Electric Motor Handbook

The inherent attributes of induction machines make them very attractive for drive applications. They are rugged, economical to build and have no sliding contacts to wear. The difficulty with using induction machines in servomechanisms and variable speed drives is that they are "hard to control," since their torque-speed relationship is complex and nonlinear. However, with modern power electronics to serve as frequency changers and digital electronics to do the required arithmetic, induction machines are seeing increased use in drive applications.
Induction machines generally tend to operate at relatively low per unit slip, so one very effective way of building an adjustable speed drive is to supply an induction motor with adjustable stator frequency. And this is, indeed, possible. One thing to remember is that flux is inversely proportional to frequency, so that to maintain constant flux, one must make stator voltage proportional to frequency (hence the name "constant volts/Hz"). However, voltage supplies are always limited, so that at some frequencies it is necessary to switch to constant voltage control. The analogy to dc machines is fairly direct here: below some "base" speed, the machine is controlled in constant flux ("volts/ Hz") mode, while above the base speed, flux is inversely proportional to speed. It is easy to see that the maximum torque is then inversely proportional to the square of flux, or therefore to the square of frequency.
To get a first-order picture of how an induction machine works...