Ned Simmons wrote:



I'll bet the generator outputs 415 Hz if the motor is running at
synchronous speed, which, assuming it's an induction motor, it never
does. In other words, the generator is nominally 415 Hz to account for
the motor's slip.

415 Hz / 400 Hz = 1800 RPM / 1715 RPM

Nope, doesn't quite work out. The alternator has to have an integral
number of poles. To get 415 Hz at 1800 RPM it would need 13.333
poles. 14 poles and 1778.6 RPM (29.64 RPS) gives 415 Hz.
1779 RPM is reasonable for a larger 3-phase induction motor.
If your line voltage were a bit low, the slip would be greater, and
the motor would spin slower, although not by much. To get down to
400 hz the motor would need to spin at 28.57 RPS or 1714 RPM.
I doubt you could get it to slip that much without burning up the
motor rotor.

Jon