Three-phase voltage unbalance equation
The calculator averages three like-for-like voltage readings and expresses the largest deviation from that average as a percentage.
Vavg = (V1 + V2 + V3) / 3Va% = (Vmax - Vmin) / Vavg × 100Vu% = max(|Vn - Vavg|) / Vavg × 100Uhigh = Un(1 + khigh), Ulow = Un(1 - klow)where:
- V1, V2, V3
- Three line-to-line or three line-to-neutral readings[V]
- Vavg
- Arithmetic average of the three readings[V]
- Va%
- Voltage spread divided by average, used for the FCP18-style asymmetry result[%]
- Vu%
- Maximum-deviation voltage unbalance shown as a secondary metric[%]
- Un
- Nominal monitored voltage[V]
- khigh, klow
- Overvoltage and undervoltage settings as decimals
Use the same measurement basis for all three readings. Equipment limits, relay delays, wiring system, and manufacturer instructions determine the final protection setting.
How to calculate voltage unbalance
Enter three line-to-line readings for a three-wire system or three line-to-neutral readings for a four-wire system. The calculator finds their average, the largest absolute deviation, and the deviation percentage.
- Use the same measurement basis for all phases.
- Record stable RMS readings.
- Calculate average voltage.
- Find maximum deviation.
- Compare with equipment and relay limits.
Voltage asymmetry example
Readings of 400 V, 392 V, and 408 V average 400 V. The FCP18-style range-to-average asymmetry is 4%, while the secondary maximum-deviation method gives 2%. The page labels both results so they are not treated as interchangeable.
Va = (408 - 392) / 400 × 100 = 4%
Vu = 8 / 400 × 100 = 2%
Why small voltage differences matter
Three-phase motors can develop a much larger current imbalance than the measured voltage imbalance, increasing negative-sequence heating, vibration, torque pulsation, and insulation stress. Use the motor manufacturer's limit rather than assuming one percentage suits every load.
Choosing an FCP18 function
Choose FCP18-01 for phase loss and sequence, FCP18-02 for a voltage window, FCP18-03 for comprehensive monitoring with adjustable delay, FCP18-04 for adjustable asymmetry, FCP18-05 for imbalance-focused protection, or FCP18-06 for fixed OEM settings. Verify voltage and wiring variants before ordering.
Assumptions
- The three entered values use the same measurement basis
- The percentage is a maximum-deviation-from-average calculation
- FCP18 selection follows the function comparison described in the VIOX product guide
Important Warnings
- Do not mix line-to-line and line-to-neutral readings in one calculation.
- Acceptable voltage unbalance depends on the motor or equipment manufacturer; even modest voltage unbalance can produce much larger current unbalance.