The AC Power Triangle
In AC circuits, three types of power exist simultaneously. Power factor (PF) measures how efficiently electrical power is converted to useful work.
Key Formulas
PF = P / S = cos(φ)
P = S × PF (Real power, Watts)
Q = S × sin(φ) (Reactive power, VAR)
S = √(P² + Q²) (Apparent power, VA)
S = V × I (single-phase)
S = √3 × V_L × I_L (three-phase)Worked Example
Industrial motor: 240V, 10A, PF=0.85
S = 240 × 10 = 2400 VA
P = 2400 × 0.85 = 2040 W (real work)
Q = 2400 × sin(acos(0.85)) = 2400 × 0.527 = 1265 VARWhy Power Factor Matters
- PF = 1.0: Perfect — all current does useful work
- PF = 0.7: 43% more current drawn for same work → higher bills
- Utilities charge penalties when PF < 0.95 on commercial accounts
- Correction: add capacitor banks to cancel inductive reactive power
Calculate power factor: Free Power Factor Calculator
Power Factor Basics
- Power factor (PF): PF = cos(φ) = Real Power (kW) / Apparent Power (kVA)
- Real power (P): Useful work power, measured in kW
- Reactive power (Q): Power oscillating between source and load, measured in kVAR
- Apparent power (S): S = √(P² + Q²), measured in kVA
- Perfect PF: 1.0 (purely resistive load). Typical industrial PF: 0.8–0.95.
Why Power Factor Matters
Low power factor means more current flows than necessary to deliver the same real power, increasing I²R losses in cables and transformers. Utilities in many countries levy a power factor penalty on industrial customers with PF below ~0.9 or 0.95. A factory drawing 500 kW at PF 0.7 draws an apparent power of 714 kVA, requiring larger transformers, cables, and switchgear than if PF were 0.95 (526 kVA). Power factor correction (PFC) — typically achieved by installing capacitor banks — injects reactive power to counteract inductive loads (motors, transformers) and brings PF closer to 1.0, reducing apparent power and utility penalties.
Frequently Asked Questions
Why do motors cause low power factor?
Induction motors are inductive loads — they require reactive power to establish the magnetic field that makes them work. This reactive power shuttles back and forth between the supply and the motor without doing useful work, but it still flows through cables and transformers, causing heating and voltage drop. The more motors, transformers, and inductors on a system, the lower the power factor.
How do I correct power factor?
Capacitors provide leading reactive power (opposite in sign to inductive lagging reactive power), cancelling each other. The required capacitor bank size in kVAR = P × (tan φ₁ - tan φ₂), where φ₁ is the current phase angle and φ₂ is the target. Automatic power factor correction panels switch capacitor banks in/out as load varies to maintain target PF. VFDs (variable frequency drives) on motors also improve PF.
Can power factor exceed 1.0?
No. Power factor is limited to 1.0 (unity) for passive networks. Values above 1.0 would imply receiving more real power than apparent power, which is impossible without a power source in the load. However, some active power factor correction devices and inverters can achieve near-unity PF and even inject reactive power to the grid.