Power triangle: P (real), Q (reactive), S (apparent)
Enter current PF, target PF, real power and frequency.
Figure 1: The power triangle shows how real power (P), reactive power (Q) and apparent power (S) relate. A correction capacitor cancels reactive power, reducing S and improving PF towards unity.
Table of Contents
- Why Power Factor Matters
- Power Factor Correction Methods
- Utility Penalties and Standards
- Harmonics and Displacement PF
What Is Power Factor?
Power factor (PF) is the ratio of real power to apparent power in an AC circuit: PF = P / S = cos(θ). It tells you how efficiently the supply current is being used. A PF of 1.0 means every amp of current delivers useful work. A PF of 0.5 means you need twice the current for the same real power — the extra current generates heat in cables and transformers without doing anything productive.
Power factor arises because inductors and capacitors store and return energy each cycle, creating reactive current that flows back and forth but does no useful work. The Phase Angle Calculator shows the angle between voltage and current that gives rise to this effect.
The Power Triangle
Reactive Power Q = V × I × sin(θ) [volt-amps reactive, VAR]
Apparent Power S = V × I [volt-amps, VA]
S = √(P² + Q²) and PF = P / S
The power triangle is a right triangle: P along the horizontal (useful work), Q along the vertical (reactive energy), and S as the hypotenuse (total current demand). The angle between P and S is the phase angle θ.
Worked Example — Industrial Motor
Step 1 — S = 230 × 10 = 2300 VA
Step 2 — P = 2300 × 0.7 = 1610 W
Step 3 — Q = 2300 × sin(45.6°) = 1643 VAR
Step 4 — θ = arccos(0.7) = 45.6°
This motor draws 2.3 kVA from the supply but only delivers 1.61 kW of useful shaft power. The remaining 1.64 kVAR of reactive power heats the wiring without doing work.
Worked Example — Office Building
Step 1 — PF = 50/62.5 = 0.80
Step 2 — Q = √(62.5² − 50²) = 37.5 kVAR
Step 3 — θ = arccos(0.80) = 36.9°
The building’s PF of 0.80 means the transformer must be rated at 62.5 kVA even though only 50 kW is used. Correcting to PF = 0.95 would allow a 52.6 kVA transformer — a 16% reduction in capacity and cost.
Worked Example — Correction Capacitor Sizing
Step 1 — Qc = P(tanθ1 − tanθ2) = 50000(0.75 − 0.329) = 21.1 kVAR
Step 2 — C = Qc / (2πfV²) = 21100 / (314.16 × 160000) = 419.6 µF
A 420 µF capacitor bank at 400V would improve the building’s PF from 0.80 to 0.95. The PF Correction Sizing tab in the calculator above performs this calculation automatically for any input values.
Why Power Factor Matters
Poor power factor increases current demand, which causes higher I²R losses in cables, requires larger transformers and switchgear, and triggers reactive power penalties from electricity suppliers. In the UK, industrial tariffs typically charge for reactive power when PF drops below 0.9. Improving PF from 0.7 to 0.95 reduces supply current by 26% and cable losses by 46%.
Power Factor Correction Methods
The most common method is adding parallel capacitors to cancel the inductive reactive power from motors and transformers. Capacitors can be fixed (for constant loads) or automatically switched (for varying loads). Synchronous condensers and active PFC circuits are used in more specialised applications.
The Impedance Calculator can model how adding correction capacitance changes the circuit’s overall impedance and phase angle.
Utility Penalties and Standards
Most UK electricity distribution codes require a PF above 0.9 for industrial connections. Below this, customers pay a reactive power charge (typically per kVAR per month) or face a maximum demand penalty based on kVA rather than kW. Some European networks require PF > 0.95 for new connections.
Harmonics and Displacement PF
The power factor described above is the displacement power factor — it measures the phase shift at the fundamental frequency. When non-linear loads (like rectifiers and VFDs) generate harmonics, the true power factor is lower because harmonic currents contribute to apparent power without useful work. True PF = displacement PF × distortion factor. The Three Phase Power Calculator handles multi-phase systems where harmonic distortion is a common concern.
Frequently Asked Questions
Can power factor be greater than 1?
What is the typical PF of a home?
Do LED lights have good power factor?
What causes leading power factor?
Is power factor the same for single and three phase?
How often should PF correction capacitors be checked?
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