Three-Phase Voltage Unbalance Calculator (NEMA and IEC)
Percentage voltage unbalance of a three-phase supply from the three line voltages, by the NEMA definition and by the IEC negative-sequence definition, with what it means for a motor.
Results
What this tool does
NEMA defines voltage unbalance as the largest deviation of a line voltage from the average, divided by the average. The IEC definition is the ratio of the negative-sequence to the positive-sequence voltage, which also depends on the phase angles and here is worked out exactly from the three magnitudes. The two agree closely for small unbalances. It matters because an induction motor sees the negative-sequence voltage as a braking field, so the current unbalance can be several times the voltage unbalance and the extra heating shortens the winding life. NEMA MG 1 advises derating the motor above 1 % and not running it above 5 %.
Formula
NEMA: %VU = maximum deviation from the average ÷ average × 100 · IEC: u₂ = √((1 − √(3 − 6β)) ÷ (1 + √(3 − 6β))), β = (U₁₂⁴ + U₂₃⁴ + U₃₁⁴) ÷ (U₁₂² + U₂₃² + U₃₁²)²
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a | Line voltage L1–L2 | V |
b | Line voltage L2–L3 | V |
c | Line voltage L3–L1 | V |
NE | Voltage unbalance (NEMA definition) | % |
IE | Negative-sequence unbalance (IEC definition) | % |
AV | Average line voltage | V |
ST | What it means for a motor | — |
Worked example
- Line voltage L1–L2400 V
- Line voltage L2–L3415 V
- Line voltage L3–L1385 V
- Voltage unbalance (NEMA definition)3.75 %
- Negative-sequence unbalance (IEC definition)4.33 %
- Average line voltage400.0 V
- What it means for a motorDerate the motor — between 1 % and 5 %
Limitations
- Electrical installations are governed by national wiring rules. Cable sizing also depends on installation method, grouping, ambient temperature and protection devices, which this calculator does not evaluate.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.