ABB REL670 2.2 IEC - Page 181

The basic loop differential equation describing the circuit in figure 83 with series
capacitor is presented by equation 57.
( )
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 57)
The solution over line current is in this case presented by group of equations
58.
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 U I
Z
K
E R
L
Z
R
L
R
L C L
2
L
EQUATION1909 V1 EN-US (Equation 58)
The transient part has an angular frequency b and is damped out with the time-
constant α.
The difference in performance of fault currents for a three-phase short circuit at the
end of a typical 500 km long 500 kV line is presented in figure 84.
The short circuit current on a non-compensated line is lower in magnitude, but
comprises at the beginning only a transient DC component, which diminishes
completely in approximately 120ms. The final magnitude of the fault current on
compensated line is higher due to the decreased apparent impedance of a line (60%
1MRK 506 369-UEN B Section 8
Impedance protection
Line distance protection REL670 2.2 IEC 175
Application manual