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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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Page edited by E.C. (Google).

One Comment


  1. ahmad
    Jan 31, 2011

    we have a 420 kva transformer and the load is about 380kva help me to find the best capasitor bank
    for this specification
    thank

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