The pilot stated that when attempting the start the engine for an intended flight, the batteries were dead. As a result he asked the fixed base operator (FBO) for an external power cart to provide an external power source for his aircraft, which was a 12 volt system. He completed a waiver, but indicated he did not recall having a conversation with personnel of the FBO about the aircraft voltage requirement. Personnel of the FBO indicated the external power cart they used has a minimum voltage of 28 volts, and they asked the pilot if his aircraft's electrical system was 28 volts, to which he replied yes. A passenger remained outside the airplane, while the pilot was inside the airplane and a ground power unit (GPU) with a minimum of 28 volts was connected to the external power receptacle. The pilot indicated that he told the line service person to turn on power and he noticed that the alternator circuit breaker tripped. An individual from the (FBO) heard a bang and saw smoke coming from the airplane. The passenger who was outside the airplane later told the pilot that the line service person was frozen, but he was able to disconnect the (GPU) from the airplane, and in doing so noted arcing. The pilot reported that he saw smoke at the rear of the airplane, and the passenger who was outside the airplane reported that when he came off the wing an explosion occurred and fire and smoke was coming from the top of the airplane. The pilot exited the airplane and using a fire extinguisher from it, extinguished the fire. Fire department personnel responded however the fire had been extinguished before their arrival. Postaccident inspection of the airframe revealed structural damage above a battery. Following the accident, the (FBO) added a line to their liability release indicating, "Aircraft voltage system is _____________ volts."