Power Factor Correction Capacitor Sizing
Power Factor Correction Capacitor Sizing
A low power factor means a load draws more current than its real power consumption alone would require, because it is also pulling reactive power from the supply. Adding capacitors that locally supply that reactive power raises the power factor toward unity without changing how much real work the load does.Utilities often penalize customers with poor power factor through demand charges, and correcting it also frees up transformer and conductor capacity that would otherwise be consumed carrying reactive current — so sizing the right capacitor bank has a direct financial payoff.
The required capacitor reactive power is Qc = P·(tan(φ_1) − tan(φ_2)), the load’s real power times the reduction in the tangent of its power factor angle. where P is the real load power, φ_1 is the power factor angle at the original (uncorrected) power factor, and φ_2 is the power factor angle at the target power factor.
Inputs
P_load := 100 kW=100000 W
pf_1 := 0.75=0.75
pf_2 := 0.95=0.95
The power factor angle is recovered from the power factor using the inverse cosine, giving the phase angle between voltage and current at the original condition.
phi_1 := acos(pf_1)=0.72 rad
The same conversion gives the phase angle corresponding to the desired, improved power factor.
phi_2 := acos(pf_2)=0.32 rad
The difference in the tangents of the two angles, scaled by the real power, is exactly the reactive power the capacitor bank must supply to shift the load from the old angle to the new one.
Q_c := P_load·(tan(phi_1) - tan(phi_2))=55323.3 W
Results
A capacitor bank sized around 55 kVAR is a realistic requirement to raise a 100 kW load from 0.75 to 0.95 power factor. Because the tangent term grows sharply at low power factors, correcting a very poor initial power factor requires disproportionately more kVAR than a similar improvement starting from a decent power factor, so it always pays to fix the worst offenders first.
Assumptions & limitations
- Sinusoidal current assumed; harmonic distortion not modeled.
- Capacitor bank assumed connected directly across the load.
- Overcorrection past unity power factor is undesirable and not checked here.