ABB RET670 - Page 225

( )
( )
( )
( )
0
2
2
sin sin w l j l j
w
w
j
- ×
=
é ù
= × × + - + - × - ×
ê ú
ë û
= + ×
æ ö
×
=
ç ÷
è ø
L
L
R
t
L
G G
L
L t
L L
L
L
E E
i t I e
Z Z
Z R L
L
atg
R
EQUATION1906 V1 EN (Equation 132)
The line fault current consists of two components:
• The steady-state component which magnitude depends on generator voltage and
absolute value of impedance included in the circuit
• The transient DC component, which magnitude depends on the fault incident angle
decays with the circuit time constant
[ ]
L L
L R s
EQUATION1907 V1 EN (Equation 133)
The basic loop differential equation describing the circuit in figure 88 with series
capacitor is presented by equation 134.
( )
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 (Equation 134)
The solution over line current is in this case presented by group of equations 135. 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
1MRK504116-UUS C Section 3
IED application
219
Application manual