Fault location detection in tapped power distribution lines
A method of detecting a location of a fault in a distribution line having a first and second terminal and a line segment disposed therebetween is provided. The method includes identifying synchronized voltage and current phasors at the first and second terminal prior to and during the fault, calculating equivalent sequence components for the voltage and current phasors, locating a virtual load point on the line segment, and calculating a voltage at the virtual load point. The method further includes calculating a compensated load current at the first and/or second terminal based on one or more of the current phasors prior to and/or after the fault, and calculating a distance from the virtual load point to the fault based on the voltage at the virtual load point, the compensated load current, and one or more of the equivalent sequence components to detect the location of the fault.
1 . A system for detecting a location of a fault in a tapped power distribution line having a first terminal, a second terminal, and a line segment disposed therebetween, the system comprising:
a first relay electrically connected to the first terminal and configured to measure a first voltage phasor and a first current phasor at the first terminal;
a second relay electrically connected to the second terminal and configured to measure a second voltage phasor and a second current phasor at the second terminal; and
a fault detector comprising:
a communication interface communicatively coupled with the first and second relays; and
at least one processor communicatively coupled to the communication interface and configured to:
retrieve, utilizing the communication interface from the first and second relays, synchronized measurements of the first and second voltage phasors and synchronized measurements of the first and second current phasors as measured by the first and second relays, respectively, prior to and during the fault;
calculate equivalent sequence components for the first and second voltage phasors and the first and second current phasors;
locate a virtual tap load point on the line segment;
calculate a voltage at the virtual tap load point based on one or more of the first and second current phasors prior to the fault;
calculate a compensated load current at the first terminal and/or the second terminal based on one or more of the first and second current phasors prior to and/or after the fault; and
calculate a distance from the virtual tap load point to the fault based on the voltage at the virtual tap load point, the compensated load current, and one or more of the equivalent sequence components to detect the location of the fault.
2 . The system of claim 1 , wherein:
the at least one processor is further configured to:
determine, based on the equivalent sequence components, whether the fault comprises a symmetric fault or a non-symmetric fault;
calculate the distance using positive sequence components of the equivalent sequence components in response to determining that the fault comprises the symmetric fault; and
calculate the distance using negative sequence components of the equivalent sequence components in response to determining that the fault comprises the non-symmetric fault.
3 . The system of claim 2 , wherein:
the fault is located between the virtual tap load point and the second terminal at a distance D1 from the virtual tap load point,
the voltage at the virtual tap load point comprises Vabc,tap,
V
abc
,
tap
=
V
abc
1
-
L
v
*
Z
abc
*
I
abc
1
(
pre
-
fault
)
,
and
Vabc1 comprises the first voltage phasor measured by the first relay at the first terminal during the fault, Lv comprises a distance between the first terminal and the virtual tap load point, Zabc comprises an impedance of the line segment in an abc-domain, and Iabc1(pre-fault) comprises the first current phasor measured by the first relay at the first terminal prior to the fault.
4 . The system of claim 3 , wherein:
the compensated load current comprises Iabc1(comp),
I
a
b
c
1
(
c
o
m
p
)
=
I
a
b
c
1
(
fault
)
-
(
I
a
b
c
1
(
p
r
e
-
fault
)
+
I
a
b
c
2
(
p
r
e
-
fault
)
)
,
and
Iabc1(fault) comprises the first current phasor measured by the first relay at the first terminal during the fault, Iabc1(pre-fault) comprises the first current phasor measured by the first relay at the first terminal prior to the fault, and Iabc2(pre-fault) comprises the second current phasor measured by the second relay at the second terminal prior to the fault.
5 . The system of claim 4 , wherein:
the fault comprises the symmetric fault,
D
1
=
(
V
+
,
t
a
p
-
V
+
2
+
L
R
*
Z
+
*
I
+
2
(
fault
)
)
/
(
Z
+
*
(
I
+
1
(
c
o
m
p
)
+
I
+
2
(
fault
)
)
)
,
and
V+,tap comprises a positive sequence voltage of Vabc,tap during the fault, V+2 comprises a positive sequence voltage of the second voltage phasor measured by the second relay at the second terminal during the fault, LR comprises a distance between the second terminal and the virtual tap load point, Z+ comprises a positive sequence impedance of the line segment, I+2(fault) comprises a positive sequence current of the second current phasor measured by the second relay at the second terminal during the fault, and I+1(comp) comprises an equivalent positive sequence current of Iabc1(comp).
6 . The system of claim 4 , wherein:
the fault comprises the non-symmetric fault, and
D
1
=
(
V
-
,
tap
-
V
-
2
+
L
R
*
Z
+
*
I
-
2
(
fault
)
)
/
(
Z
+
*
(
I
-
1
(
c
o
m
p
)
+
I
-
2
(
fault
)
)
,
and
V−,tap comprises a negative sequence voltage of Vabc,tap during the fault, V−2 comprises a negative sequence voltage of the second voltage phasor measured by the second relay at the second terminal during the fault, LR comprises a distance between the second terminal and the virtual tap load point, Z+ comprises a positive sequence impedance of the line segment, I−2(fault) comprises a negative sequence current of the second current phasor measured by the second relay at the second terminal during the fault, and I−1(comp) comprises an equivalent negative sequence current of Iabc1(comp).
7 . The system of claim 2 , wherein:
the fault is located between the virtual tap load point and the first terminal at a distance D2 from the virtual tap load point,
the voltage at the virtual tap load point comprises Vabc,tap,
V
a
b
c
,
t
a
p
=
V
a
b
c
2
-
L
r
*
Z
a
b
c
*
I
a
b
c
2
(
p
r
e
-
fault
)
,
and
Vabc2 comprises the second voltage phasor measured by the second relay at the second terminal during the fault, Lr comprises a distance between the second terminal and the virtual tap load point, Zabc comprises an impedance of the line segment in an abc-domain, and Iabc2(pre-fault) comprises the second current phasor measured by the second relay at the second terminal prior to the fault.
8 . The system of claim 7 , wherein:
the compensated load current comprises Iabc2(comp),
I
a
b
c
2
(
c
o
m
p
)
=
I
a
b
c
2
(
fault
)
-
(
I
a
b
c
1
(
p
r
e
-
fault
)
+
I
a
b
c
2
(
p
r
e
-
fault
)
)
,
and
Iabc2(fault) comprises the second current phasor measured by the second relay at the second terminal during the fault, Iabc1(pre-fault) comprises the first current phasor measured by the first relay at the first terminal prior to the fault, and Iabc2(pre-fault) comprises the second current phasor measured by the second relay at the second terminal prior to the fault.
9 . The system of claim 8 wherein:
the fault comprises the symmetric fault, and
D
2
=
(
V
+
,
t
a
p
-
V
+
1
+
L
v
*
Z
+
*
I
+
1
(
fault
)
)
/
(
Z
+
*
(
I
+
1
(
fault
)
+
I
+
2
(
comp
)
)
,
and
V+,tap comprises a positive sequence voltage of Vabc,tap during the fault, V+1(fault) comprises a positive sequence voltage of the first voltage phasor measured by the first relay at the first terminal during the fault, Lv comprises a distance between the first terminal and the virtual tap load point, Z+ comprises a positive sequence impedance of the line segment, I+1(fault) comprises a positive sequence current of the first current phasor measured by the first relay at the first terminal during the fault, and I+2(comp) comprises an equivalent positive sequence current of Iabc2(comp).
10 . The system of claim 8 , wherein:
the fault comprises the non-symmetric fault,
D
2
=
(
V
-
,
tap
-
V
-
1
+
L
v
*
Z
+
*
I
-
1
(
fault
)
)
/
(
Z
+
*
(
I
-
1
(
fault
)
+
I
-
2
(
comp
)
)
,
and
V−,tap comprises a negative sequence voltage of Vabc,tap during the fault, V−1(fault) comprises a negative sequence voltage of the first voltage phasor measured by the first relay at the first terminal during the fault, Lv comprises a distance between the first terminal and the virtual tap load point, Z+ comprises a positive sequence impedance of the line segment, I−1(fault) comprises a negative sequence current of the first current phasor measured by the first relay at the first terminal during the fault, and I−2(comp) comprises an equivalent negative sequence current of Iabc2(comp).
11 . A method operable by at least one processor of a fault detector of system for detecting a location of a fault in a tapped power distribution line having a first terminal, a second terminal, and a line segment disposed therebetween, wherein:
the system comprises:
a first relay electrically connected to the first terminal and configured to measure a first voltage phasor and a first current phasor at the first terminal;
a second relay electrically connected to the second terminal and configured to measure a second voltage phasor and a second current phasor at the second terminal; and
a fault detector comprising:
a communication interface communicatively coupled with the first and second relays; and
the least one processor communicatively coupled to the communication interface,
the method comprising:
retrieving, utilizing the communication interface from the first and second relays, synchronized first and second voltage phasors and synchronized first and second current phasors measured by the first and second relays, respectively, prior to and during the fault;
calculating equivalent sequence components for the first and second voltage phasors and the first and second current phasors;
locate a virtual tap load point on the line segment;
calculating a voltage at the virtual tap load point based on one or more of the first and second current phasors prior to the fault;
calculating a compensated load current at the first terminal and/or the second terminal based on one or more of the first and second current phasors prior to and/or after the fault; and
calculating a distance from the virtual tap load point to the fault based on the voltage at the virtual tap load point, the compensated load current, and one or more of the equivalent sequence components to detect the location of the fault.
12 . The method of claim 11 , further comprising:
determining, based on the equivalent sequence components, whether the fault comprises a symmetric fault or a non-symmetric fault;
calculating the distance using positive sequence components of the equivalent sequence components in response to determining that the fault comprises the symmetric fault; and
calculating the distance using negative sequence components of the equivalent sequence components in response to determining that the fault comprises the non-symmetric fault.
13 . The method of claim 12 , wherein:
the fault is located between the virtual tap load point and the second terminal at a distance D1 from the virtual tap load point,
the voltage at the virtual tap load point comprises Vabc,tap,
V
a
b
c
,
t
a
p
=
V
abc
1
-
L
v
*
Z
a
b
c
*
I
a
b
c
1
(
pre
-
fault
)
,
and
Vabc1 comprises the first voltage phasor measured by the first relay at the first terminal during the fault, Lv comprises a distance between the first terminal and the virtual tap load point, Zabc comprises an impedance of the line segment in an abc-domain, and Iabc1(pre-fault) comprises the first current phasor measured by the first relay at the first terminal prior to the fault.
14 . The method of claim 13 , wherein:
the compensated load current comprises Iabc1(comp),
I
a
b
c
1
(
c
o
m
p
)
=
I
a
b
c
1
(
fault
)
-
(
I
a
b
c
1
(
p
r
e
-
fault
)
+
I
a
b
c
2
(
p
r
e
-
fault
)
)
,
and
Iabc1(fault) comprises the first current phasor measured by the first relay at the first terminal during the fault, Iabc1(pre-fault) comprises the first current phasor measured by the first relay at the first terminal prior to the fault, and Iabc2(pre-fault) comprises the second current phasor measured by the second relay at the second terminal prior to the fault.
15 . The method of claim 14 , wherein:
the fault comprises the symmetric fault,
D
1
=
(
V
+
,
t
a
p
-
V
+
2
+
L
R
*
Z
+
*
I
+
2
(
fault
)
)
/
(
Z
+
*
(
I
+
1
(
c
o
m
p
)
+
I
+
2
(
fault
)
)
)
,
and
V+,tap comprises a positive sequence voltage of Vabc,tap during the fault, V+2 comprises a positive sequence voltage of the second voltage phasor measured by the second relay at the second terminal during the fault, LR comprises a distance between the second terminal and the virtual tap load point, Z+ comprises a positive sequence impedance of the line segment, I+2(fault) comprises a positive sequence current of the second current phasor measured by the second relay at the second terminal during the fault, and I+1(comp) comprises an equivalent positive sequence current of Iabc1(comp).
16 . The method of claim 14 , wherein:
the fault comprises the non-symmetric fault, and
D
1
=
(
V
-
,
tap
-
V
-
2
+
L
R
*
Z
+
*
I
-
2
(
fault
)
)
/
(
Z
+
*
(
I
-
1
(
c
o
m
p
)
+
I
-
2
(
fault
)
)
,
and
V−,tap comprises a negative sequence voltage of Vabc,tap during the fault, V−2 comprises a negative sequence voltage of the second voltage phasor measured by the second relay at the second terminal during the fault, LR comprises a distance between the second terminal and the virtual tap load point, Z+ comprises a positive sequence impedance of the line segment, I−2(fault) comprises a negative sequence current of the second current phasor measured at the second terminal during the fault, and I−1(comp) comprises an equivalent negative sequence current of Iabc1(comp).
17 . The method of claim 12 , wherein:
the fault is located between the virtual tap load point and the first terminal at a distance D2 from the virtual tap load point,
the voltage at the virtual tap load point comprises Vabc,tap,
V
a
b
c
,
t
a
p
=
V
a
b
c
2
-
L
r
*
Z
a
b
c
*
I
a
b
c
2
(
p
r
e
-
fault
)
,
and
Vabc2 comprises the second voltage phasor measured by the second relay at the second terminal during the fault, Lr comprises a distance between the second terminal and the virtual tap load point, Zabc comprises an impedance of the line segment in an abc-domain, and Iabc2(pre-fault) comprises the second current phasor measured by the second relay at the second terminal prior to the fault.
18 . The method of claim 17 , wherein:
the compensated load current comprises Iabc2(comp),
I
a
b
c
2
(
c
o
m
p
)
=
I
a
b
c
2
(
fault
)
-
(
I
a
b
c
1
(
p
r
e
-
fault
)
+
I
a
b
c
2
(
p
r
e
-
fault
)
)
,
Iabc2(fault) comprises the second current phasor measured by the second relay at the second terminal during the fault, Iabc1(pre-fault) comprises the first current phasor measured by the first relay at the first terminal prior to the fault, and Iabc2(pre-fault) comprises the second current phasor measured by the second relay at the second terminal prior to the fault.
19 . The method of claim 18 wherein:
the fault comprises the symmetric fault, and
D
2
=
(
V
+
,
t
a
p
-
V
+
1
+
L
v
*
Z
+
*
I
+
1
(
fault
)
)
/
(
Z
+
*
(
I
+
1
(
fault
)
+
I
+
2
(
comp
)
)
,
and
V+,tap comprises a positive sequence voltage of Vabc,tap during the fault, V+1(fault) comprises a positive sequence voltage of the first voltage phasor measured by the first relay at the first terminal during the fault, Lv comprises a distance between the first terminal and the virtual tap load point, Z+ comprises a positive sequence impedance of the line segment, I+1(fault) comprises a positive sequence current of the first current phasor measured by the first relay at the first terminal during the fault, and I+2(comp) comprises an equivalent positive sequence current of Iabc2(comp).
20 . The method of claim 18 , wherein:
the fault comprises the non-symmetric fault,
D
2
=
(
V
-
,
tap
-
V
-
1
+
L
v
*
Z
+
*
I
-
1
(
fault
)
)
/
(
Z
+
*
(
I
-
1
(
fault
)
+
I
-
2
(
comp
)
)
,
and
V−,tap comprises a negative sequence voltage of Vabc,tap during the fault, V−1(fault) comprises a negative sequence voltage of the first voltage phasor measured by the first relay at the first terminal during the fault, Lv comprises a distance between the first terminal and the virtual tap load point, Z+ comprises a positive sequence impedance of the line segment, I−1(fault) comprises a negative sequence current of the first current phasor measured by the first relay at the first terminal during the fault, and I−2(comp) comprises an equivalent negative sequence current of Iabc2(comp).