What is the NEMA voltage unbalance formula?

Percent voltage unbalance equals the maximum deviation of any line voltage from the average line voltage, divided by the average line voltage, multiplied by 100. The average is the mean of the three line-to-line readings.

How much unbalance is acceptable?

NEMA MG1 recommends operating motors at no more than 1 percent voltage unbalance. Above 1 percent the motor must be derated, and operation above 5 percent is not recommended because the heating becomes severe and damaging.

Why does small voltage unbalance cause large current unbalance?

A small voltage unbalance produces a negative-sequence voltage that drives a large negative-sequence current because motor negative-sequence impedance is low. The current unbalance is roughly 6 to 10 times the voltage unbalance, which causes localized overheating.

What derating does NEMA require?

NEMA MG1 gives a derating curve: about 1.0 at 1 percent unbalance, 0.95 at 2 percent, 0.88 at 3 percent, 0.82 at 4 percent, and 0.75 at 5 percent. The motor must run below its nameplate horsepower by this factor to avoid overheating.

Could my readings indicate a real problem?

Yes. Persistent unbalance above 2 to 3 percent often signals a loose connection, an unbalanced single-phase load on the same transformer, a failing utility tap, or a weak phase. Investigate the supply before the motor fails from overheating.

Three-Phase Voltage Imbalance Calculator

A few volts of difference between phases can shorten a three-phase motor’s life dramatically, because voltage unbalance drives a much larger current unbalance and localized heating. This calculator applies the standard NEMA MG1 method to three measured line-to-line voltages and tells you both the percent unbalance and the derating factor you must apply.

How it works

The NEMA MG1 definition is based on the average of the three line voltages and the single largest deviation from that average:

average      = (V1 + V2 + V3) / 3
max deviation= max( |V1 − avg|, |V2 − avg|, |V3 − avg| )
% unbalance  = (max deviation / average) × 100

The percent unbalance is then mapped to the NEMA derating curve. Because the motor’s negative-sequence impedance is low, a 3 percent voltage unbalance can cause roughly a 20 to 30 percent current unbalance, which is why even small numbers matter.

Example and notes

For readings of 460, 467, and 450 volts, the average is 459 volts. The largest deviation is 9 volts (459 minus 450), giving 9 / 459 × 100 = about 1.96 percent unbalance, which requires a derating factor near 0.95. That means a 10 horsepower motor should be loaded to no more than about 9.5 horsepower. Sustained unbalance above 1 percent is worth investigating: check terminal connections, look for an unbalanced single-phase load sharing the transformer, and verify the utility supply.