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

Abstract

This 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.

An improved fractional‐order state estimation algorithm based on an unscented particle filter for state of charge estimation of lithium‐ion batteries with adaptive estimations of unknown parameters

“…Still, a considerable number of particles also slow down the computation. The unscented particle filter (UPF) 22 reduces the reliance on the number of particles and enhances the estimation accuracy via PF by replacing the updating of particles in PF with unscented transform (UT) 23 . Compared with the UKF, the UPF uses the mathematical expectation of particles to approximate the real states and proposes the processes of importance sampling and resampling.…”