Unbalance Formulas: Voltage and Neutral Current
Three-phase unbalance formulas: percent voltage unbalance, neutral current from unequal phase currents and a table of neutral current, with worked examples.
The formulas
| To find | Formula |
|---|---|
| Average voltage | Vavg = (V1 + V2 + V3) / 3 |
| Voltage unbalance (percent) | max |V − Vavg| / Vavg × 100 |
| Neutral current, resistive loads | IN = √(Ia² + Ib² + Ic² − Ia×Ib − Ib×Ic − Ic×Ia) |
The voltage formula is the NEMA definition, using the line-to-line voltages. The IEC definition uses the negative-sequence component, which needs the phase angles as well. The neutral current formula assumes three currents 120° apart with the same power factor in each phase.
Worked example: voltage unbalance
The line voltages are 400 V, 410 V and 396 V.
- Vavg = (400 + 410 + 396) / 3 = 402 V
- The largest deviation is 8 V (the 410 V line)
- Unbalance = 8 / 402 × 100 = 1.99%
Worked example: neutral current
The phase currents are 100 A, 80 A and 60 A.
- IN = √(100² + 80² + 60² − 100×80 − 80×60 − 60×100) = √1,200 = 34.64 A
Neutral current with phases A and C at 100 A
| Phase B current | Neutral current |
|---|---|
| 100 A | 0 A |
| 80 A | 20 A |
| 60 A | 40 A |
| 40 A | 60 A |
| 20 A | 80 A |
| 0 A | 100 A |
Frequently asked questions
Why does unbalance matter for motors?
A small voltage unbalance causes a much larger current unbalance in an induction motor. The extra current heats the windings, so the motor is derated as unbalance rises.
What causes voltage unbalance?
Unequal single-phase loads, a blown fuse on a capacitor bank, uneven transformer taps and loose connections.
Why is the neutral current zero for equal loads?
The three currents are equal in size and 120° apart, so their sum is zero.
Does the neutral formula include harmonics?
No. Third harmonic currents add in the neutral on top of this. See the harmonics page.
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