The EEC's permanent magnet "dedicated alternator" is mechanically driven (via a gearbox) by the spinning "N3 rotor" of the aircraft's engine: The Rolls Royce Trent on the Boeing 777 has 3 rotors (N1, N2 and N3).
For beginners: A rotor is basically a shaft (solid or hollow) with "stages" of blades at intervals along it. The only rotor you can really see is the big N1 compressor "fan" at the front of the engine. If you looked in the back of the engine, you would see the N1 "turbine" blades. The N2 and N3 rotors are nestled inside the engine (between the N1 compressor and turbine blades).
If the engine is turning, either by normal means.. or by windmilling (at flight speeds), the N3 will be turning.