Where:
A B
1
A L L ADD
V Z
K 1
I Z Z Z
= + +
× +
EQUATION1601 V1 EN (Equation 189)
A B
2
A L L ADD
V Z
K 1
I Z Z Z
= × +
× +
æ ö
ç ÷
è ø
EQUATION1602 V1 EN (Equation 190)
K
3
I
FA
I
A
Z
L
×
----------------
Z
A
Z
B
+
Z
1
Z
A DD
+
---------------------------
1+
è ø
æ ö
×=
EQUATION106 V1 EN (Equation 191)
and:
• Z
ADD
= Z
A
+ Z
B
for parallel lines.
• I
A
, I
FA
and V
A
are given in the above table.
• K
N
is calculated automatically according to equation 187.
• Z
A
, Z
B
, Z
L
, Z
0L
and Z
0M
are setting parameters.
For a single line, Z
0M
= 0 and Z
ADD
= 0. Thus, equation 188 applies to both single and
parallel lines.
Equation
188 can be divided into real and imaginary parts:
p
2
p Re K
1
( ) Re K
2
( ) R
F
Re K
3
( ) 0=×–+×–
EQUATION107 V1 EN
(Equation 192)
p Im K
1
( ) Im K
2
( ) R
F
Im K
3
( ) 0=× ×–×+× ×–
EQUATION108 V1 EN (Equation 193)
If the imaginary part of K
3
is not zero, R
F
can be solved according to equation 193, and
then inserted to equation 192. According to equation 192, the relative distance to the
fault is solved as the root of a quadratic equation.
Equation
192 gives two different values for the relative distance to the fault as a
solution. A simplified load compensated algorithm, which gives an unequivocal figure
for the relative distance to the fault, is used to establish the value that should be selected.
Section 15 1MRK505222-UUS C
Monitoring
944
Technical reference manual
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