You need to be running over the synchronous speed of the motor
If you are not grid connected, there is no synchronous speed. The output frequency will be about poles*rpm/285. If you are not trying to hit 60 Hz, then you can push the rpm a bit, and get a bit more power, but this increases voltage as well, so the caps need to be able to stand it, though the caps "look" bigger at higher frequency, so you can back off the uF a little.
If you ARE grid connected you need to run about 0-5% over synchronous speed, or 5-10% over rated motor speed, and you will be generating with or without caps. The higher you are above sync speed, the more power the generator will put out, and the more torque it will demand of the prime mover. The grid will supply the reactive power (VARs) to the generator, and the generator will return watts to the grid. The caps, if present, supply the VARs instead of the grid, and reduce the line current for a given output power.