For a standard squirrel-cage induction machine, most people are used to thinking of it as a motor, so let's start there.
At speeds near synchronous speed, the relationship between torque and slip is very nearly linear. Let's take a common 4-pole motor for 60Hz operation listed at 1740rpm at rated torque. 1740rpm is 29rps, or 58Hz on a 4-pole motor. The slip is 2Hz at this rated torque. If the load torque were increased to 150% of rated, the motor would decelerate, increasing the slip and therefore the generated torque, until the slip hit 3Hz at 1710rpm and the motor generated 150% of rated torque, balancing the load torque. Similarly, if the load torque were reduced to half of rated, the motor would accelerate, decreasing the slip until it reached 1 Hz at a speed of 1770 rpm, generating only 50% of rated torque to balance the load.
This relationship continues on the other "side" of synchronous speed. If the machine is mechanically driven with a torque equivalent to the rated torque, it will have a -2Hz slip frequency, so the electrical frequency on the rotor will be 62Hz and the mechanical speed will be 1860rpm. Driven mechanically at 150% of rated torque, it will get to -3Hz slip and 1890rpm. Or at 50% of rated, the slip will be -1Hz, and 1830rpm.
In all of these cases, it will be taking power from the grid (for the motoring cases below synchronous speed) or putting power into the grid (for the generating cases above synchronous speed) at 60Hz. All of this assumes that the grid is "big" (to use the technical term) compared to the machine, so the action of the machine has minimal effect on the frequency of the grid.
Curt Wilson
Delta Tau Data Systems