An auxiliary power unit for an aircraft includes a rotary intermittent internal combustion engine, a turbine having an inlet in fluid communication with an outlet of the engine, the turbine compounded with the engine, a compressor having an inlet in fluid communication with an environment of the aircraft and an outlet in fluid communication with the aircraft, the compressor rotatable independently of the turbine, an electric motor drivingly engaged to the compressor, and a transfer generator drivingly engaged to the engine, the transfer generator and the electric motor being electrically connected to allow power transfer therebetween. The compressor or an additional compressor may be in fluid communication with the inlet of the engine. A method of operating an auxiliary power unit of an aircraft is also discussed.