A battery charging apparatus includes a bi-directional charger including a first switching circuit connected to an AC terminal, a second switching circuit connected to a battery, and a transformer connected between the first switching circuit and the second switching circuit. The battery charging apparatus also includes a controller configured to switch a leg included in the first switching circuit based on a first carrier wave and a first duty command, configured to switch a leg included in the second switching circuit based on a second carrier wave and a second duty command, configured to adjust a phase of the second carrier wave compared to a phase of the first carrier wave by a phase shift angle according to an active power command, and configured to adjust a phase of the second duty command according to the reactive power command.