A method and the device are provided for determining state of health of the battery, in addition to the power supply system using the device, to reduce operational and processing load by expanding the data sampled at the time when the battery is caused to discharge square wave pulses into the square wave is provided. The method includes determining state of health of a battery by causing the battery to discharge square wave pulses with a prescribed cycle at a prescribed current value. Response voltages are sampled at a time of a pulse-discharge. The sampled response voltages are sampled into orthogonal square wave components. An amplitude of the square wave component is divided by the current value of the pulse-discharge to obtain a pseudo-impedance. A state of health of the battery based on the pseudo-impedance is determined.