Fault location method for series-compensated double-circuit transmission lines
A highly accurate fault location method for series-compensated double-circuit transmission lines having series compensation devices and metal oxide varistors (SC&MOV) at first and second terminal ends is provided. Synchronized or unsynchronized current phasors and local voltage phasors are used as input to the fault location method. The voltages and currents at the fault point are formulated as a function of the unknown fault location. Boundary conditions for the particular IED-determined fault type are used to derive the fault location formulas.
1. A method for identifying the location of a fault in double-circuit power transmission lines of a power network extending between a first terminal and a second terminal, and wherein each circuit has a series compensation device and metal oxide varistor (SC&MOV) installed at first and second terminal ends, the method comprising:
detecting a fault occurrence on a circuit of the transmission lines between the first and second terminals;
determining a fault type for the fault occurrence;
obtaining, by a substation of the power network, synchronized during-fault first terminal voltage measurements and first and second terminal current measurements from an intelligent electronic device (IED);
formulating: zero-, positive-, and negative-sequence circuits between the first and second terminals, and which include the SC&MOV at the first and second terminal ends, by distributing as a function of the unknown fault location, m, along the transmission lines, zero-sequence parameters, the formulated zero-sequence circuit being based at least in part by the exact zero-sequence mutual impedance between the parallel lines based a distributed parameter line model:
an equivalent mutual series impedance and a mutual shunt-admittance of parallel lines between the first terminal and the unknown fault location, an equivalent mutual series-impedance and a mutual shunt-admittance of parallel lines between the second terminal and the unknown fault location, and zero, positive and negative sequence parameters: an equivalent self-series impedance and a self shunt-admittance of the transmission line between the first terminal and the unknown fault location, and an equivalent self series-impedance and a self shunt-admittance of the transmission line between the second terminal and the unknown fault location;
formulating zero-sequence during-fault voltage and negative- and positive-sequence during-fault voltage and a current at a fault point as a function of the unknown fault location, m, as given by:
V
f
(
0
)
=
V
p
1
(
0
)
-
[
I
p
1
(
0
)
-
V
p
1
(
0
)
Y
pf
(
0
)
2
-
(
V
p
1
(
0
)
-
v
p
2
(
0
)
)
Y
1
m
(
0
)
2
]
Z
pf
(
0
)
-
[
I
p
2
(
0
)
-
V
p
2
(
0
)
Y
pf
(
0
)
2
-
(
V
p
2
(
0
)
-
V
p
1
(
0
)
)
Y
1
m
(
0
)
2
]
Z
1
m
(
0
)
and
V
f
(
i
)
=
V
p
1
(
i
)
-
(
I
p
1
(
i
)
-
V
p
1
(
i
)
Y
pf
(
i
)
2
)
Z
pf
(
i
)
and
I
f
(
i
)
=
I
p
1
(
i
)
(
1
+
Y
qf
(
i
)
Z
pf
(
i
)
2
1
+
Y
qf
(
i
)
Z
qf
(
i
)
2
+
Y
pf
(
i
)
+
Y
qf
(
i
)
2
Z
pf
(
i
)
)
+
I
q
1
(
i
)
e
j
δ
(
1
-
Y
qf
(
i
)
Z
qf
(
i
)
2
1
+
Y
qf
(
i
)
Z
qf
(
i
)
2
)
-
V
p
1
(
i
)
[
Y
pf
(
i
)
2
+
Y
qf
(
i
)
2
1
+
Y
pf
(
i
)
Z
pf
(
i
)
2
1
+
Y
qf
(
i
)
Z
qf
(
i
)
2
+
Y
pf
(
i
)
+
Y
qf
(
i
)
2
(
1
+
Y
pf
(
i
)
Z
pf
(
i
)
2
)
]
;
determining a fault location distance from the first terminal by a boundary condition for the determined fault type and the zero-sequence during-fault voltage at the fault point formulated as the function of the unknown fault location, and the negative- and positive-sequence during-fault voltage at the fault point and the current at the fault point as the function of the unknown fault location
outputting a control signal, by the substation in electrical communication with the IED, based on the determined fault location distance, the control signal controlling transmission of electrical power over the power network.
2. The method of claim 1 wherein when the first and second terminal current and voltage measurements are not synchronized, a synchronization angle is derived to synchronize the first and second terminal current and voltage measurements, the method having the following steps:
receiving a pre-fault first terminal voltage measurement and the first and second terminal current measurements;
obtaining a positive-sequence equivalent self series-impedance and a positive-sequence equivalent self shunt-admittance of the transmission line between first and second terminals;
obtaining voltage and current relationships as expressed below:
e
j
δ
=
I
p
1
(
1
)
0
-
V
p
1
(
1
)
0
Y
pq
(
1
)
2
-
[
V
p
1
(
1
)
0
-
Z
pq
(
1
)
(
I
p
1
(
1
)
0
-
V
p
1
(
1
)
0
Y
pq
(
1
)
2
)
]
Y
pq
(
1
)
2
I
q
1
(
1
)
0
using measurements of: a positive-sequence pre-fault voltage phasor at the first terminal of a first circuit, a positive-sequence pre-fault current phasor at the first terminal of the first circuit, a positive-sequence pre-fault current phasor at the second terminal of the first circuit, and transmission line parameters of a positive-sequence equivalent self series-impedance and a positive-sequence equivalent self shunt-admittance of the transmission line between the first and second terminals and the synchronization angle; and
calculating: the synchronization angle from the expression of voltage and current relationships using the measurements of the positive-sequence pre-fault voltage phasor at the first terminal of the first circuit, the positive-sequence pre-fault current phasor at the first terminal of the first circuit, the positive-sequence pre-fault current phasor at the second terminal of the first circuit, and transmission line parameters of the positive-sequence equivalent self series-impedance and the positive-sequence equivalent self shunt-admittance of the transmission line between the first and second terminals.
3. A system for detecting a fault in series-compensated double-circuit transmission lines on a power network, and wherein each circuit has a series compensation device and metal oxide varistor (SC&MOV) installed at a first and second terminal ends, the system comprising:
a non-transitory computer readable storage medium of a substation of the power network having embodied thereon a plurality of machine-readable instructions that when executed by at least one computer processor cause the at least one computer processor to perform a method for detecting a fault in series-compensated double-circuit transmission lines between first and second terminals, the plurality of machine-readable instructions comprising instructions to carry out the following steps:
detecting a fault on a circuit of the transmission lines between the first and second terminals;
determining a fault type for the detected fault;
obtaining synchronized during-fault first terminal voltage measurements and first and second terminal current measurements from an intelligent electronic device (IED) that is in electrical communication with the substation;
formulating: zero, positive, and negative sequence circuits between the first and second terminals, and which include the SC&MOV at the first and second terminal ends, by distributing as a function of the unknown fault location, m, along the transmission lines, zero sequence parameters, the formulated zero-sequence circuit being based at least in part by the exact zero-sequence mutual impedance between the parallel lines based a distributed parameter line model: an equivalent mutual series impedance and a mutual shunt-admittance of parallel lines between the first terminal and the unknown fault location, an equivalent mutual series-impedance and a mutual shunt-admittance of parallel lines between the second terminal and the unknown fault location, and zero, positive and negative sequence parameters: an equivalent self-series impedance and a self shunt-admittance of the transmission line between the first terminal and the unknown fault location, and an equivalent self series-impedance and a self shunt-admittance of the transmission line between the second terminal and the unknown fault location;
formulating zero-sequence during-fault voltage and negative- and positive-sequence during-fault voltage and a current at a fault point as a function of the unknown fault location, m, as given by:
V
f
(
0
)
=
V
p
1
(
0
)
-
[
I
p
1
(
0
)
-
V
p
1
(
0
)
Y
pf
(
0
)
2
-
(
V
p
1
(
0
)
-
V
p
2
(
0
)
)
Y
1
m
(
0
)
2
]
Z
pf
(
0
)
-
[
I
p
2
(
0
)
-
V
p
2
(
0
)
Y
pf
(
0
)
2
-
(
V
p
2
(
0
)
-
v
p
1
(
0
)
)
Y
1
m
(
0
)
2
]
Z
1
m
(
0
)
and
V
f
(
i
)
=
V
p
1
(
i
)
-
(
I
p
1
(
i
)
-
V
p
1
(
i
)
Y
pf
(
i
)
2
)
Z
pf
(
i
)
and
I
f
(
i
)
=
I
p
1
(
i
)
(
1
+
Y
qf
(
i
)
Z
pf
(
i
)
2
1
+
Y
qf
(
i
)
Z
qf
(
i
)
2
+
Y
pf
(
i
)
+
Y
qf
(
i
)
2
Z
pf
(
i
)
)
+
I
q
1
(
i
)
e
j
δ
(
1
-
Y
qf
(
i
)
Z
qf
(
i
)
2
1
+
Y
qf
(
i
)
Z
qf
(
i
)
2
)
-
V
p
1
(
i
)
[
Y
pf
(
i
)
2
+
Y
qf
(
i
)
2
1
+
Y
pf
(
i
)
Z
pf
(
i
)
2
1
+
Y
qf
(
i
)
Z
qf
(
i
)
2
+
Y
pf
(
i
)
+
Y
qf
(
i
)
2
(
1
+
Y
pf
(
i
)
Z
pf
(
i
)
2
)
]
;
and
determining a fault location distance from the first terminal by a boundary condition for the determined fault type and the zero-sequence during-fault voltage at the fault point formulated as the function of the unknown fault location, and the positive/negative-sequence during-fault voltage at the fault point and the current of the fault point as the function of the unknown fault location;
wherein the substation is configured to output a control signal based on the determined fault location distance, the control signal controlling transmission of electrical power over the power network.
4. A system for detecting a fault in series-compensated double-circuit transmission lines on a power network, and wherein each circuit has a series compensation device and metal oxide varistor (SC&MOV) installed at a first and a second terminal ends, the system comprising:
a non-transitory computer readable storage medium of a substation of the power network having embodied thereon a plurality of machine-readable instructions that when executed by at least one computer processor cause the at least one computer processor to perform a method for determining a synchronization angle for use in synchronizing measurements retrieved at first and second terminals of series-compensated double-circuit transmission lines, the plurality of machine-readable instructions comprising instructions to:
receive a pre-fault first terminal voltage measurement and first and second terminal current measurements from an intelligent electronic device (TED) that is in electrical communication with the substation;
obtain a positive-sequence equivalent self series-impedance and a positive-sequence equivalent self shunt-admittance of the transmission line between first and second terminals, and which include the SC&MOV at the first and the second terminal ends,
obtain voltage and current relationships as expressed below:
e
j
δ
=
-
I
p
1
(
1
)
0
-
V
p
1
(
1
)
0
Y
pq
(
1
)
2
-
[
V
p
1
(
1
)
0
-
Z
pq
(
1
)
(
I
p
1
(
1
)
0
-
V
p
1
(
1
)
0
Y
pq
(
1
)
2
)
]
Y
pq
(
1
)
2
I
q
1
(
1
)
0
using measurements of: a positive-sequence pre-fault voltage phasor at only one of the first terminal and the second terminal of a first circuit, a positive-sequence pre-fault current phasor at the first terminal of the first circuit, a positive-sequence pre-fault current phasor at the second terminal of the first circuit, and transmission line parameters of a positive-sequence equivalent self series-impedance and a positive-sequence equivalent self shunt-admittance of the transmission line between the first and second terminals and the synchronization angle; and
calculate: the synchronization angle from the expression of voltage and current relationships using the measurements of the positive-sequence pre-fault voltage phasor at only one of the first terminal and the second terminal of the first circuit, the positive-sequence pre-fault current phasor at the first terminal of the first circuit, the positive-sequence pre-fault current phasor at the second terminal of the first circuit, and transmission line parameters of the positive-sequence equivalent self series-impedance and the positive-sequence equivalent self shunt-admittance of the transmission line between the first and second terminals
wherein the substation is configured to output a control signal based at least in part on the calculated synchronization angle, the control signal controlling transmission of electrical power over the power network.