A method for generating electrical power may include the steps of rotating a rotor of a generator at a speed in excess of about 12,000 revolutions per minute (rpm) to about 25,000 rpm and producing power with the generator at a rate in excess of about 800 kilowatts (kW). The generator has a power/weight ratio no smaller than about 3 kW/lbs. A rotor is cooled with cooling oil internally circulated through the rotor of the generator so that contact of cooling oil with external surfaces of the rotor may be precluded. The stator is also cooled with oil that is prevented from contacting the external surfaces of the rotor. Pressurized airflow may be produced in a gap between the rotor and a stator of the generator to preclude entry of cooling oil into the gap.