As I understand things, if you connect an induction motor to the grid it will run at its nameplate speed. Any torque you apply to it will produce current. Right? You then want to size your runner's peak efficiency to this speed.
Close.
The field-rotation speed is the line Hz, time 60 (to get to RPMinute from RPSecond), divided by half the number of poles. I.e.:
60 Hz, 2 poles = 3600 RPM.
60 Hz, 4 poles = 1800 RPM
50 Hz, 2 poles = 3000 RPM
50 Hz, 4 poles = 1500 RPM
and so on.
If the rotor were frictionless, not under load, and running in a vacuum, it would quickly end up being dragged around at the field rotation rate.
Now assuming it's spinning: If you put a load on it, it starts to "slip" with respect to the field rotation rate. This causes the field to move (slowly) through the rotor, which induces currents in the "squirrelcage" conductors, which induce a magnetic field in the rotor. This magnetic field is a bit behind the rotating field and attracts it, causing the field to pull the rotor along harder. The more the load, the more the slippage, the stronger the eddy currents, the stronger the induced field, and the harder the fields on the rotor and the stator pull against each other.
Energy from the line provides power to overcome the resistive losses in the squirrel cage and to tug the load along, in good old conservation-of-energy fashion: Voltages induced in the stator windings by the lagging magnetized rotor cause the current from the line through the stator coils to increase, pulling power from the line.
The nameplate RPM is the field rotation RPM for the rated frequency minus the slippage under the rated load. That's why you see numbers like "3550 RPM" rather than "3600 RPM".
Now if, instead of dragging the rotor slower, you push it faster, it similarly slips as it speeds up beyond the field RPM. Again the rotor's field, and the resulting drag against the rotating field from the stator, increases with additional torque and excess RPM. But this time the drag is pulling energy from whatever is providing the push and putting it into the line. The field induced in the stator by the rotor's field pushes current back INTO the power lines, for a net gain (once the current you're pushing exceeds the in-phase current pulled by the stator windings to make up the resisitve losses of the current magnetizing the stator). Meanwhile, there's some additional drag from generating the squirrel-cage currents. Thus energy is again conserved.
This time the rotor RPM is HIGHER than the field rotation RPM by the amount of the slippage - and higher than the nameplate RPM by TWICE the slippage (once you're pushing hard enough that you're getting as much slippage in the generator mode as you'd have in the motor mode at rated load).
So if your nameplate RPM is, say, 1775 RPM your field rotation will be 1800 RPM and you'll want your turbine trying to push it at something like 1825 RPM with up to a bit more torque than the motor would have provided at full load.