A method for cooling a synchronous electrical machine comprising a machine housing including a stator and a rotor lodged in the stator, the rotor being separated from the stator by an airgap, the stator comprises stacks of laminations and at least one channel extending along a longitudinal direction of the stator and formed in the laminations, two adjacent stacks of laminations being separated by pins or spacers to form an extraction duct connected to the channel, the machine housing further comprising an extraction opening, the method comprising:
- injecting a fluid in the airgap at the ends of the stator so that the fluid flows in the extraction duct and in the channel and is extracted from the machine through the opening to cool the stator, and
- transferring the thermal losses conducted by the machine housing to another fluid.