Fault location using measurements of current and voltage from one end of a line
View Patent ↗A method to locate a fault from one end of a section of a power line utilizing measurements of current, voltage and angles between the phases at a first end of said section. Symmetrical components of currents are calculated for the current and voltage measurement at the first end. A value of impedance is calculated for an extra link between the terminals with the impedance for the positive sequence. A compensation is determined for the shunt capacitance. The zero-sequence current is determined from the healthy line of a section of parallel power lines. A distance to a fault is calculated for the parallel line section. The distance to the fault from the first end is calculated. The fault is located utilizing the calculate distances.
1. A method to locate a fault from one end of a section of a power line by means of measurements of current, voltage and angles between the phases at a first end of said section, the method comprising:
calculating symmetrical components of currents for said current and voltage measurement at said first end,
calculating a value of impedance for an extra link between the terminals with the impedance for the positive sequence equal to:
(
Z
_
1
LB
&
AB
=
Z
_
1
LB
Z
_
1
AB
Z
_
1
LB
+
Z
_
1
AB
)
where
:
Z 1AB =impedance for the positive sequence of the extra link,
Z 1LA =positive-sequence impedance of the healthy line,
determining a compensation for the shunt capacitance with the aid of an equation of the form:
B 2 comp —1 ( d comp — 1 ) 2 +B 1 comp — 1 d comp — 1 +B 0 comp— 1 =0 where:
B 2 comp — 1 =A 2 — Re comp — 1 A 00 — Im comp — 1 −A 2 — Im comp — 1 A 00 — Re comp — 1
B 1 comp — 1 =A 1 — Re comp — 1 A 00 — Im comp — 1 −A 1 — Im comp — 1 A 00 — Re comp — 1
B 0 comp — 1 =A 0 — Re comp — 1 A 00 — Im comp — 1 −A 0 — Im comp — 1 A 00 — Re comp — 1
determining the zero-sequence current from the healthy line of a section of parallel power lines,
calculating a distance to a fault for the parallel line section,
calculating the distance to the fault from said first end using a quadratic equation of the form:
B 2 d 2 +B 1 d+B 0 =0 where:
B 2 =A 2 — Re A 00 — Im −A 2 — Im A 00 — Re
B 1 =A 1 — Re A 00 — Im −A 1 — Im A 00 — Re
B 0 =A 0 — Re A 00 — Im −A 0 — Im A 00 — Re and
locating the fault utilizing the calculated distances.
2. The method according to claim 1 , wherein the distance to the fault is calculated using an equation of the form:
K
_
1
Z
_
1
L
d
2
+
(
L
_
1
Z
_
1
L
-
K
_
1
Z
_
AA_p
)
d
-
L
_
1
Z
_
AA_p
+
R
F
M
_
1
(
a
_
F
1
Δ
I
_
AA
1
+
a
_
F
2
I
_
AA
2
)
I
_
AA_p
=
0
(
8
)
where:
Z
_
AA_p
=
V
_
AA_p
I
_
AA_p
calculated fault loop impedance.
3. The method according to claim 1 , wherein the distance to the fault is calculated using an equation of the form:
A 2 d 2 +A 1 d+A 0 +A 00 R F =0
where:
A 2 =A 2 — Re +jA 2 — Im =K 1 Z 1LA
A 1 =A 1 — Re +jA 1 — Im =L 1 Z 1LA −K 1 Z AA — p
A 0 =A 0 — Re +jA 0 — Im =−L 1 Z AA — p
A
00
_Re
+
j
A
00
_Im
=
M
_
1
(
a
_
F1
Δ
I
_
AA1
+
a
_
F2
I
_
AA2
)
I
_
AA_p
Z
_
AA_p
=
V
_
AA_p
I
_
AA_p
=
calculated
fault
loop
impedance
K 1 , L 1 , M 1 =coefficients gathered in TABLE 3.
4. The method according to claim 1 , further comprising:
determining source impedance at said first end as a representative value, and
determining a value for source impedance at said second end as a representative value.
5. The method according claim 1 , further comprising
calculating symmetrical components of currents for said current and voltage measured at said first end by:
inputting instantaneous phase voltages,
filtering the values to determine the phasors, and
calculating phasors of symmetrical components of voltages.
6. The method according to claim 1 , further comprising
calculating symmetrical components of currents for said current and voltage measured at said first end by:
inputting instantaneous phase currents and instantaneous zero-sequence current from a healthy line,
filtering the values to determine the phasors, and
calculating phasors of symmetrical components of currents.
7. The method according to claim 1 , further comprising
determining a compensation for shunt capacitance by means of an equation of the form:
A
_
2
comp_
1
(
d
comp_
1
)
2
+
A
_
1
comp_
1
d
comp_
1
+
A
_
0
comp_
1
+
A
_
00
comp_
1
R
F
=
0
A
_
2
comp_
1
=
A
2
_Re
comp_
1
+
j
A
2
_Im
comp_
1
=
K
_
1
Z
_
1
L
long
A
_
1
comp_
1
=
A
1
_Re
comp_
1
+
j
A
1
_Im
comp_
1
=
L
_
1
Z
_
1
L
long
-
K
_
1
Z
_
A_p
comp_
1
A
_
0
comp_
1
=
A
0
_Re
comp_
1
+
j
A
0
_Im
comp_
1
=
-
L
_
1
Z
_
A_p
comp_
1
A
_
00
comp_
1
=
A
00
_Re
comp_
1
+
j
A
00
_Im
comp_
1
=
M
_
1
(
a
_
F1
Δ
I
_
AA1
+
a
_
F2
I
_
AA2
)
I
_
A_p
comp_
1
(21a) where:
Z
_
A_p
com_
1
=
V
_
A_p
I
_
A_p
comp_
1
fault loop impedance calculated from:
V A — p —original (uncompensated) fault loop voltage,
I A — p comp — 1 =a 1 I A1 — comp — 1 +a 2 I A2 — comp — 1 +a 0 I A0 — comp — 1 —fault loop current composed of the positive, negative and zero sequence currents obtained after deducing the respective capacitive currents from the original currents, and
K 1 , L 1 , M 1 =coefficients gathered in TABLE 3.
8. The method according to claim 1 , further comprising
measuring the source impedance Z 1sA at said first end A.
9. The method according to claim 1 , further comprising:
measuring the source impedance Z 1sB at said second end,
sending a communication of the measured value of source impedance Z 1sB at said second end to a fault locator at said first end.
10. The method according to claim 1 , further comprising
determining the distance to a single phase to ground fault without measurements from an operating healthy parallel line by means of complex coefficients P 0 according to a formula of the form:
P
_
0
=
Z
_
0
LB
-
Z
_
0
m
Z
_
0
LA
-
Z
_
0
m
and K 1 , L 1 , M 1 according to
K 1 =−Z 1LA ( Z 1sA +Z 1sB +Z 1LB )
L 1 =−K 1 +Z 1LB Z 1sB
M 1 =Z 1LA Z 1LB +Z 1LA (Z 1sA +Z 1sB )+ Z 1LB ( Z 1sA +Z 1sB ).
11. The method according to claim 1 , further comprising
determining the distance to a single phase to ground fault without measurements from switched off and grounded parallel line by means of complex coefficients P 0 according to
P
_
0
=
-
Z
_
0
LB
Z
_
0
m
and K 1 , L 1 , M 1 according to
K 1 =−Z 1LA
L 1 =Z 1LA +Z 1sB
M 1 =Z 1sA +Z 1sA +Z 1LA .
12. The method according to claim 1 , further comprising
determining the distance to a single ground fault using a first order formula of the form:
d
=
imag
{
V
_
AA_p
[
3
(
I
_
AA
0
-
P
_
0
I
_
AB
0
)
]
*
}
imag
{
(
Z
_
1
LA
I
_
AA_p
)
[
3
(
I
_
AA
0
-
P
_
0
I
_
AB
0
)
]
*
}
.
13. The method according to claim 1 , further comprising
determining the distance to a phase-to-phase ground fault using pre-fault measurements and a first order formula of the form:
d
=
imag
{
V
_
AA_p
[
W
_
(
I
_
AA
0
-
P
_
0
I
_
AB
0
)
]
*
}
imag
{
(
Z
_
1
LA
I
_
AA_p
)
[
W
_
(
I
_
AA
0
-
P
_
0
I
_
AB
0
)
]
*
}
.
14. The method according to claim 1 , further comprising
determining the distance to a phase-to-phase ground fault avoiding pre-fault measurements and using a first order formula of the form:
d
=
imag
[
(
V
_
a
+
V
_
b
)
(
I
_
AA
0
-
P
_
0
I
_
AB
0
)
*
]
imag
[
Z
_
1
LA
(
I
_
a
+
I
_
b
+
2
k
_
0
I
_
AA
0
2
k
_
0
m
I
_
AB
0
)
(
I
_
AA
0
-
P
_
0
I
_
AB
0
)
*
]
.
15. A device for locating a fault from one end of a section of a power line having means for receiving and storing measurements of current, voltage and angles between the phases at one first end, means for receiving and storing a detection of a fault condition between said first and second ends, the device comprising:
means for calculating symmetrical components of currents for said current and voltage measured at said first end,
means for calculating a value of impedance for an extra link between the terminals,
means for determining a compensation for shunt capacitance,
means for determining the zero-sequence current from the healthy line of a section of parallel power lines,
means for calculating a distance to a fault for the parallel line section,
means for calculating a distance from said first end to the fault.
16. The device according to claim 15 , further comprising:
means for determining a value for source impedance at said first end,
means for determining a value for source impedance at said second end.
17. The device according to claim 15 , further comprising:
means for receiving a measurement of source impedance at said first end.
18. The device according to claim 15 , further comprising:
means for receiving a measurement of source impedance made at said second end.
19. The device according to claim 15 , further comprising
means to receive a measured value for remote source impedance at said second end communicated by means of a communication channel.
20. Use of a fault locator device according to claim 15 , by a human operator to supervise a function in an electrical power system.
21. Use of a fault locator device according to claim 15 , by means of a process running on one or more computers to supervise and/or control a function in an electrical power system.
22. Use of a fault locator device according to claim 15 , to locate a distance to a fault in a power transmission or distribution system.
23. Use of a device according to claim 15 , for locating a fault on parallel power lines.
24. A computer program product, comprising
a computer readable medium; and
computer code means and/or software code portions recorded on the computer readable medium for making a computer or processor perform a method for locating a fault from one end of a section of a power line by means of measurements of current, voltage and angles between the phases at a first end of said section, the method comprising
calculating symmetrical components of currents for said current and voltage measurement at said first end,
calculating a value of impedance for an extra link between the terminals with the impedance for the positive sequence equal to:
(
Z
_
1
LB
&
AB
=
Z
_
1
LB
Z
_
1
AB
Z
_
1
LB
+
Z
_
1
AB
)
where
:
Z 1AB =impedance for the positive sequence of the extra link,
Z 1LA =positive-sequence impedance of the healthy line,
determining a compensation for the shunt capacitance with the aid of an equation of the form:
B 2 comp — 1 ( d comp — 1 ) 2 +B 1 comp — 1 d comp — 1 +B 0 comp — 1 =0 where:
B 2 comp — 1 =A 2 — Re comp — 1 A 00 — Im comp — 1 −A 2 — Im comp — 1 A 00 Re comp — 1
B 1 comp — 1 =A 1 — Re comp — 1 A 00 — Im comp — 1 −A 1 — Im comp — 1 A 00 Re comp — 1
B 0 comp — 1 =A 0 — Re comp — 1 −A 00 — Im comp — 1 A 0 — Im comp — 1 A 00 Re comp — 1
determining the zero-sequence current from the healthy line of a section of parallel power lines,
calculating a distance to a fault for the parallel line section,
calculating the distance to the fault from said first end using a quadratic equation of the form:
B 2 d 2 +B 1 d+B 0 =0 where:
B 2 =A 2 — Re A 00 — Im −A 2 Im A 00 — Re
B 1 =A 1 — Re A 00 — Im −A 1 Im A 00 — Re
B 0 =A 0 — Re A 00 — Im −A 0 Im A 00 — Re and
locating the fault utilizing the calculated distances.