fÓrmulas de reactores
TRANSCRIPT
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Useful Formula
Asso cia t ed w it h t he Applica t io n o f Rea ct o rs
E 600.11
XL = System inductive reactance (ohms)
XLpu = Per unit system inductive reactanceLR = Reactor inductance (henries)
XR = Reactor reactance (ohms)
XC = Capacitive reactance (ohms)
w = 2 f = angular velocity (radians per second)
f = System frequency in hertz
L = Inductance in henries
C = C apacitance in farads
R = Resistance in ohms
(assumed negligible except where noted)
IFL = Reactor rated RM S current (Amps)
ISC = Short-circuit RM S current (symmetrical)(A mps)
Ipk = Crest value of first half cycle of ISCVS= VL-L = Nominal line-to-line supply voltage in kilovolts
VL-N = Nominal line-to-neutral voltage of symmetrical
wye connected system in kilovolts
VR = Reactor voltage drop in volts
Symbols
Conventions
1.The kVA rating of a generator,
transformer or capacitor bank is
the three-phase value unless
otherwise specif ied.
2.The kVA rating of a Trench
Dry-Type A ir C ore Reactor is the
single-phase value unless otherwise
specified.
3.The voltage of a three-phase
system is the line-to-line voltage
unless otherwise specified.
4.The M VA fault level of a system
is the three-phase symmetrical
value unless otherwise specified.
NO TE: A ll values used are nominal
values with no allowance made
for system overvoltages or over-
currents.
Formula No. 1 XR = 2 fLR
Formula No. 2 VR = IFL x XR
Formula No. 3 VL-N = VL-L /3
Formula No. 4 Reactor Power (kVA r) = (IR2 XR) / 1000
Formula No. 5 Reactor Power (kVA r) = VR2 / 1000 XR
Formula No. 6 Ipk max = k x 2 x ISC
where, k = 2 or less (A NSI)
k = 1.8 or less (IEC)
VS2
Formula No. 7 XL =
M VA
where, XL = system reactance
M VA = three-phase fault level in M VA
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1 1Formula No. 8 XR = VS
2 -
M VA a M VA b
where, M VA a = three-phase fault level after series connected reactor in M VA
where, M VA b = three-phase fault level before series connected reactor in M VA
VS 1 1Formula No. 9 XR = -
3 ISCa ISCb
where, ISCa = short-circuit current after series connected reactor in kA
where, ISCb = short-circuit current before series connected reactor in kA
M VAFormula No. 10 ISC (kA ) =
3VS
where, M VA = three-phase fault level in M VA
Formula No. 11 XR (in % ) = (3 IR XR / VS) 100
XL (in % )Formula No. 12 XLpu =
100
M VA baseFormula No. 13 XLpu = XL (ohms) x
VS2
base
where, M VA = three-phase fault level in M VA
XLpu = total per unit system reactance
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XL(% ) VS2
baseFormula No. 14 XL (ohms) = x
100 M VA base
where, VS base is line-to-line value in kV
usually nominal system voltage
M VA base is three-phase value in M VA selected often 100 M VA or M VA of supply transformer
Formula No. 15 XL(% ) to new M VA base = XL (% ) x VS2
base x M VA baseoriginal new
M VA base M VA base VS2
base
original
if VS base is common then
XL (% ) = XL(% ) x M VA base
original new
M VA baseoriginal
1Formula No. 16 XC =
2 fC
M VA rFormula No. 17 IC (in kA ) =
(3) x VS
where, M VA r = rating of three-phase capacitor bank in M VA
IC = rms current at fundamental frequency in conductor supplying capacitor bank
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LFormula No. 18 T =
R
where, T = time constant in seconds
diFormula No. 19 E = -Ldt
where, E = induced voltage in volts
di= rate-of-change of current
dt
1Formula No. 20 Energy stored in an inductor = LRI
2
2
where, I = rms current flowing through inductor
2 fLR kVA fFormula No. 21 Q f = =
Req kWf
where, Q f = Q uality Factor at frequency f
Req = Equivalent coil resistance at frequency f,
comprising A C winding resistance and reflected resistance due
to eddy losses in winding conductors, 'Spiders' , insulators, etc.
kVA f = 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.
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