Description
DESIGN OF DETUNED CAPACITOR STAGE
INTRODUCTION: This document derives the formulae and provides the method to calculate capacitor unit and detuning reactor ratings as relevant to a stage of a detuned capacitor bank. DEFINITIONS: FN VN VL VC VCR IS QS QCR XS XC XL L D
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= = = = = = = = = = = = =
nominal system frequency nominal system phase to neutral voltage voltage across the reactor at nominal phase to neutral voltage voltage across the capacitor unit at nominal phase to neutral voltage selected capacitor unit rated voltage nominal phase current in the detuned stage nominal single phase reactive power output of the detuned stage capacitor unit rated single phase reactive power output capacitive reactance of the detuned stage capacitive reactance of the capacitor unit inductive reactance of the detuning reactor inductance of the detuning reactor detuning factor = X L (i.e. for 5% detuning D = 0.05) XC
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TB-008-0.doc
DESIGN OF DETUNED CAPACITOR STAGE
DERIVATION OF FORMULAE : VN
IS
XL = D.XC XS XC
XL
= D. XC
XS
= XC - XL = XC.(I – D)
IS
= VN = VN XS XC.(I –D)
VL
= Is.XL = VN XC.(I - D)
. D XC = VN .D (I - D)
VC
= IS. XC = VN XC.(I - D)
. XC = VN__ (I – D)
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THIS IS FORMULA 1
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TB-008-0.doc
DESIGN OF DETUNED CAPACITOR STAGE
QS
= VN2 XS
= V N2 XC.(I – D)
Transposing, = VN2____ (I-D).Qs Now, XC
QCR = VCR2 XC XL = D. XC
XL
= VCR2 . QS (I-D) VN2 = D.VN2__ (1-D).QS
THIS IS FORMULA 2
= 2πFL
Therefore, . I L = XL = DVN2 2πF (I – D).QS 2πF
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THIS IS FORMULA 3
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TB-008-0.doc
DESIGN OF DETUNED CAPACITOR STAGE
WORK SHEET: PARAMETERS: VN =
Volts
Qs =
VAr
Fn =
Hertz
VC =
Volts
VCR =
Volts
QCR =
VAr
STEP 1 – Calculate VC from Formula 1 VC = VN (I – D)
STEP 2 – Calculate VCR VCR > VC
STEP 3 – Calculate QCR from Formula 2 QCR
= VCR2 . QS . (I-D) V N2
STEP 4 – Calculate L from Formula 3 L =
D. VN2 . I (I – D). QS 2πF
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L=
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Henry
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