Identification of the non-linear dynamics and state of charge estimation of a LiFePO<inf>4</inf> battery using constrained unscented Kalman filter

State of charge (SOC) estimation of a LiFePO4 battery exhibiting significant hysteresis is considered. The dynamics of the battery is modeled as a linear system in conjunction with a non-linear hysteresis block. The linear part is assumed to be of a second order equivalent circuit model along with an open circuit voltage (OCV) source Voc. The circuit model is descretised and the resulting parameters are modeled as a multivariate random walk with a diagonal noise covariance matrix. These parameters are estimated using a Kalman filter. The linear model is then validated using a hybrid pulse power characterisation (HPPC) current profile. The major loop of the non-linear hysteresis relating Voc and SOC is experimentally determined by charging and discharging the battery with low magnitude currents. Using Chebyshev polynomials, a model is fit for the hysteresis curves. Constrained unscented Kalman filter (CUKF) is used for estimating the minor loops of the hysteresis, and the SOC. The SOC estimation is then validated from a full electrochemical model simulation of the battery using COMSOL software.