And in general you still need to be within same volts/frequency ratio as the nameplate volts/frequency. As Jraef said you could still have over excitation at a lesser load and cause excess heating eventually destroying the insulation of the windings.
My concern would be the heating in the rotor, not stator - in a case of overmagnetizing - ie., supplying HIGHER voltage; I would have to study the effects of large over or under magnetization on rotor currents: I strongly suspect undermag (low voltage like this) would cause LESS rotor heating and over mag would cause more than the design called for. Anyone ever looked at this and can give info?
Since this post is about undervoltage, the issue of heat should all be in the stator windings. Undervoltage means under magnetization (Isd is lower) which means the motor Kt is lower (it produces LESS torque per amp put in, so for the same load, it will simply require more Isq torque producing amps. Lower Isd, higher Isq. Since heat is vector sum of these, it does not matter which is at what level, as long at the vector sum is = or less than the nameplate amps.
a couple times per year I must commission unkown spindle motors knowing only the motor amp and generic (usually fake) base speed voltage rating. I begin, unloaded of course, a typical 460v type motor with about 100v@50hz - it runs fine. I slowly increase voltage watching Isq/Isd . Then we load the motor with simple linear accel/decels and do it again. Pretty easy to find the sweet spot where the motor uses min vector current; but that still does not gaurantee I found the designed /hz rating. But there are a lot of motors running out there making their rated hp cuts all these years without overheating.
In addition, we also sometimes eliminated motor self resonant points by manipulating the v/hz curve on skalar drives by as much as 2x hi or lower than correct at some frequencies.
As previously stated for this undervoltage case (& probably overvoltage within reason - swag guess 2x v/hz curve - but I won't swear to that), if vector sum of both currents (reads = what seen on clamp on ammeter around a leg) is below the nameplate current rating, one will not cause excess heat in the stator windings. Simple math here; can't happen.
