A Comparative Study of Fractional Order Models on State of Charge Estimation for Lithium Ion Batteries

State of charge (SOC) estimation for lithium ion batteries plays a critical role in battery management systems for electric vehicles. Battery fractional order models (FOMs) which come from frequency-domain modelling have provided a distinct insight into SOC estimation. In this article, we compare five state-of-the-art FOMs in terms of SOC estimation. To this end, firstly, characterisation tests on lithium ion batteries are conducted, and the experimental results are used to identify FOM parameters. Parameter identification results show that increasing the complexity of FOMs cannot always improve accuracy. The model R(RQ)W shows superior identification accuracy than the other four FOMs. Secondly, the SOC estimation based on a fractional order unscented Kalman filter is conducted to compare model accuracy and computational burden under different profiles, memory lengths, ambient temperatures, cells and voltage/current drifts. The evaluation results reveal that the SOC estimation accuracy does not necessarily positively correlate to the complexity of FOMs. Although more complex models can have better robustness against temperature variation, R(RQ), the simplest FOM, can overall provide satisfactory accuracy. Validation results on different cells demonstrate the generalisation ability of FOMs, and R(RQ) outperforms other models. Moreover, R(RQ) shows better robustness against truncation error and can maintain high accuracy even under the occurrence of current or voltage sensor drift.