Fault location using measurements from two ends of a line
View Patent ↗The present invention relates to a method to locate a fault in a section of a transmission line using measurements of current, voltage and angles between the phases at a first (A) and a second (B) end of said section. The invention is characterised by the steps of, after the occurrence of a fault along the section, calculating a distance (d A , d B ) to a fault dependent on a fault current measured at one of said first and second ends and phase voltages measured at both of said first and second ends (A, B), where the distance to fault is calculated from the end (A or B) where the fault current is measured. The invention is particularly suitable when a current transformer at either of the first or second ends (A, B) is saturated. If so, then, a distance (d) to a fault is calculated dependent on a fault current measured at the non-affected end and phase voltages measured at both the affected end and the non-affected end.
1. A method to locate a fault in a section of a transmission line using measurements of current and voltage at a first end and a second end of said section, the method comprising after the occurrence of a fault along the section:
receiving post-fault phase voltages and post fault phase currents from each of said first end and said second end;
determining whether a current transformer at said first end is saturated;
determining whether a current transformer at said second end is saturated; and
locating the fault by calculating a distance to said fault using the post-fault phase voltages and by using only the post-fault phase currents from one of the first end and the second end where no current transformer is saturated; and providing the calculation result on a computer readable medium.
2. The method according to claim 1 , wherein the distance to a fault is calculated by means of a formula:
d
A
=
real
(
A
_
v
)
imag
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
-
imag
(
A
_
v
)
real
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
real
(
Z
_
L
1
A
_
i
)
imag
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
-
imag
(
Z
_
L
1
A
_
i
)
real
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
where
:
A
_
v
=
a
_
1
V
_
A
1
ⅇ
jδ
+
a
_
2
V
_
A
2
ⅇ
jδ
+
a
_
0
V
_
A
0
ⅇ
jδ
A
_
i
=
a
_
1
I
_
A
1
ⅇ
jδ
+
a
_
2
I
_
A
2
ⅇ
jδ
+
a
_
0
Z
_
L
0
Z
_
L
1
I
_
A
0
ⅇ
jδ
M
_
1
A
=
-
V
_
A
1
ⅇ
jδ
+
V
_
B
1
Z
_
L
1
+
I
_
A
1
ⅇ
jδ
M
_
2
A
=
-
V
_
A
2
ⅇ
jδ
+
V
_
B
2
Z
_
L
1
+
I
_
A
2
ⅇ
jδ
Z L1 —impedance of a whole line for the positive (negative) sequence,
l—total line length,
α 1 , α 2 , α 0 , α F1 , α F2 —are coefficients dependent on a fault type, wherein the distance to a fault d B is calculated by means of a corresponding formula by substituting the values measured at end A with values measured at end B and vice versa.
3. The method according to claim 1 , further comprising calculating in the case of a non-zero synchronisation angle δ≠0 a value for a term e jδ using a formula:
ⅇ
jδ
=
-
I
_
B_pre
_
1
+
j0
.5
ω
1
C
L
1
V
_
B_pre
_
1
I
_
A_pre
_
1
-
j0
.5
ω
1
C
L
1
V
_
A_pre
_
1
where:
I A — x = I A — pre — 1 e jδ −j 0.5ω 1 C L1 V A — pre 1 e jδ
I B — x = I B — pre — 1 j 0.5ω 1 C L1 V B — pre — 1
I A — pre —a , I A — pre — b , I A — pre — c are the pre-fault currents from phases (a, b, c) at the station A,
I A — pre — 1 is the positive sequence phasor, wherein, when calculating at end B, index A is substituted with index B and vice versa.
4. The method according to claim 1 , further comprising calculating a compensation value for a shunt capacitance of said section of a line according to a formula:
d
A
-
comp
=
(
real
(
A
_
v
)
imag
(
a
_
F
1
M
_
1
A
+
a
_
F2
M
_
2
A
)
-
imag
(
A
_
v
)
real
(
a
_
F
1
M
_
1
A
+
a
_
F2
M
_
2
A
)
)
(
real
(
Z
_
L
1
long
A
_
i
-
comp
)
imag
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
-
imag
(
Z
_
L
1
long
A
_
i
-
comp
)
real
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
)
where
:
A
_
i
-
comp
=
a
_
1
I
_
A
1
-
comp
e
jδ
+
a
_
2
I
_
A
2
-
comp
e
jδ
+
a
_
0
Z
_
L
0
long
Z
_
L
1
long
I
_
A
0
-
comp
e
jδ
I A1 — comp , I A2 — comp , I A0 — comp —are the positive, negative and zero sequence currents after the compensation,
Z
_
long
L
1
-
is the positive sequence impedance of a line with taking into account the distributed long line model
Z
_
long
L
0
-
as above, but for the zero sequence,
wherein a compensation value for a shunt capacitance d B — comp is calculated by means of a corresponding formula by substituting the values measured at end A with values measured at end B and vice versa.
5. A device for fault location in a section of a transmission line using measurements of current and voltage at a first end and a second end of said section, the device comprising:
means for storing said measurements of post-phase voltages and post-phase currents from each of said first end and said second end,
means for determining whether a current transformer at said first end is saturated,
means for determining whether a current transformer at said second end is saturated, and
calculating means for calculating a distance to said fault using said post-fault phase voltages and by using only the post-fault phase currents from one of said first end and said second end where no current transformer is saturated.
6. The device according to claim 5 , wherein the means for calculating the distance to a fault includes a formula:
d
A
=
real
(
A
_
v
)
imag
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
-
imag
(
A
_
v
)
real
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
real
(
Z
_
L
1
A
_
i
)
imag
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
-
imag
(
Z
_
L
1
A
_
i
)
real
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
where
:
A
_
v
=
a
_
1
V
_
A
1
ⅇ
jδ
+
a
_
2
V
_
A
2
ⅇ
jδ
+
a
_
0
V
_
A
0
ⅇ
jδ
A
_
i
=
a
_
1
I
_
A
1
ⅇ
jδ
+
a
_
2
I
_
A
2
ⅇ
jδ
+
a
_
0
Z
_
L
0
Z
_
L
1
I
_
A
0
ⅇ
jδ
M
_
1
A
=
-
V
_
A
1
ⅇ
jδ
+
V
_
B
1
Z
_
L
1
+
I
_
A1
ⅇ
jδ
M
_
2
A
=
-
V
_
A
2
ⅇ
jδ
+
V
_
B
2
Z
_
L
1
+
I
_
A
2
ⅇ
jδ
(
10
)
Z L1 —impedance of a whole line for the positive (negative) sequence,
l—total line length,
α 1 , α 2 , α 0 , α F1 , α F2 —are coefficients dependent on a fault type, wherein the distance to fault d B is calculated means of a corresponding formula by substituting the values measured at end A with values measured at end B and vice versa.
7. The device according to claim 5 , wherein the means for calculating the distance to a fault includes a formula to calculate a compensation value for a shunt capacitance of said section of a line:
d
A
-
comp
=
(
real
(
A
_
v
)
imag
(
a
_
F
1
M
_
1
A
+
a
_
F2
M
_
2
A
)
-
imag
(
A
_
v
)
real
(
a
_
F
1
M
_
1
A
+
a
_
F2
M
_
2
A
)
)
(
real
(
Z
_
L
1
long
A
_
i
-
comp
)
imag
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
-
imag
(
Z
_
L
1
long
A
_
i
-
comp
)
real
(
a
_
F
1
M
_
1
A
+
a
_
F
2
M
_
2
A
)
)
where
:
A
_
i
-
comp
=
a
_
1
I
_
A
1
-
comp
e
jδ
+
a
_
2
I
_
A
2
-
comp
e
jδ
+
a
_
0
Z
_
L
0
long
Z
_
L
1
long
I
_
A
0
-
comp
e
jδ
,
I A1 — comp , I A2 — comp , I A0 — comp —are the positive, negative and zero sequence currents after the compensation,
Z
_
L
1
long
-
is the positive sequence impedance of a line with taking into account the distributed long line model
-
Z
_
long
L
0
-
as above, but for the zero sequence,
wherein the distance to a fault d B is calculated by means of a corresponding formula by substituting the values measured at end A with values measured at end B and vice versa.
8. A computer program product, comprising:
a computer readable medium; and
at least one of computer code means or software code portions recorded on the computer readable medium for making a computer or processor perform the steps of
receiving post-fault phase voltages and post fault phase currents from each of said first end and said second end;
determining whether a current transformer at said first end is saturated;
determining whether a current transformer at said second end is saturated; and
locating the fault by calculating a distance to a said fault using the post-fault phase voltages and by using only the post-fault phase currents from one of the first end and the second end where no current transformer is saturated.
9. A method according to claim 1 , further comprising:
carrying out at least one of repair or maintenance of the section of the transmission line.