Fault location method and device
View Patent ↗The present invention relates to a method for calculating the distance to fault in a section of a power transmission network, which section is arranged with line terminals at both ends, each terminal including impedance relays (AA, BB), including the steps of, at the occurence of a fault; measuring the apparent impedances by each relay, measuring the relaying currents, determining the type of fault, checking whether the fault involves a fault resistance or not, and, if so, solving a quadratic equation for complex numbers, resolving the quadratic equation for the real and imaginary components, obtaining two quadratic equations for a fault distance in which the coefficients are real numbers, combining the two equations and obtaining a distance to fault, or, if not so, solving a quadratic equation for real numbers, obtaining two solutions for the distance to fault d 1 , d 2 and comparing the solutions as 0<(d 1 or d 2 )<1 pu, where pu is the length of transmission lines between the line terminals.
1. Method for calculating the distance to fault in a section of a power transmission network (AA-BB), which section is arranged with line terminals at both ends, each terminal comprising impedance relays (AA, BB), comprising the steps of, at the occurrence of a fault:
measuring the apparent impedances by each relay ( Z AA — p , Z BA — p ),
measuring the relaying currents (| I AA — p |, | I BA — p |),
determining the type of fault,
characterised in
checking whether the fault involves a fault resistance or not according to
| Z AA — p + Z BA — p − Z 1L |<γ| Z 1L |
where Z 1L —impedance of a whole line for the positive sequence
γ—small fraction coefficient <0,01,
and, if fulfilled,
solving a quadratic equation for complex numbers according to
D 2 d 2 + D 1 d+ D 0 =0
where D 2 , D 1 , D 0 are complex coefficients,
resolving the quadratic equation for the real and imaginary components
obtaining two quadratic equations for a fault distance in which the coefficients are real numbers,
combining the two equations and obtaining a distance to fault as:
d
s
=
-
real
(
D
_
0
)
imag
(
D
_
2
)
+
imag
(
D
_
0
)
real
(
D
_
2
)
real
(
D
_
1
)
imag
(
D
_
2
)
-
imag
(
D
_
1
)
real
(
D
_
2
)
or, if not fulfilled
solving a quadratic equation for real numbers according to
F A ( d )= A 2 d 2 +A 1 d+A 0 =0
obtaining two solutions for the distance to fault according to
d
1
=
-
A
1
-
A
1
2
-
4
A
2
A
0
2
A
2
d
2
=
-
A
1
+
A
1
2
-
4
A
2
A
0
2
A
2
comparing the solutions as
0<( d 1 or d 2 )<1 pu
where pu is the length of transmission lines between the line terminals.
2. Method according to claim 1 , characterised in the further steps, if the comparison 0<(d 1 and d 2 )<1 pu is fulfilled:
utilizing information contained in the amplitudes of relaying currents from both line terminals according to
Q
=
I
_
AA_p
ⅇ
jδ
I
_
BA_p
=
I
_
AA_p
I
_
BA_p
=
Z
_
BA_p
-
(
1
-
d
)
Z
_
IL
Z
_
AA_p
-
d
Z
_
IL
,
solving a quadratic equation according to
F B ( d )= B 2 d 2 +B 1 d+B 0 =0
where:
B 2 =| Z 1L | 2 (1 −Q 2 )
B 1 =2real{( Z BA — p − Z 1L ) Z 1L *}+2 Q 2 real{ Z AA — p Z 1L *}
B 0 =| Z BA — p − Z 1L | 2 −Q 2 | Z AA — p | 2 ,
where | | and *—denote absolute value and conjugate of a complex number, respectively,
obtaining two two solutions for a distance to fault (d 3 , d 4 ):
d
3
=
-
B
1
-
B
1
2
-
4
B
2
B
0
2
B
2
d
4
=
-
B
1
+
B
1
2
-
4
B
2
B
0
2
B
2
comparing all four solutions: (d 1 , d 2 , d 3 , d 4 ) which coincide with (d i −d j =0 where: i=1 or 2, j=3 or 4), thereby obtaining the valid solution for the fault distance (d v ).
3. Method according to claim 2 , characterised in the further step for taking into consideration of shunt capacitances of a line, comprising performing:
if | d i −d j |=min
then
d
v
=
d
i
+
d
j
2
where: i=1 or 2, j=3 or 4.
4. Device for calculating the distance to fault in a section of a power transmission network, which section is arranged with line terminals at both ends, each terminal comprising impedance relays (AA, BB), comprising:
means for measuring the apparent impedances by each relay ( Z AA — p , Z BA — p ),
means for measuring the relaying currents (| I AA — p |, | I BA — p ),
means determining the type of fault,
means for checking whether the fault involves a fault resistance or not according to
| Z AA — p + Z BA — p − Z 1L |<γ| Z 1L |
where Z 1L —impedance of a whole line for the positive sequence,
/γ—small fraction coefficient<0,01,
and, if fulfilled,
means for solving a quadratic equation for complex numbers according to
D 2 d 2 + D 1 d+ D 0 =0
where D 2 , D 1 , D 0 are complex coefficients,
means for resolving the quadratic equation for the real and imaginary components
means for obtaining two quadratic equations for a fault distance in which the coefficients are real numbers,
means for combining the two equations and obtaining a distance to fault as:
d
s
=
-
real
(
D
_
0
)
imag
(
D
_
2
)
+
imag
(
D
_
0
)
real
(
D
_
2
)
real
(
D
_
1
)
imag
(
D
_
2
)
-
imag
(
D
_
1
)
real
(
D
_
2
)
or, if not fulfilled
means for solving a quadratic equation for real numbers according to
F A ( d )= A 2 d 2 +A 1 d+A 0 =0
means for obtaining two solutions for the distance to fault according to
d
1
=
-
A
1
-
A
1
2
-
4
A
2
A
0
2
A
2
d
2
=
-
A
1
+
A
1
2
-
4
A
2
A
0
2
A
2
means for comparing the solutions as
0<( d 1 or d 2 )<1pu
where pu is the length of transmission lines between the line terminals.
5. Use of a device according to claim 4 to determine the distance to fault in a single transmission line.
6. Use of a device according to claim 4 to determine the distance to fault in parallel mutually coupled transmission line.