dear tc002,
go by this fundamental approach and apply to motor/trf/etc without any fear(as i see you are in Chemical Engineering group):
V (Voltage) = fx (flux) X fr (frequency)
[forget about the constant for the moment]
So,
fx = v/fr
Hence, if fr is decreased with V constant you will see a rise in fx, which leads to
1)higer iron losses and heating,
2)waveform distortions (flat topping) accompanied by generation of harmonics, again leading to higher losses and heating.
3)The decrease in fr itself leads to lower speeds (specific to running equipment), increased slip, increased losses and increased heating;
4)add to it the lowered cooling by the rotor/shaft driven fan.
5)lower speed will result in lowered output in Q and H of pumps, outputs of mills, etc
Gloomy picture, isn't it?
But then if the decrease in fr is accompanied by a decrease in V, to hold fx constant, you have none of these problems, but then torques decrease because they are proportional to V X V.
However, intelligent plant operators, while operating systems in ISLANDED mode, resort to short periods of lower frequency operations since the load imposed on the islanded system generators decreases on lower frequency. You can run longer with limited supply of steam. A good technique, before fuel supplies are restored to normalcy! Some even use it for better coupling of rotor to stator on Syn Motor if rotor current rise is under some influence of a limiter!
Now the effects of increasing the frequency (with / without constant voltage) might be clear to you. But lowering the working flux level is accompanied by poor rotor to stator coupling, tendency to overspeed, inefficient power trf, etc
In order to ensure the system behaves as per the intent of the design, it is necessary that you run the equipment within tolerance limits such as +/- a or b % frequency variation unaccompanied by voltage variations, +/- c or d % Voltage variation unaccompanied by frequency variations, +/- e or f % combined voltage and frequency variation.
a...f can be found by consulting electrical engineering codes/standards.
hope this helps
best regards