I originally had a 3500 watt generator and tried to run the compressor. After about a minute it started to release the factory smoke. I stopped it and inspected the motor. One of the points on the centrifugal switch was completely melted off. I McGivered it as the motor is 35 years old and I couldn't find a replacement part. I dug through my junk box and found an old set of automotive points that had a large contact. Silver soldered it to a piece of brass shim material and then silver soldered that to the metal spring that contacted the centrifugal mechanism. The nylon "rubbing block" was also gone so I found a small piece ofnylon and epoxy'd it to the spring.
This has worked for about a year when I could access shop power. I got a new 9000 watt running 10000+ starting generator and thought it would do the trick for remote operation. I hooked it up and tried it again, closely watching the motor. After about 10 seconds,the factory smoke started to reappear. I quickly killed it. No noticeable damage this time. Tried it again on shop power and it runs OK.
The only thing I can think of on the generator power is that for some reason the motor is not geting up to full speed and the centrifical switch is not disengaging allowing the start capacitor to remain in circuit. This will cook the windings in short order.
The 9000 has more than 3 times the power needed to run this motor which has a RLA of 12 amps.
Since I just use this compressor a couple of times a year for small projects, I think I will just install a 120PSI blow off and let it run. This motor doesn't have a governor so there is no practical way to make it idle down. I'll just manually adjust the speed to keep the pressure close to blow off pressure.