Useful Formula
Associated with the Application of Reactors
Symbols
XL
XLpu
LR
XR
=
=
=
=
System inductive reactance (ohms)
Per unit system inductive reactance
Reactor inductance (henries)
Reactor reactance (ohms)
XC
=
=
=
=
=
=
Capacitive reactance (ohms)
2 πf = angular velocity (radians per second)
System frequency in hertz
Inductance in henries
Capacitance in farads
Resistance in ohms
(assumed negligible except where noted)
Reactor rated RMS current (Amps)
Short-circuit RMS current (symmetrical)(Amps)
Crest value of first half cycle of ISC
Nominal line-to-line supply voltage in kilovolts
Nominal line-to-neutral voltage of symmetrical
wye connected system in kilovolts
Reactor voltage drop in volts
w
f
L
C
R
IFL
=
ISC
=
Ipk
=
VS=VL-L =
VL-N
=
VR
=
Conventions
1.The kVA rating of a generator,
transformer or capacitor bank is
the three-phase value unless
otherwise specified.
Formula No. 1
XR = 2π fLR
Formula No. 2
VR = IFL x XR
2.The kVA rating of a Trench
Dry-Type Air Core Reactor is the
single-phase value unless otherwise
specified.
Formula No. 3
VL-N = VL-L /√3
Formula No. 4
Reactor Power (kVAr) = (IR2 XR) / 1000
Formula No. 5
Reactor Power (kVAr) = VR2 / 1000 XR
3.The voltage of a three-phase
system is the line-to-line voltage
unless otherwise specified.
Formula No. 6
Ipk max
= k x √2 x ISC
where, k = 2 or less (ANSI)
k = 1.8 or less (IEC)
4.The MVA fault level of a system
is the three-phase symmetrical
value unless otherwise specified.
VS2
NOTE: All values used are nominal
values with no allowance made
for system overvoltages or overcurrents.
Formula No. 7
XL =
MVA
where, XL = system reactance
MVA = three-phase fault level in MVA
Formula No. 8
[
XR = VS2
1
1
-
MVAa
MVAb
]
where, MVAa = three-phase fault level after series connected reactor in MVA
where, MVAb = three-phase fault level before series connected reactor in MVA
Formula No. 9
Formula No. 10
XR
=
VS
√3
[
1
ISCa
-
1
ISCb
where, ISCa = short-circuit current after series connected reactor in kA
where, ISCb = short-circuit current before series connected reactor in kA
MVA
ISC (kA) =
√3VS
where, MVA = three-phase fault level in MVA
Formula No. 11
XR (in %) = (√3 IR XR / VS) 100
Formula No. 12
XLpu
=
Formula No. 13
XLpu
= XL (ohms) x
XL (in %)
100
MVAbase
VS2base
where, MVA = three-phase fault level in MVA
XLpu = total per unit system reactance
2
]
Formula No. 14
XL (ohms) =
XL(%)
VS2base
x
100
MVAbase
where, VS base is line-to-line value in kV
• usually nominal system voltage
MVAbase is three-phase value in MVA selected
• often 100 MVA or MVA of supply transformer
Formula No. 15
XL(%) to new MVA base =
[ ]
XL (%)
original
MVAbase
x
[ ]
VS2base
MVAbase
original
x
[
MVAbase
new
VS2base
]
if VS base is common then
XL (%) = XL(%)
original
x
MVAbase
new
MVAbase
original
1
Formula No. 16
XC =
Formula No. 17
IC (in kA) =
2 π fC
MVAr
√(3) x VS
where, MVAr = rating of three-phase capacitor bank in MVA
IC = rms current at fundamental frequency in conductor supplying capacitor bank
3
Formula No. 18
T =
L
R
where, T = time constant in seconds
Formula No. 19
E = -L
di
dt
where, E = induced voltage in volts
di
= rate-of-change of current
dt
Formula No. 20
Energy stored in an inductor =
1
2
LRI2
where, I = rms current flowing through inductor
Formula No. 21
2π fLR
Qf =
Req
where, Qf
Req
=
kVAf
kWf
= Quality Factor at frequency f
= Equivalent coil resistance at frequency f,
comprising AC winding resistance and reflected resistance due
to eddy losses in winding conductors, 'Spiders', insulators, etc.
kVAf
= Reactor VA at frequency f in kVA
kWf
= Total watts-loss at frequency f in kW
Note: Some of the components of Req are both temperature and frequency dependent.
4
Trench Facilities
The Trench Group is your
partner of choice for electrical
power transmission and
distribution solutions today;
and for the development of
your new technology solutions
of tomorrow.
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Canada M1V 2P9
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MWB (Shanghai) Co., Ltd.
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200245
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Basel
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NE 31 1 UW
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www.trenchgroup.com
E 600.11
Subject to change without notice (05.2006)
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