C210 pilot reported a loss of electrical power while on downwind for landing. Pilot exited the area; contacted ATC via cell phone and coordinated a return to field for a safe landing.

Narrative

While traveling to ZZZ on Day 0 I was cleared to the downwind for the runway. During this phase I began to have trouble with my radio. I entered the downwind.The tower then asked me to do a right 360 for spacing. As I pressed my mike button I lost all electrical power to the aircraft.I immediately turned and headed south away from the airport. While trying to diagnose the problem I tried to reach for my handheld radio. The radio was out of my reach. The next step was to contact the tower by use of the a cell phone. After talking with the tower we came up with a game plan to travel North until perpendicular with the end of the runway. I would then turn and watch for the light gun to show a solid green light (OK to Land). Prior to starting the turn to the north I proceeded to follow the emergency checklist to lower the landing gear. After ensuring all emergency steps were complete traveled north as planned. Reached the turning point and turned towards the runway XX. I was able to see the green light and proceeded to land. Landing was without issues. Got off at the first available taxiway and started to taxi to the ramp. I saw the flashing green light and taxi to a parking spot. After shutting down the engine I was met with the Fire crew and gave them my information. The plane is currently at ZZZ with the mechanic.