Three-Phase Voltage Unbalance Calculator
Enter the three line-to-line voltage readings to calculate percent voltage unbalance, compare it with a NEMA-style limit, and estimate motor derating. The tool also solves the acceptable range for one selected third voltage while the other two readings stay fixed.
Voltage unbalance0.84%
- Average line voltage
- 479
- Maximum voltage deviation
- 4
- Limit check
- Within the selected 1.00% limit; no NEMA derating is indicated.
- Acceptable range for selected voltage
- 470.74 V to 484.39 V
- Estimated NEMA derating factor
- 100%
- Estimated maximum motor load
- 10.00 hp
Measured line voltages
| Reading | Voltage |
|---|---|
| A-B | 480 |
| B-C | 475 |
| C-A | 482 |
Uses the NEMA percent voltage unbalance method on line-to-line RMS readings.
Derating is interpolated from the NEMA MG 1 curve and is not extrapolated above 5% unbalance.
How to use this calculator
- Measure and enter the A-B, B-C, and C-A RMS line-to-line voltages.
- Set the maximum allowed unbalance, using 1% when you want the common NEMA motor threshold.
- Choose which voltage to treat as the unknown for the acceptable-range solver.
- Enter the motor nameplate power and unit to estimate the derated maximum load.
How voltage unbalance is calculated
This calculator uses the NEMA percent-voltage-unbalance method for three-phase motor checks. It starts with the three RMS line-to-line readings: Vab, Vbc, and Vca. The average line voltage is A = (Vab + Vbc + Vca) / 3. The maximum deviation is the largest absolute difference between one reading and that average: D = max(|Vab - A|, |Vbc - A|, |Vca - A|). Percent voltage unbalance is U = 100 x D / A.
NEMA guidance treats 1% voltage unbalance as the point above which an AC motor should be derated, and 5% as a practical upper boundary for operation. This tool reports whether the entered readings are within the selected limit, above the selected limit with derating indicated, or above the 5% boundary where the load estimate is suppressed.
How the acceptable voltage range is solved
The reverse solver answers a field question: if two line voltages stay where they are, what third reading could still pass the selected limit? Let p and q be the two fixed readings, x the selected unknown reading, s = p + q, and t = limit / 100. The lower bound is max(3p / (1 + t) - s, 3q / (1 + t) - s, (1 - t)s / (2 + t)). The upper bound is min(3p / (1 - t) - s, 3q / (1 - t) - s, (1 + t)s / (2 - t)).
If the lower bound is greater than the upper bound, the two fixed readings are already too far apart for any third voltage to satisfy that limit. Otherwise, every third-voltage value inside the displayed interval keeps the NEMA percent unbalance at or below the selected limit.
Motor derating estimate
The derating factor is a piecewise-linear interpolation of the published NEMA MG 1 curve points: 100% through 1% unbalance, 95% at 2%, 89% at 3%, 82% at 4%, and 75% at 5%. The estimated maximum motor load is rated power x derating factor, shown in the unit you entered.
What this calculator leaves out
The NEMA method is not the IEC negative-sequence voltage ratio. The calculator does not diagnose the cause of unbalance, model current unbalance, evaluate harmonics, or replace the motor manufacturer's instructions. Take the three measurements at approximately the same time, preferably at the motor terminals under representative load.
Worked example
Suppose the measured voltages are 480 V A-B, 475 V B-C, and 482 V C-A. The average is (480 + 475 + 482) / 3 = 479 V. The deviations from average are 1 V, 4 V, and 3 V, so the maximum deviation is 4 V. The unbalance is 100 x 4 / 479 = 0.84%.
With a 1% limit, the readings are within the selected limit and no NEMA derating is indicated. Holding A-B at 480 V and B-C at 475 V, the acceptable C-A range is 470.74 V to 484.39 V. A 10 hp motor keeps a 100% derating factor, so the estimated maximum load remains 10.00 hp.
Common questions
How do you calculate three-phase voltage unbalance?
Average the three line-to-line voltage readings, find the largest absolute deviation from that average, then divide that deviation by the average and multiply by 100. For example, 480 V, 475 V, and 482 V average to 479 V; the largest deviation is 4 V, so unbalance is 0.84%.
What is the difference between voltage unbalance and current unbalance?
Voltage unbalance compares the three supply voltages. Current unbalance compares the phase currents drawn by the load, and it can be several times larger than the voltage unbalance in a motor. This calculator estimates only voltage unbalance and motor derating from that voltage result.
Is 1% voltage unbalance acceptable for a motor?
NEMA MG 1 guidance uses 1% voltage unbalance as the point above which a motor should be derated. At or below 1%, the calculator shows a 100% derating factor. Above 1%, the estimated factor decreases along the NEMA curve.
When must a three-phase motor be derated?
A motor should be derated when the NEMA percent voltage unbalance is above 1%. This calculator interpolates the derating curve through 5% unbalance. Above 5%, it does not extrapolate a load estimate because the condition should be corrected rather than treated as a normal operating point.
Should measurements be line-to-line or line-to-neutral?
Use line-to-line RMS voltages for this NEMA calculation: A-B, B-C, and C-A. Line-to-neutral readings can be useful for troubleshooting, but they are not the three values used in the percent-voltage-unbalance formula here.
How can voltage unbalance be corrected?
Common corrections include redistributing single-phase loads, checking transformer taps, tightening or repairing poor connections, and investigating supply-side voltage problems. The calculator flags the unbalance level, but it does not identify which cause is present.