3.2 Power Factor, Voltage Unbalance & Negative Sequence
Key Takeaways
- Power factor PF = kW / kVA = cos θ, where θ is the angle between the fundamental voltage and current; PF is leading for capacitive loads and lagging for inductive loads.
- NEMA MG-1 voltage unbalance % = 100 × (max deviation from average voltage / average voltage); at 5% unbalance motors must be derated to about 75% load and operation above 5% is not recommended.
- Voltage unbalance produces negative-sequence currents in motor rotors that rotate opposite to the rotor, inducing double-frequency (2f) eddy-current heating.
- Rule of thumb: roughly 1% voltage unbalance produces about 2% temperature rise in an induction motor; current unbalance is typically 6-10× the voltage unbalance.
- Utilities and NETA field tests track PF (billing, conductor sizing, losses) and voltage unbalance (motor life, relay directionality) because both directly affect equipment health and system capacity.
Power Factor: True, Apparent, and Reactive
Quick Answer: Power factor is PF = kW / kVA = cos θ. Real power (kW) does work; reactive power (kVAR) magnetizes transformers and motors; apparent power (kVA) is the vector sum. A 0.85 lagging PF means current lags voltage by 31.8°.
True power (P, kW) is the average real power delivered to the load — the energy that turns into heat, mechanical work, or light. Reactive power (Q, kVAR) oscillates between source and load magnetic fields and does no net work. Apparent power (S, kVA) is the product of RMS voltage and RMS current and is what transformers, conductors, and switchgear are rated to carry. The power triangle relates them: S² = P² + Q², and PF = P / S = cos θ.
A lagging PF (current lags voltage) is caused by inductive loads — motors, transformers, ballasts. A leading PF (current leads voltage) is caused by capacitive loads — capacitor banks, long lightly loaded cables. Unity PF (1.0) means current is in phase with voltage and all delivered power is real.
Low PF forces more current for the same real power: a 100 kW load at 0.7 PF draws 143 kVA, while at 1.0 PF it draws only 100 kVA. Utilities penalize low PF because the extra current heats conductors and transformers without delivering billable work. NETA technicians measure PF during commissioning to verify capacitor bank sizing and to confirm PF correction capacitors haven't failed.
Voltage Unbalance: The NEMA Definition
NEMA MG-1 defines percent voltage unbalance as:
% Unbalance = 100 × (maximum voltage deviation from average / average voltage)
Step-by-step:
- Measure all three line-to-line voltages.
- Compute the average: Vavg = (Vab + Vbc + Vca) / 3.
- Find the maximum deviation from the average: max(|Vab − Vavg|, |Vbc − Vavg|, |Vca − Vavg|).
- Divide by Vavg and multiply by 100.
Example: Measured voltages 460, 470, 455 V.
- Vavg = (460 + 470 + 455) / 3 = 461.7 V
- Deviations: 1.7, 8.3, 6.7 V → max = 8.3 V
- % Unbalance = 100 × 8.3 / 461.7 = 1.8%
The NEMA Derating Curve
NEMA MG-1 publishes a derating factor that tells you how much a motor must be unloaded as voltage unbalance grows. Operation above 5% unbalance is not recommended.
| % Voltage Unbalance | Approx. Derating Factor |
|---|---|
| 0% | 1.00 |
| 1% | 0.98 |
| 2% | 0.95 |
| 3% | 0.88 |
| 4% | 0.83 |
| 5% | 0.75 |
The rule of thumb is that about 1% voltage unbalance produces roughly 2% temperature rise in the winding. Because insulation life roughly halves for every 10°C of additional heat, even small sustained unbalance shortens motor life dramatically. Current unbalance is typically 6-10× the voltage unbalance, so a 2% voltage unbalance can show up as 12-20% current unbalance on the clamp-on ammeter.
Negative-Sequence Currents and 2f Heating
A balanced three-phase voltage set contains only positive-sequence components. An unbalanced set can be decomposed (via symmetrical components, covered in 3.3) into positive, negative, and zero sequence. The negative-sequence set rotates opposite to the positive-sequence set — in the opposite direction to the motor's rotor.
When a motor rotor spins forward at near-synchronous speed and a small negative-sequence field rotates backward at synchronous speed, the relative slip is nearly 2.0. The rotor sees the negative-sequence field at twice line frequency (2f, about 120 Hz on a 60 Hz system). This induces large eddy currents in the rotor bars and surface, causing localized 2f heating that the motor's cooling fan cannot dissipate efficiently. The result is premature insulation failure, particularly in larger motors.
This is why NEMA MG-1 derating exists — not because the motor can't produce torque, but because negative-sequence heating cooks the rotor. NETA field tests often include a voltage unbalance measurement as part of motor commissioning and periodic maintenance.
Why Utilities and Test Techs Care
- PF: Low PF increases line losses (I²R), requires larger conductors and transformers, and triggers utility penalties. Field technicians verify PF to confirm capacitor bank health and to size PF correction.
- Unbalance: Even 2-3% voltage unbalance reduces motor life and can cause nuisance tripping of phase-loss or voltage-balance relays. Technicians measure unbalance at the motor terminals and at the service entrance to localize the cause.
- Negative sequence: Protective relays (46, negative-sequence overcurrent) are designed to detect sustained negative-sequence current and trip before rotor damage occurs. Understanding the heating mechanism explains why the 46 relay exists.
Power factor is defined as:
An unbalanced three-phase system feeding an induction motor can result in: