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Formulas

If a node in a power system operating at frequency f has a inductive source reactance XL per phase and has power factor correction with a capacitive reactance XC per phase, the source inductance L and the correction capacitance C are:

L = XL / w

C = 1 / wXC

where w = 2pf

The series resonance angular frequency wr of an inductance L with a capacitance C is:

wr = (1 / LC)½ = w(XC / XL)½

The three phase fault level Ssc at the node for no-load phase voltage E and source impedance Z per-phase star is:

Ssc = 3E2 / |Z| = 3E2 / |R + jXL|

If the ratio XL / R of the source impedance Z is sufficiently large, |Z| » XL so that:

Ssc » 3E2 / XL

The reactive power rating QC of the power factor correction capacitors for a capacitive reactance XC per phase at phase voltage E is:

QC = 3E2 / XC

The harmonic number fr / f of the series resonance of XL with XC is:

fr / f = wr / w = (XC / XL)½ » (Ssc / QC)½

Note that the ratio XL / XC which results in a harmonic number fr / f is:

XL / XC = 1 / ( fr / f )2

so for fr / f to be equal to the geometric mean of the third and fifth harmonics:

fr / f = Ö15 = 3.873

XL / XC = 1 / 15 = 0.067

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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