A novel Dual Fractional-Order Extended Kalman Filter for the improved estimation of battery state of charge

Fractional-order models are gaining increasing relevance in battery modeling in light of the experimental measurements from Electrochemical Impedance Spectroscopy (EIS) tests, unequivocally indicating the presence of equivalent circuit components with an impedance of non-integer order. To attain their discrete state-space representation, the approach based on the Grunwald-Letnikov (GL) definition of the fractional derivative has been widely used, albeit its applicability beyond driving cycles remains open to discussion. In this article, we present a novel Dual Fractional-Order Extended Kalman Filter (DFOEKF) for the simultaneous estimation of State of Charge (SOC) and all fractional parameters, based on the multiple-RC approximation instead. We discuss the parameter identification of fractional-order elements on a NMC811/Si-Gr cell from both frequency and time-domain data, highlighting the importance of EIS measurements for the search of appropriate time domain values. We validate the performance of this method experimentally at different operation stages, as well as its robustness to incorrect initializations, obtaining a SOC root-mean-square (RMS) error of 0.28% and voltage RMS error of 15.2 mV in 20 complete charge-discharge cycles. The greatly accurate estimation results both within and outside the driving cycle stage make this method an interesting alternative for the fractional modeling of LIBs in online applications.