What Is Power Factor?
Power factor (PF) is the ratio of real power (kW — the useful power doing work) to apparent power (kVA — the total power drawn from the utility). PF = kW / kVA = cos(θ), where θ is the phase angle between voltage and current waveforms.
A PF of 1.0 (unity) means all power is doing useful work. A PF of 0.80 means only 80% of the current draw is productive — the remaining 20% is reactive current (kVAR) that creates magnetic fields in motors, transformers, and inductors without doing useful work.
Low power factor increases current draw for the same useful power: a 100 kW load at 0.80 PF draws 125 kVA (150A at 480V 3Φ), while the same load at 0.95 PF draws only 105 kVA (126A). The utility must supply more current, requiring larger transformers, cables, and generators.
Utility Penalties
Most utilities in the US charge power factor penalties when PF drops below 0.85 or 0.90 (varies by utility). Penalties are structured as: kVA demand charges (billing on apparent power), reactive power charges ($/kVAR), power factor adjustment multipliers, or minimum PF requirements with surcharges.
Example: A facility with 800 kW demand at 0.72 PF: kVA = 800 / 0.72 = 1,111 kVA. If the utility bills demand at $12/kVA: monthly demand charge = $13,333. At 0.95 PF: kVA = 842, demand charge = $10,105. Monthly savings: $3,228.
Annual savings from PF correction often exceed $20,000-$50,000 for medium industrial facilities. Capacitor bank payback is typically 6-18 months.
Sizing Correction Capacitors
Formula: kVAR_needed = kW × (tan(θ₁) − tan(θ₂)). Where θ₁ = arccos(existing PF) and θ₂ = arccos(target PF). This can also be looked up in kVAR multiplier tables.
Example: 500 kW at 0.75 PF, target 0.95 PF. θ₁ = arccos(0.75) = 41.4°, tan(41.4°) = 0.882. θ₂ = arccos(0.95) = 18.2°, tan(18.2°) = 0.329. kVAR = 500 × (0.882 - 0.329) = 276.5 kVAR. Select nearest standard bank: 300 kVAR.
Capacitor bank types: fixed (always on — simplest), switched (contactors cycle banks as load changes), automatic (controller monitors PF and switches steps in real-time). Automatic is preferred for variable loads.
Installation and Resonance
Location: Capacitors can be installed at the service entrance (easiest, reduces utility billing), at individual motor starters (most effective for voltage improvement), or at distribution panels (compromise approach).
DANGER — Harmonic Resonance: When the system's inductive reactance (transformers, motors) and capacitive reactance (correction capacitors) are equal at a harmonic frequency, resonance occurs. This can amplify harmonic currents 10-50× normal levels, destroying capacitors, overheating transformers, and damaging equipment.
Resonance frequency: f_r = f_system × √(kVA_transformer / kVAR_capacitor). If f_r falls near a major harmonic (5th = 300 Hz, 7th = 420 Hz, 11th = 660 Hz on 60 Hz systems), resonance is likely. Solution: detuned reactors (typically 5-7% series reactors that shift resonance above the 5th harmonic).
NEC 460.8 requires capacitor disconnecting means rated at 135% of capacitor rated current. NEC 460.9 requires a means to discharge capacitors to ≤ 50V within 1 minute for ≤ 600V systems.
Common Mistakes to Avoid
Overcorrecting to leading PF — Capacitors that push PF above unity (leading) can cause voltage rise, generator instability, and some utility penalties for leading PF. Target 0.95-0.97 lagging, never unity or leading.
Installing capacitors on VFD outputs — VFDs produce PWM waveforms that destroy capacitors within minutes. Install PF correction capacitors on the LINE side of VFDs only.
Ignoring harmonics — Standard capacitors in facilities with significant non-linear loads (VFDs, UPS, large LED installations) risk harmonic resonance. Always calculate resonant frequency before installing capacitors in industrial facilities.
Leaving fixed capacitors on during low-load periods — At night or weekends, fixed capacitors with no load to correct can cause leading PF and voltage rise. Use switched or automatic banks for variable loads.