Three-Phase Voltage Unbalance Calculator
Enter the three line-to-line voltages to get percent unbalance, the NEMA derating factor and expected heating.
Step-by-step
- Enter valid values to begin.
Measure line-to-line voltages at the motor terminals under load with a true-RMS meter. The derating curve is read from NEMA MG-1 Figure 14-1 by interpolation (about 0.95 at 2%, 0.88 at 3%, 0.82 at 4% and 0.75 at 5%) and the current-unbalance estimate is a 6 to 10 times rule of thumb.
Voltage Unbalance: Why 3% Can Cook a Motor
Core Engineering Principles
When the three line-to-line voltages aren’t equal, the stator field is no longer a clean rotating circle. Mathematically the unbalanced set splits into a positive-sequence part, which rotates forward and makes torque, and a negative-sequence part, which rotates backwards at twice the line frequency relative to the rotor. The motor has almost no impedance to that backward field, roughly the locked-rotor impedance, so a small voltage unbalance produces a big negative-sequence current. A 3.5% voltage unbalance can produce a 25% current unbalance in the stator, and the extra heat is concentrated in the rotor and one or two windings.
The rule I teach technicians is the NEMA definition, because you can do it with a meter in your hand. Take the three line-to-line voltages, average them, find the one that deviates most from the average, divide by the average. That’s your percent unbalance. The temperature rise goes up approximately with twice the square of that percentage, which is why NEMA says to derate the motor and not to run it at all above 5%.
True factor (IEC): V2 / V1 = √[(1 − √(3 − 6β)) / (1 + √(3 − 6β))], β = (Vab&sup4; + Vbc&sup4; + Vca&sup4;) / (Vab² + Vbc² + Vca²)²
NEC & Standard References
NEMA MG-1 14.36 defines the percent voltage unbalance above and says motors should not be operated above 5%. Figure 14-1 gives the derating curve: roughly 0.95 at 2%, 0.88 at 3%, 0.82 at 4% and 0.75 at 5%. ANSI C84.1 recommends that electric suppliers hold no-load unbalance to 3% or less at the service point. IEC 60034-26 uses the negative-sequence ratio V2/V1, which is what the second number on this page shows. Measure the voltages at the motor terminals under load, not at the transformer, because single-phase loads and a bad connection upstream will show up there.1. Average = (480 + 472 + 456) / 3 = 469.3 V.
2. Largest deviation is the 456 V leg: 469.3 − 456 = 13.3 V.
3. %VUB = 13.3 / 469.3 × 100 = 2.84%.
4. Derating between 0.95 (2%) and 0.88 (3%) is about 0.89, so a 50 HP motor should carry no more than roughly 44.6 HP of load.
5. Heat: 2 × 2.84² = 16.1% extra temperature rise, and current unbalance is probably 6 to 10 times the voltage figure, about 17–28%.
- Rotate the leads and measure again. If the high current stays on the same motor lead after you rotate the connections, the problem is the motor. If it follows the supply leg, the problem is upstream.
- Single-phase loads on three-phase banks are the usual cause: large lighting or welders loaded on one phase.
- A loose connection looks like unbalance. Thermal-scan the lugs and the fuse clips before you blame the utility.
- Open delta and open wye banks naturally have more unbalance than a full bank, so check the bank before the motor.
- Single-phasing is the extreme case. A motor will keep running on two phases and burns up in minutes, so use phase-failure relays on critical motors.