Page 819 - Industrial Power Engineering and Applications Handbook

23/774 Industrial Power Engineering and Applications Handbook

List of formulae used Filter circuits: use of reactor enhances voltage
across the capacitor hanks
Influence of harmonics on the performance of a Rise in voltage,
capacitor unit
(23.8)
(i) By the harmonic voltage
Vph = system voltage
v, =1/(v,2+v;+v;+v;+...v;") (13.1) Vc = voltage across the capacitor banks
Xc = capacitive reactance
V, = effective harmonic voltage XL = inductive reactance
VI = system voltage
V,,, V,,, V,, and V,, etc, = magnitudes of the harmonic
voltage components in terms of fundamental Single-capacitor switching
voltage. at different harmonic orders
(i) Inrush current
(ii) By the harmonic currents I,, = I,( 1 + F)

I,, =,/(I:+ 91:h3 + 251:h,+ 491:,,,+ ... n2 I&) (23.2) (23.9)
I,, = effective harmonic current I, = maximum inrush or making current, while switching
I, = rated current of the capacitor an unchanged capacitor unit.
Ich5, I,,, and ILhn ctc. = magnitude of the harmonic I, = maximum stead -state current (capacitor peak full
current components at different harmonic orders load current (&Ic ))
Isc = fault level of the system
(iii) Harmonic output of a capacitor unit
Rating of a shunt capacitor
(23.10)
43. v'
kVAr = (23.3)
1000 ' X' L, and C, are the switching circuit parameters
&.V'.2?rf.c
or kVAr = (23.4) (ii) Switching frequency
IO00 i;'-=f.F
Effective harmonic output (Short circuit kVA) (23.11)
'' =f (Capacitor kVAr) XL
.f, = switching or transient frequency
(23.5) f = powcr frequency
X, = power frequency capacitive reactance of the circuit
X, = power frequency inductive reactance of the circuit
Influence of harmonics on telephone lines
(I) Electrostatic induction Parallel switching of capacitor banks
Blockirig circuit
(i) Inrush current
1 (23.6)
= 2n.
(23.12)
,fh = notch frequency
Z, = surge impedance
(23.7) L2 = circuit inductance between the capacitors in
henry
V, = induced electrostatic voltage in the Communication C,, C2 = capacitances of two capacitors
lines
c, ' c2
C, = coupling capacitance between the power and the = JG (23.13)
communication lines
Cg = ground circuit capacitance of the communication
lines