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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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