Lithium-Ion Battery Modeling and State of Charge Prediction Based on Fractional-Order Calculus

Abstract

Predicting lithium-ion batteries’ state of charge (SOC) is essential to electric vehicle battery management systems. Traditional lithium-ion battery models mainly include equivalent circuit models (ECMs) and electrochemical models (EMs). ECMs are based on integer-order component modeling, which cannot characterize the internal electrochemical reaction mechanism of the battery, resulting in lower SOC prediction accuracy. In contrast, due to their complex structure, EMs are limited in their application. This study takes lithium batteries as the research object and proposes a fractional-order impedance model (FOIM) that characterizes the dynamic properties of the internal behavior of lithium-ion batteries using fractional-order elements. Considering the highly nonlinear characteristics of lithium-ion batteries, this study introduces the theory of fractional-order calculus into the extended Kalman filter (EKF) algorithm, and proposes the fractional-order extended Kalman filter (FEKF) algorithm applied to the prediction of battery charge state. Comparative analysis of simulation and experimental results shows that the accuracy of the FOIM, compared to ECMs, is significantly improved. The FEKF algorithm has good robustness in estimating the SOC, and the SOC prediction accuracy achieved with the algorithm is also improved compared with that obtained using the EKF algorithm of the integer-order model.