Temperature dependent fractional order selfcorrecting model with hysteresis for LFP batteries

Lithium iron phosphate (LFP) cells are attractive due to their thermal stability, safety, and cycle-life characteristics. However, estimating the state-of-charge (SOC) for LFP cells is challenging because the open-circuit voltage (OCV) curve is relatively flat over a wide middle SOC region. This paper develops and evaluates a fractional-order extension of the enhanced self-correcting (ESC) equivalent-circuit model for LFP cell modelling and SOC estimation. The conventional ESC model represents polarisation using an integer-order (IO) resistor-capacitor branch, which summarises the dynamic voltage response using a finite exponential state. To introduce memory-dependent polarisation dynamics while retaining the ESC structure, the capacitor in the polarisation branch is replaced by a fractional-order element. The resulting fractional-order ESC (FO-ESC) model is evaluated using measured ATL and A123 LFP datasets over eight temperatures. The tuned FO-ESC model produced modest average terminal-voltage RMSE reductions relative to the tuned IO-ESC model. SOC-estimation tests using coulomb counting, OCV lookup, EKF, and SPKF/UKF showed that the FO plant did not destabilise the estimators. The results support FO-ESC as a temperature-dependent refinement of the ESC framework and motivate the development of future FO-aware SOC estimators.