Power Factor Correction kvar

Estimate capacitive reactive power needed to improve a lagging displacement power factor.

How this calculation works

Power-factor correction reduces the reactive demand associated with a lagging load while the model holds active power constant. Enter steady active power in kW, the initial lagging displacement power factor and a target factor at least as high as the initial value. Both factors are fractions, not percentages. The calculation finds the difference between the initial and target reactive powers using the power triangle. It also divides active power by each factor to show initial and target apparent power in kVA. The resulting kvar is a preliminary compensation quantity, not a capacitor-bank specification. The model assumes sinusoidal steady-state conditions and does not correct harmonic distortion. Changing loads, switching, resonance and detuning need a separate engineering study, especially for near-unity targets.

Inputs and units

Steady active power (kW)
Initial lagging power factor (1)
Target lagging power factor (1)

Method and formula

Qc = P[tan(arccos(PF1)) − tan(arccos(PF2))]; apparent power S = P/PF. PF is lagging displacement factor.

Worked example

Example inputs

Steady active power: 100 kW
Initial lagging power factor: 0.8 1
Target lagging power factor: 0.95 1

Calculation steps

Calculate the initial reactive-to-active ratio: tan(arccos(0.8)) = sqrt(1 − 0.8²)/0.8 = 0.75.
Calculate the target ratio: tan(arccos(0.95)) = sqrt(1 − 0.95²)/0.95 = 0.328684.
Required capacitive compensation = 100 × (0.75 − 0.3286841052) = 42.131589 kvar.
Initial apparent power = 100/0.8 = 125 kVA; target apparent power = 100/0.95 = 105.263158 kVA.

Example results

Required capacitive compensation: 42.13158948 kvar
Initial apparent power: 125 kVA
Target apparent power: 105.2631579 kVA

Assumptions

Sinusoidal steady-state load; unchanged active power
Correction targets lagging displacement power factor, not harmonic distortion

Limitations

Not capacitor-bank hardware selection or installation advice
Harmonics, resonance, switching, detuning and changing loads require a separate engineering study

Sources

Eaton: Power Factor Correction Guide for the Plant Engineer: p. 22, reactive-power correction and power triangle equations