A controller of a vehicle may be programmed to charge and discharge a battery according to a state of charge derived from model parameters defining one of a series of RC circuits that characterize frequency response of the battery to input current and that each has a time constant proportional to another of the time constants, and a proportionality parameter indicative of proportional relationship between the time constants. The proportionality parameter may be such that a ratio of the resistances of the RC circuits is equal to a ratio of the capacitances of the RC circuits.