Electrical power generation system for an aircraft, including: a gas turbine having a high-pressure shaft and outputting a gas flow to actuate a free turbine, a polyphase permanent magnet generator coupled to the gas turbine and able to output a first alternating voltage for supplying through first conversion means a primary power supply network of the aircraft, the free turbine and the permanent magnet generator being mounted on the same drive shaft concentric with the high-pressure shaft of the gas turbine, a starter mounted on the high-pressure shaft able to ensure the starting of the gas turbine, the starter being a permanent magnet starter/generator able to output a second alternating voltage for supplying a secondary power supply network of the aircraft and auxiliary equipment of the gas turbine and the first conversion means include two first AC/DC converters controlled from a management unit.