Integration of Non-monotonic Cell Swelling Characteristic for State-of-Charge Estimation

Traditionally, battery State of Charge (SOC) is estimated using measurements of current, temperature, and Terminal Voltage (TV). For some battery chemistry, such as Lithium Iron Phosphate (LFP), the voltage is flat (low slope) making the rate of convergence of the SOC estimation relatively slow. In this case, measurement of the cell expansion caused by swelling of the electrode active material during charging can be used to augment the estimation scheme. In previous work [1] [2], the force (F) generated by cell swelling in a constrained package has an affine dependency on SOC. In this paper we consider the LFP chemistry with phase transition of the active electrode material resulting in non-unique F-SOC relation, hence requiring a novel estimator. The non-monotonic (F) could potentially drive any output based observer, like the Linear Quadratic Estimator (LQE), to an incorrect equilibrium. To address this problem, a piecewise-linear (PWL) model is used to approximate the F-SOC curve, which enables the automatic selection of the gain with the correct (positive or negative) slope. The comparison between the TV, F, and the fusion of both sensors is investigated via simulations of a nonlinear higher order model of the battery eletro-mechanical behavior. The electrical battery model is described by an equivalent circuit model and a nonlinear open circuit plus hysteresis model. The performance of the estimators based on the TV and F sensors are compared and evaluated against the ±5% absolute error of the SOC using the Dynamic Stress Test (DST) protocol.