Fractional variable-order calculus based state of charge estimation of Li-ion battery using dual fractional order Kalman filter

Although fractional order based models and approaches have been proposed to determine battery key state characteristics, the inflexible order has a detrimental impact on battery modeling and SOC calculation. In this study, a novel SOC estimation strategy based on the combination of simplified fractional variable-order equivalent circuit model (FVOECM) and FVO adaptive dual Kalman filter (FVOADKF) algorithm is proposed. The simplified FVOECM is designed to represent the battery's dynamic external electrical characteristics. The FVO-based adaptive extended Kalman filter algorithm is utilized for the battery SOC estimation, while the FVO-based adaptive unscented Kalman filter algorithm is used to determine the order of the FVOECM. Consequently, the updated order effectively tracks the transaction of the battery FVOECM thus improving the SOC estimation accuracy. Furthermore, the influences of SOC initialization error and FO backtracking length on the algorithm convergence are analyzed. The effectiveness of the FVOECM is confirmed under two different conditions, and four experiment results indicate that the effectiveness of the FVOADKF is superior to other estimation methods. •Derived a simplified Li-ion battery equivalent circuit model based on fractional order calculus.•Fractional variable order adaptive extended Kalman filter is introduced for the SOC estimation.•Fractional variable order adaptive unscented Kalman filter is designed for the order estimation.•Discussed the influences of SOC initialization error and fractional order backtracking length on estimation convergence.