NEMA defines % unbalance this way. Average all three values. Calculate the three differences between the original values and the average and throw away the signs. Then multiply by 100 and divide by the average. IEC does it differently and it requires a bunch of engineering math (ratio of the negative sequence to positive sequence). IEC is more accurate but hard to use,
If you have say two high currents and a low one, that missing current creates a negative torque, creating heat rather than output power. If one current is higher the effect is similar...the extra current just contributes to motor heating. Whether the current unbalance is caused externally (voltage unbalance) or internally (weak connections or turn to turn faults) does not matter...the effect is the same.
If you are looking at currents it’s almost linear so if you have say 10% current imbalance, derate the motor 10%. But if you have only voltages a 1% voltage unbalance will cause a 6-8% current unbalance, and NEMA derates accordingly.
So it’s OK if all voltages or all currents are a little high or a little low but if they are even a little bit different phase to phase that’s a huge issue.
This is where electricians are generally taught that anything “close” like say 440 to 500 V is “close enough” or that 1 or 2 A won’t make much of a difference. If all three values are the same, it doesn’t. But small differences have a huge impact.
Also if you are operating the motor at low loads a bad (or missing) capacitor won’t make much difference. Under load though the voltage unbalance will be much more obvious, especially at stall. At low loads the motor flux is most of what you see which is almost purely inductive (all VARs) and low load do voltage drop is small. At name plate current flux will be only 10-15% of the total (the rest is torque...resistive) and voltage unbalance will be much more obvious since most of that 10-15% flux current should be cancelled by the capacitors.
In my area in Dominion and Duke West areas power factor is a big deal and capacitors frequently get ignored and subsequently cause trouble. In Duke East there is almost no value so they aren’t typically used.
