Provided is a power supply apparatus including a power storage module, a DC-AC inverter, a bypass circuit, and a controller. The DC-AC inverter converts output of the power storage module into AC power. The bypass circuit directly transmits the AC power. The controller switches between a discharge mode for supplying output of the DC-AC inverter to a load, and a bypass mode for supplying output of the bypass circuit to the load. A threshold for switching between the discharge mode and the bypass mode is set to a range that enables the power storage module to provide output in an overload state.