An Initial Value Problem for State of Charge Estimation of Lithium‐Ion Batteries with an Adaptive Fractional‐Order Unscented Particle Filter

Abstract

AbstractThis paper proposes an adaptive fractional‐order unscented particle filter (AFOUPF) with the initial value compensation (IVC) to enhance the estimation accuracy of the state of charge (SOC) for lithium‐ion batteries (LIBs). First, to correctly reflect the dynamic properties of LIBs, a fractional‐order system (FOS) with a constant phase component is constructed. Second, to discretize the FOS equation of LIBs, the Grünwald–Letnikov difference, Caputo derivative and Rieman–Liouville difference are employed to establish the corresponding difference equation. Third, a map function is applied to keep the order and SOC of the FOS within an appropriate interval. Further, an approach of IVC is provided for the AFOUPF to increase the accuracy of SOC estimation, taking into account that the accuracy of SOC estimation is impacted if the order of the FOS is relatively small in (0, 1). By utilizing the augmented vector approach, the simultaneous estimations of order, parameters, initial value, and SOC are resolved. Besides, an iterative approach that accommodates the noise covariance matrices is proposed to improve the estimation accuracy. The AFOUPF conducts an unscented transform and resampling on each particle, resulting in a high SOC estimation accuracy in complicated situations. Finally, the availability of AFOUPF is tested by several experiments.