Hong Life CalculatorsUnderstanding the power factor correction calculator — concept and principle
This calculator sizes the capacitor bank needed to raise a load's power factor from its present value to a target, in kvar, and converts that into the capacitance per phase for a delta-connected three-phase bank. Factories and commercial buildings use power factor correction to avoid utility penalties, free up transformer and cable capacity, and reduce losses.
How it is calculated
- Required capacitor rating: Q_c = P · (tan φ₁ − tan φ₂), where φ₁ = arccos(present PF) and φ₂ = arccos(target PF). With P in kW, Q_c is in kvar.
- Capacitance per phase (delta): C = Q_c / (3 · 2πf · V_L²), with Q_c in var and V_L the line-to-line voltage. The result is shown in µF.
The principle
An inductive load draws reactive power Q = P · tan φ. A capacitor draws reactive power of the opposite sign, so placing it in parallel with the load cancels part of the inductive kvar locally. The real power P does not change; only the reactive part supplied by the network shrinks, from P tan φ₁ to P tan φ₂. The difference is exactly the capacitor rating. In a delta bank, each of the three capacitors sits across the full line voltage and supplies one third of Q_c, and a capacitor's reactive power is V² · 2πfC, which rearranges to the capacitance formula above.
Worked example
- Inputs: P = 50 kW, present PF 0.75, target PF 0.95, 400 V, 50 Hz.
- tan(arccos 0.75) = 0.88192; tan(arccos 0.95) = 0.32868.
- Q_c = 50 × (0.88192 − 0.32868) = 27.662 kvar.
- Per phase: 27,661.6 ÷ (3 × 2π × 50 × 400²) = 1.8344 × 10⁻⁴ F = 183.44 µF.
- Effect: apparent power falls from 50/0.75 = 66.7 kVA to 50/0.95 = 52.6 kVA, and line current at 400 V falls from about 96.2 A to 76.0 A.
| Real power (kW) | Capacitor (kvar) |
|---|---|
| 12.5 | 6.915412481 |
| 25 | 13.83082496 |
| 37.5 | 20.74623744 |
| 50 | 27.66164993 |
| 62.5 | 34.57706241 |
| 75 | 41.49247489 |
| 100 | 55.32329985 |
How to read the result
Choose the nearest standard capacitor or bank step at or slightly above the computed kvar, at a voltage rating suited to the system. Targets of 0.95 to 0.98 are common; pushing to exactly 1.0 gives little extra benefit and risks overcorrection to a leading power factor when the load drops.
Common mistakes
- Using kVA instead of kW for P.
- Using phase voltage in the delta formula; a star (wye) bank needs three times more capacitance per phase at the same kvar.
- Installing fixed capacitors on a load that varies widely, which can overcorrect at light load.
Frequently asked questions
Does correcting power factor lower my energy bill?
It reduces reactive-power charges and cable losses where the tariff includes them. The real energy (kWh) used by the load stays the same.
Where should the capacitors be installed?
At the main switchboard for central correction or at large motors for individual correction. Local correction also relieves the feeder cables.
What is the formula for a single-phase load?
The kvar formula is the same; the capacitance is C = Q_c / (2πf · V²).
Sources: IEC 60831-1, Shunt power capacitors of the self-healing type for AC systems having a rated voltage up to and including 1000 V · IEEE Std 1036, IEEE Guide for the Application of Shunt Power Capacitors