Improved State of Charge estimation of a Li-ion cell using a Fractional Order Model with hysteresis

Accurate State of Charge (SoC) estimation is a main function of Battery Management Systems (BMS) to ensure safety and good performance of Electric Vehicles (EVs). Lithium Ferro Phosphate (LFP) is one of the most preferred cell chemistry for EV and Hybrid Electric Vehicles (HEV) applications. The estimation of LFP cells is fraught with difficulties due to the presence of high hysteresis and the flat nature of SoC-OCV characteristics. To enhance the accuracy of the SoC estimate, this paper attempts to model LFP cells using a Fractional Order Model (FOM) and incorporate the dynamic hysteretic nature into the same model. An FOM is able to capture the battery dynamics over the entire frequency range of interest better than the conventional Integer Order Model (IOM). To build the FOM at first, EIS tests are performed at varying SoC levels to obtain the complex impedance function of frequency. Then, an FOM-based Equivalent Circuit Model (ECM) is obtained from the impedance data from the EIS test using Levenberg–Marquardt (LM) Algorithm. The hysteresis effect is captured as a non-linear state dynamic characterised by a decay rate parameter. A novel method for estimating the hysteresis decay rate parameter, independent of ECM, is proposed and implemented using DEKF. The overall model is validated using voltage-current data for standard drive cycles like UDDS and NEDC. The model is compared against those using an FOM with a switched hysteresis model, an Integer Order Model (IOM) with a dynamic hysteresis model, and an IOM with a switched hysteresis model with laboratory test data. The estimation accuracy is observed to be considerably and consistently better for the proposed model, even under different ambient temperatures with a Mean Absolute Error of less than 1.5%. Such improvements will, in turn, lead to improvements in various EV functions such as the estimation of Electric Range, Remaining Useful Life as well as Energy Management.