( )
sin
w l
× + × = × × +
L
L L L G
di
L R i E t
dt
EQUATION1905 V1 EN (Equation 57)
The solution over line current is presented by group of equations 58
( )
( )
( )
( )
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 58)
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
EQUATION1907 V1 EN (Equation 59)
The basic loop differential equation describing the circuit in figure 85 with series
capacitor is presented by equation 60.
( )
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 60)
The solution over line current is in this case presented by group of equations 61. 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
Section 8 1MRK 506 369-UUS -
Impedance protection
186 Line distance protection REL670 2.2 ANSI
Application manual
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