A compound engine assembly for use as an aircraft auxiliary power unit, having an engine core including internal combustion engine(s) in driving engagement with an engine shaft, a generator having a generator shaft directly engaged to the engine shaft such as to be rotatable at a same speed, a compressor having an outlet in communication with the engine core inlet, and a turbine section having aninlet in communication with the engine core outlet and configured to compound power with the engine core. The turbine section may include a first stage turbine having an inlet in communication with the engine core outlet, and a second stage turbine having an inlet in communication with the first stage turbine outlet. A method of providing electrical power to an aircraft is also discussed.