An electric vehicle supply equipment receives an external AC power source. The electric vehicle supply equipment includes a relay apparatus and a controller. The relay apparatus has a master relay, an auxiliary relay, and a controllable switch. The master relay is connected to a master power loop. The controllable switch is connected in series to the auxiliary relay to form a series path and connected to an auxiliary power loop. When the controller detects the external AC power source, the controller turns on the auxiliary relay. Afterward, when the controller detects that the external AC power source is in a zero-crossing condition, the controller drives the controllable switch to be turned on. Accordingly, the relays are controlled in coordinated timing, and further the external AC power source is detected, thus implementing the zero-voltage and zero-current turning on of the relay apparatus.