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.

What is the Three-Phase Voltage Imbalance Calculator?

Computes NEMA MG1 percent voltage unbalance as the maximum deviation from the average divided by the average, times 100, from three measured line-to-line voltages, and returns the motor derating factor from NEMA MG1 for the calculated unbalance. Runs entirely in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

Three-Phase Voltage Imbalance Calculator

Name: Three-Phase Voltage Imbalance Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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.

Why voltage unbalance is more damaging than it looks

The disproportionate effect on motors comes from the physics of three-phase induction machines. Any unbalanced three-phase voltage can be decomposed into a positive-sequence component (which drives the motor normally) and a negative-sequence component (which opposes the rotation). The negative-sequence current is amplified by the motor’s low negative-sequence impedance — roughly five to seven times lower than its positive-sequence impedance at full load — which is why even a 2 percent voltage unbalance can produce a 10 to 15 percent current unbalance or more.

This elevated current concentrates in one or two stator windings, causing localized heating that ages the winding insulation far faster than the average temperature would suggest. The result is premature motor failure — often appearing as a randomly “weak” phase winding — without any obvious external cause.

Where unbalance typically comes from

On a three-phase system, voltage unbalance usually has one of three origins:

Single-phase loads on the same transformer. A large air conditioning unit or a bank of office equipment on one phase of a shared distribution transformer can pull that phase’s voltage down, creating unbalance for everything else on the feeder.
Loose or corroded connections. A high-resistance connection at a terminal block, disconnect, or motor starter creates a voltage drop on that leg. The resistance often varies with load and temperature, so the unbalance may appear only under load.
Utility supply issues. Occasionally the problem originates at the utility transformer taps, especially on aging rural infrastructure or after recent maintenance work. If unbalance is consistent across multiple feeders, the utility is a likely source.

Measurement tips

Always measure at the motor terminals, not at the distribution panel. The resistance and inductance of the supply conductors means the unbalance seen by the motor can be significantly higher than what is measured upstream. Measure under loaded conditions — at no-load or light load, the motor draws little current and the resistive drops that cause unbalance are suppressed. Use a true-RMS meter and record all three line-to-line voltages (L1-L2, L2-L3, L3-L1) in the same measurement pass.

When to investigate further

A result above 1 percent on this calculator is a reason to investigate the supply, not just to derate and move on. Derating means the motor runs cooler but the underlying cause continues to stress connections, the transformer, and other equipment on the same feeder. Sustained unbalance above 3 percent typically warrants a power-quality survey or utility contact. Above 5 percent, NEMA MG1 advises against operating the motor entirely until the supply is corrected.