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Formulas

Shunt Reactors

For star-connected shunt reactors each of inductance Lstar on a three phase system of line voltage Vline and frequency f, the lagging reactive power demand QLstar and the lagging reactive line current Iline are:

QLstar = Vline2 / XLstar = Vline2 / 2pfLstar

Iline = QLstar / Ö3Vline = Vline / Ö3XLstar

Lstar = Vline2 / 2pfQLstar

For delta-connected shunt reactors each of inductance Ldelta on a three phase system of line voltage Vline and frequency f, the lagging reactive power demand QLdelta and the lagging reactive line current Iline are:

QLdelta = 3Vline2 / XLdelta = 3Vline2 / 2pfLdelta

Iline = QLdelta / Ö3Vline = Ö3Vline / XLdelta

Ldelta = 3Vline2 / 2pfQLdelta

Note that for the same lagging reactive power QL:

XLdelta = 3XLstar

Ldelta = 3Lstar

Series Reactors

For series line reactors each of inductance Lseries carrying line current Iline on a three phase system of frequency f, the voltage drop Vdrop across each line reactor and the total lagging reactive power demand QLseries of the set of three line reactors are:

Vdrop = IlineXLseries = 2pfLseriesIline

QLseries = 3Vdrop2 / XLseries = 3VdropIline = 3Iline2XLseries = 6pfLseriesIline2

Lseries = QLseries / 6pfIline2

Note that the apparent power rating Srating of the set of three series line reactors 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).

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