A 400 V supply at 400, 404 and 394 V
The average is 399.3 V and the furthest reading, 394 V, is 5.333 V below it: 1.336% by the NEMA method. The negative-sequence ratio is 1.454%.
Voltage unbalance 1.336 % Open in the calculator
Voltage unbalance calculator
Work out the voltage unbalance of a three-phase supply from three line-to-line readings, by the NEMA maximum-deviation method and the IEC negative-sequence method.
Voltage unbalance
1.336%
Check the values to see a result.
- Average line-to-line voltage
- 399.3 V
- Largest deviation, CA
- 5.333 V
- IEC negative-sequence unbalance
- 1.454%
- Spread, BC to CA
- 10 V
The headline is the NEMA maximum-deviation method used for motors; the IEC figure is the negative-sequence ratio used in EN 50160.
How it’s calculated
- Vavg = (VAB + VBC + VCA) ÷ 3=(400 + 404 + 394) ÷ 3=399.3 V
- Unbalance = max |V − Vavg| ÷ Vavg × 100=5.333 ÷ 399.3 × 100=1.336%
- IECβ = (VAB4 + VBC4 + VCA4) ÷ (VAB2 + VBC2 + VCA2)2=0.3335
- u2 = √((1 − √(3 − 6β)) ÷ (1 + √(3 − 6β))) × 100=1.454%
NEMA unbalance = 100 × max |V − Vavg| ÷ VavgIEC u2 = √((1 − √(3 − 6β)) ÷ (1 + √(3 − 6β))) × 100
Line voltages of 400 V, 404 V and 394 V are 1.336% unbalanced by the NEMA method and 1.454% by the IEC negative-sequence method.
Tip: Take the three readings at the same moment and the same point, with the same instrument.
How to calculate voltage unbalance
Voltage unbalance measures how far the three line-to-line voltages of a supply differ from each other. The NEMA method takes the largest deviation from the average as a percentage of the average; the IEC method takes the ratio of negative-sequence to positive-sequence voltage. From 400, 404 and 394 V the NEMA figure is 1.336% and the IEC figure 1.454%.
NEMA method (motors)
unbalance = max |V − Vavg| ÷ Vavg × 100
Average the three line-to-line voltages, find the reading furthest from the average, and express that deviation as a percentage. NEMA MG 1 uses this to derate motors.
IEC method (supply quality)
u2 = √((1 − √(3 − 6β)) ÷ (1 + √(3 − 6β))) × 100
With β = (VAB4 + VBC4 + VCA4) ÷ (VAB2 + VBC2 + VCA2)2. This gives the negative-sequence ratio from the three magnitudes alone, as IEC 61000-4-30 describes. It is the figure EN 50160 and network codes set limits on.
The two methods are close for small unbalance but not identical, and limits written for one do not apply to the other. Take the three readings at the same time, at the same point, with the same instrument.
Voltage unbalance examples
A 480 V supply at 460, 467 and 453 V
The average is 460 V and the largest deviation 7 V, so the NEMA unbalance is 1.522%. A motor on this supply runs warmer than on a balanced one, because a small voltage unbalance drives a much larger current unbalance.
Voltage unbalance 1.522 % Open in the calculator
A weak rural supply
Readings of 415, 408 and 396 V give 2.543% by NEMA and 2.724% by IEC. EN 50160 expects the 10-minute negative-sequence value to stay within 2% for 95% of a week on most low-voltage networks, so a reading like this is worth logging over time.
Voltage unbalance 2.543 % Open in the calculator
Voltage unbalance for one line off a 400 V supply
Two lines at 400 V and the third lower by the amount shown, by both methods.
| Third line (V) | NEMA (%) | IEC (%) |
|---|---|---|
| 398 | 0.33 | 0.33 |
| 396 | 0.67 | 0.67 |
| 394 | 1.01 | 1.00 |
| 392 | 1.34 | 1.34 |
| 390 | 1.68 | 1.67 |
| 388 | 2.02 | 2.01 |
| 385 | 2.53 | 2.52 |
| 380 | 3.39 | 3.36 |
| 375 | 4.26 | 4.21 |
| 370 | 5.13 | 5.07 |
| 360 | 6.90 | 6.79 |
Questions about voltage unbalance
What is an acceptable voltage unbalance?
For supply quality, EN 50160 expects the negative-sequence unbalance within 2% for 95% of the 10-minute values in a week on most networks. For motors, NEMA MG 1 advises against operation above 5% and derates motors from 1%.
Why does a small voltage unbalance matter?
An induction motor presents a low impedance to negative-sequence voltage, so a few percent of voltage unbalance can cause several times that in current unbalance. The extra current heats the windings and shortens motor life.
What causes voltage unbalance?
Mostly single-phase loads spread unevenly across the phases, and on weak networks long lines or a faulty tap. Rebalancing single-phase loads is often the cheapest fix.
Limits of this result
- The NEMA and IEC figures are different definitions and are not interchangeable. Compare each with a limit written in the same definition.
- The IEC figure uses RMS magnitudes; IEC 61000-4-30 specifies fundamental-frequency values, which differ slightly on a distorted supply.
- Do not infer current unbalance, motor temperature rise, derating or safe operation from this voltage percentage alone.
- Measurements must be simultaneous, at the same point and on the same RMS basis; instrument and transformer errors are not included.
- No pass/fail threshold is applied because the equipment, operating state and governing requirement are not known.
Measure it continuously
A ZEM measures RMS voltage on each phase continuously, so unbalance can be followed over a week rather than judged from one set of readings.
