A totally coupled multi time-scale framework containing full parameters online identification and SOC real-time estimation of lithium-ion battery based on a fractional order model

Fractional order model (FOM) is one of the most promising choices for lithium-ion battery simulation and internal states estimation due to its high modeling accuracy. However, online identifying the order and parameters of FOM is extremely tough, which also makes it difficult to be applied in complex and variable operating conditions. To address this issue, this paper proposes a totally coupled multi time-scale framework that contains full parameters online identification of FOM and state-of-charge (SOC) real-time estimation of lithium-ion battery. Firstly, a novel global optimization algorithm named improved particle swarm optimization is designed to update the order of FOM on macro-time scale with low computational burden. On the basis of the determined order, the rest parameters of FOM are further identified by forgetting factor recursive least square algorithm on micro-time scale. With those online identified parameters, adaptive extended Kalman filter is finally adopted to track battery SOC in every instant. The estimation accuracy, adaptability to different operating temperatures and battery aging, and robustness ability against uncertain initialization of the developed method is verified under Federal Urban Driving Schedule tests. The corresponding results demonstrate that the proposed method can realize accurate full parameters online identification of FOM and precise SOC real-time estimation against different temperatures, battery aging states and initialization. Using the developed method, the mean absolute error (MAE) and root mean square error (RMSE) of SOC estimation of the fresh battery under temperature ranging from 0 °C to 50 °C can be limited below 0.9 % and 1.1 %, respectively. Even if the SOC-OCV relationship is not timely updated, those two indexes of the aged battery achieved by the proposed method can still be controlled within 3 % under temperature ranging from 0 °C to 50 °C. Moreover, the comparison with other typical FOM-based estimation methods is also conducted, whose results indicate that the developed method has apparently superior comprehensive performance on estimation accuracy and adaptation.