Accurate estimation on a single cell of LiFePO₄ battery state of charge (SOC) is the main objective of this paper. The battery SOC is described based on the Thevenin equivalent circuit model along with other algebraic equations. The battery SOC is modeled as a three-mode switched system. In mode-0, the battery is discharging; in mode-1, the battery is being charged; in mode-2, the load current is about zero and the recovery effect takes place inside the battery. The concept of state of available charge and state of trapped charge are also provided to physically mimic the battery recovery effect. In contrast to more complicated model such as electrochemical reaction model, the dynamical equations in this study are rather simple but captures important phenomenon inside the LiFePO₄ battery. The parameters for relationships in this battery model are also computed and provided. The obtained switched system can be solved by various switched optimization tool or hybrid optimization algorithms to arrive at superior battery management strategy.