An auxiliary power unit (10) for an aircraft includes a rotary intermittent internal combustion engine (12) drivingly engaged to an engine shaft (16), a turbine section having an inlet in fluid communication with an outlet of the engine(s) (12), the turbine section including at least one turbine (22, 26) compounded with the engine shaft (16), and a compressor (20) having an inlet in fluid communication with an environment of the aircraft and an outlet in fluid communication with a bleed duct (72) for providing bleed air to the aircraft, the compressor (20) having a compressor rotor connected to a compressor shaft (24), the compressor shaft (24) drivingly engaged to the engine shaft (16). The driving engagement between the compressor shaft (24) and the engine shaft (16) is configurable to provide at least two alternate speed ratios between the compressor shaft (24) and the engine shaft (16).