A Novel Fractional Order Model for State of Charge Estimation in Lithium Ion Batteries

Battery models are the cornerstone to battery state of charge (SOC) estimation and battery management systems in electric vehicles. This paper proposes a novel fractional-order model for a battery, which considers both Butler–Volmer equation and fractional calculus of constant phase element. The structure characteristics of the proposed model are then analyzed, and a novel identification method, which combines least squares and nonlinear optimization algorithm, is proposed. The method is proven to be efficient and accurate. Based on the proposed model, a fractional-order unscented Kalman filter is developed to estimate SOC, while singular value decomposition is applied to tackle the nonlinearity of Butler–Volmer equation and fractional calculus of constant phase element. The systematic comparison between the proposed model and traditional fractional order model is carried out on two LiNiMnCo lithium-ion batteries at different temperatures, ageing levels, and electric vehicle current profiles. The comparison results show that the proposed model has higher estimation accuracy in battery terminal voltage and SOC than the traditional model over wide range of temperature and ageing level under electric vehicle operation conditions. Furthermore, the hardware-in-the-loop test validates that the proposed SOC estimation method is suitable for SOC estimation in electric vehicles.