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# Power Factor Correction

### Formulas

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 tanf1

Q2 = P tanf2

where tanfn = (1 / cos2fn – 1)½

The leading (capacitive) reactive power demand QC which must be connected across the load is:

QC = Q1 – Q2 = P (tanf1 – tanf2)

The uncorrected and corrected apparent power demands, S1 and S2, are related by:

S1cosf1 = P = S2cosf2

Comparing corrected and uncorrected load currents and apparent power demands:

I2 / I1 = S2 / S1 = cosf1 / cosf2

If the load is required to have a corrected power factor of unity, Q2 is zero and:

QC = Q1 = P tanf1

I2 / I1 = S2 / S1 = cosf1 = 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 = 2pfCstarVline2

Iline = QCstar / Ö3Vline = Vline / Ö3XCstar

Cstar = QCstar / 2pfVline2

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 = 6pfCdeltaVline2

Iline = QCdelta / Ö3Vline = Ö3Vline / XCdelta

Cdelta = QCdelta / 6pfVline2

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 / 2pfCseries

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

 NOTATION The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae. B C E f G h I j L P Q susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power [siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] Q R S t V W X Y Z f w quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency [number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec]

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