Three-Phase Voltage Unbalance

Calculate the NEMA-style magnitude unbalance from three measured line-to-line RMS voltages.

How this calculation works

This magnitude-only calculation expresses voltage unbalance as the largest deviation from the three-reading average, divided by that average. Enter simultaneous steady RMS measurements for the AB, BC and CA line-to-line voltages. The calculator first checks that the three magnitudes can form a voltage phasor triangle, then finds their mean and maximum absolute departure. The percentage reported follows the NEMA-style maximum-deviation definition; it is not the IEC negative-sequence voltage ratio. If unbalance exceeds one percent, the model directs attention to motor-manufacturer operating limits and derating guidance. It does not diagnose a wiring or supply fault, apply motor derating or provide fault protection. Use consistently measured line-to-line values rather than mixing them with line-to-neutral readings.

Inputs and units

Line-to-line voltage AB (V)
Line-to-line voltage BC (V)
Line-to-line voltage CA (V)

Method and formula

Vavg = (VAB + VBC + VCA)/3; unbalance = 100 × max(|Vi − Vavg|)/Vavg.

Worked example

Example inputs

Line-to-line voltage AB: 400 V
Line-to-line voltage BC: 410 V
Line-to-line voltage CA: 390 V

Calculation steps

Average the three line-to-line readings: Vaverage = (400 + 410 + 390)/3 = 400 V.
Find absolute deviations: |400 − 400| = 0 V, |410 − 400| = 10 V and |390 − 400| = 10 V; the maximum is 10 V.
Calculate unbalance: 100 × 10/400 = 2.5%. This exceeds the model's 1% advisory threshold.

Example results

Average line-to-line RMS voltage: 400 V
Maximum deviation from average: 10 V
NEMA-style voltage unbalance: 2.5 %

Example notes

Unbalance exceeds 1%; consult the motor manufacturer for operating limits and derating

Assumptions

Simultaneous steady RMS measurements of all three line-to-line voltages

Limitations

Magnitude-only NEMA definition; not IEC negative-sequence voltage unbalance
No diagnosis, fault protection or automatic motor derating

Sources

U.S. DOE: Energy Management for Motor-Driven Systems: Section 3, p. 3-4: NEMA maximum-deviation voltage unbalance definition