Three-Phase Voltage Unbalance Calculator (NEMA)

How it works

NEMA: % unbalance = 100 × (maximum deviation from the average line voltage) ÷ average · IEC: VUF = V₂ ÷ V₁ = √[(1 − √(3 − 6β)) ÷ (1 + √(3 − 6β))], β = (Vab⁴ + Vbc⁴ + Vca⁴) ÷ (Vab² + Vbc² + Vca²)² · extra temperature rise ≈ 2 × (% unbalance)²

Unequal phase voltages create negative-sequence currents that spin against the motor’s rotating field, heating the windings far more than the small voltage difference suggests. NEMA MG-1 defines unbalance as the largest deviation from the average line voltage, recommends derating motors above 1% and advises against operation above 5%; the US Department of Energy notes winding temperature rises by about 2 × (% unbalance)² percent. The IEC definition — negative- to positive-sequence voltage — gives almost the same number and is computed here from the three magnitudes alone.

Worked example

With line voltages of 460, 467 and 450 V the average is 459 V and the largest deviation is 9 V (from 450 V), so the NEMA unbalance is 9 ÷ 459 = 1.96% (IEC: 2.15%). Interpolating the NEMA curve, the motor should be derated to about 0.95 of its rating; the winding temperature rise increases by about 7.7%, and phase currents may be unbalanced 12–20%.

Sources: US DOE — Motor Systems Tip Sheet #7: Eliminate voltage unbalance · NEMA MG 1 — Motors and Generators, 14.36 Effects of unbalanced voltages

Frequently asked questions