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Power factor correct.

 

If an inductive load with an active power demand P has an uncorrected power factor of cosf1 lagging, and is required to have a corrected power factor of cosf2 lagging, the uncorrected and corrected reactive power demands, Q1 and Q2, are:
Q1 = P tan
f1
Q2 = P tan
f2
where tan
fn = (1 / cos2fn
- 1)½

The leading (capacitive) reactive power demand QC which must be connected across the load is:
QC = Q1 - Q2 = P (tan
f1 - tanf2)

The uncorrected and corrected apparent power demands, S1 and S2, are related by:
S1cos
f1 = P = S2cosf2
Comparing corrected and uncorrected load currents and apparent power demands:
I2 / I1 = S2 / S1 = cos
f1 / cosf2

If the load is required to have a corrected power factor of unity, Q2 is zero and:
QC = Q1 = P tan
f1
I2 / I1 = S2 / S1 = cos
f1 = P / S1

Shunt Capacitors
For star-connected shunt capacitors each of capacitance Cstar on a three phase system of line voltage Vline and frequency f, the leading reactive power demand QCstar and the leading reactive line current Iline are:
QCstar = Vline2 / XCstar = 2
pfCstarVline2
Iline = QCstar /
Ö3Vline = Vline / Ö3XCstar
Cstar = QCstar / 2
pfVline2

For delta-connected shunt capacitors each of capacitance Cdelta on a three phase system of line voltage Vline and frequency f, the leading reactive power demand QCdelta and the leading reactive line current Iline are:
QCdelta = 3Vline2 / XCdelta = 6
pfCdeltaVline2
Iline = QCdelta /
Ö3Vline = Ö3Vline / XCdelta
Cdelta = QCdelta / 6
pfVline2

Note that for the same leading reactive power QC:
XCdelta = 3XCstar
Cdelta = Cstar / 3

Series Capacitors
For series line capacitors each of capacitance Cseries carrying line current Iline on a three phase system of frequency f, the voltage drop Vdrop across each line capacitor and the total leading reactive power demand QCseries of the set of three line capacitors are:
Vdrop = IlineXCseries = Iline / 2
pfCseries
QCseries
= 3Vdrop2 / XCseries = 3VdropIline = 3Iline2XCseries = 3Iline2 / 2pfCseries
Cseries
= 3Iline2 / 2pfQCseries

Note that the apparent power rating Srating of the set of three series line capacitors is based on the line   voltage Vline and not the voltage drop Vdrop:
Srating =
Ö3VlineIline