current and output voltage, is insufficiently rich in frequency content, the estimation performance is poor. Thus, the excitation current should be optimized for the accurate estimation of parameters and states. A Cramer-Rao bound analysis is conducted considering voltage noise, current amplitude, and current frequency, which shows the loss of accuracy in multi-parameter estimation (estimating all states and parameters) when compared to single-parameter estimation (estimating only one parameter/state). However, it also shows that the loss of accuracy can be significantly reduced when the excitation current is carefully chosen to satisfy certain criteria. Both simulation and experimental results verify the analysis results and show that a current profile with optimal frequency components achieves the best estimation performance, thereby, providing guidelines for designing battery current profiles for improved SoC and SoH estimation performance.