The generator works by a moving a conductor across a magnetic field. With a permanent magnet generator,the magnetic field is always there. Therefore all you have to do is move the conductors. In the asynchronous generator, a sufficiently strong enough magnetic field is NOT present until an electric current is run through the stator windings.
The capacitors referenced are just used as storage. Once the rotor is moving, the capacitors are dicharged into the stator windings. At this point you will have a magnetic field plus moving conductors. The generator will start producing electricity and the control circuits will control the stator winding current to regulate the generator output.
If the capacitors do not have enough energy to start the electricity production, that is when you need the power grid or a small generator to provide the "excitation" to get the big generator to start producing usefull power.
I hope this helps.
Larry C