A Variational Theorem-Based Uncertain Initialization SOC Estimation Technique in Li-Ion Battery Applications

State of charge (SOC) is extremely critical to the reliability of lithium-ion (Li-ion) battery utilization. In this study, a novel problem in which internal differences occurred in the battery package, causing uncertain SOC initialization of each battery unit, is solved by combining the variational theorem and the extended Kalman filter (EKF) algorithm. First, the importance of the initialized SOC setting of each unit in the battery package is proposed by determining the theoretical relationship between the initialization value and the current estimation result. To deal with such a problem, the backward smoother technique is used to derive the unbiased initialized value expectations depending on the current observations. Then, the uncertain initialized SOC setting can be updated based on the unbiased initialization expectations with the help of the variational initialization technique. Certainly, the updated initialized SOC will track the true initialization value closer to more observations introduced, which results in better estimation performance at the current moment. Therefore, the estimation performance is greatly improved, especially in the beginning moments. The experiment results provide the lab test data, open-access test data from CALCE, and a practical electric vehicle (EV) application as instances to compare the performance of the variational initialization EKF (VIEKF) and other improved EKF algorithms, which demonstrate the effectiveness and superiority of the proposed technique.