There are Three (3) methods of Powering an AVR (Automatic Voltage Regulation) or AVC (Automatic Voltage Control).
There is the PMG (Permanent Magnet Generator) which others have mentioned and hopefully made it clear that this is an independent AC generator on the same rotating shaft, so its output voltage is proportional to the speed of the Generator rotation. So should be independent of almost anything else.
"With PMG excitation, a permanent magnet generator (PMG) added to the alternator supplies the AVR with voltage which is independent of the main alternator winding. This system provides the machine with a short-circuit current capacity of 3 IN for 10 s."
There is the SHUNT which provides the power for the AVG from the Generators own output voltage, usually from just across one winding in the 100V to 150V range.
"With SHUNT excitation, the AVR is powered by the main winding (100V to 120V - 50/60 Hz) by using X1, X2 on the AVR."
It is presumably this power input that some are worried might cause problems with the working of the AVR. But why? How?
This AC supply is taken into the AVR, voltage dropped by a series Capacitor, then Half wave rectified and then smoothed by storage capacitors and stabilized by a Zener diode or other form of Regulation. So how can generator output voltage noise or problems cause a problem here.
Then there is the third method, that is the AREP (Axillary Winding Power) which is powered by separate windings in the Alternator, one gives voltage proportional to the Generators output voltage but not interfered with by external Loads and the other winding give voltage proportional to the Generators output Current, thus compensating for Alternator voltage drop due to LOAD.
"With AREP excitation, the electronic AVR is powered by two auxiliary windings which are independent of the voltage sensing circuit. The first winding has a voltage proportional to the alternator main voltage (Shunt characteristic), the second one has a voltage proportional to the stator current (compound characteristic: Booster effect). The power supply voltage is rectified and filtered before being used by the AVR monitoring transistor. This system provides the machine with a short-circuit current capacity of 3 IN for 10 s."