EQUATION1907 V1 EN-US (Equation 64)
The basic loop differential equation describing the circuit in figure 96 with series
capacitor is presented by equation 65.
( )
2
2
1
( ) cos
w w l
× + × + = × × × +
l
L
L L L G
L
d i
di
L R i t E t
dt dt C
EQUATION1908 V1 EN-US (Equation 65)
The solution over line current is in this case presented by group of equations 66. The
fault current consists also here from the steady-state part and the transient part. The
difference with non-compensated conditions is that
•
The total loop impedance decreases for the negative reactance of the series
capacitor, which in fact increases the magnitude of the fault current
• The transient part consists of the damped oscillation, which has an angular
frequency b and is dying out with a time constant a
( ) ( ) ( )
[ ]
( )
( ) ( )
( )
1 2
2
2
1 ( 0)
( 0) ( 0)
2
2
sin cos sin
1
sin
sin cos
2
1
sin
2
2
1
4
a
w l j b b
w
w
l j
w
l l j
b
l j
a
b
- ×
=
= =
= × × + - + × × + × × ×
= + × -
×
= - × -
× ×
× - - × - × - -
=
×
×
- × -
×
=
×
= -
× ×
æ ö
ç ÷
è ø
é ù
ê ú
ê ú
ê ú
ê ú
ë û
t
G
L
SC
SC L L
L
G
L t
SC
G L
L
G C t L t
SC
G L
L
SC
L
L
L
L L
E
i t K t K t e
Z
Z R L
C
E
K I
Z
E L
R
E V I
Z
K
E R
L
Z
R
L
R
L C L
2
L
EQUATION1996-ANSI V1 EN-US (Equation 66)
Section 8 1MRK 504 163-UUS A
Impedance protection
220 Transformer protection RET670 2.2 ANSI
Application manual
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