Fault location during pole-open condition
View Patent ↗The present disclosure illustrates the errors that are encountered when using both single-ended and double-ended normal-mode fault location calculations when a fault occurs in a pole-open condition. The disclosure provides systems and methods for accurately calculating the location of faults that occur during pole-open conditions, including single-ended approaches and double-ended approaches.
1. A single-ended fault location determination system, comprising:
one or more computer-readable storage media;
a processor operatively coupled to the one or more computer-readable storage media, wherein the processor is configured to:
determine current values on at least two phase lines of a three-phase transmission system during a pole-open condition;
determine a fault current value, I AG , of a faulted loop during a fault;
determine a prefault sequence current value, IXL pref , of the three-phase transmission system during the pole-open condition;
determine a sequence fault current value, IXL, during the fault, wherein an incremental value of the sequence current, ΔIXL, corresponds to the difference between the prefault sequence current value, IXL pref , and the sequence fault current value, IXL;
determine a current distribution factor phase angle, e −jψx , based on impedance values of at least two sequence networks;
calculate a tilt value corresponding to a conjugate of a product of the incremental value of the sequence current, ΔIXL, and the current distribution factor phase angle, e −jψx ;
calculate a distance dividend corresponding to an imaginary part of a product of the voltage of the faulted loop, VAL, and the tilt value;
calculate a distance divisor corresponding to an imaginary part of a product of a positive-sequence impedance, ZL1, the fault current value, I AG , and the tilt value;
determine a distance to the fault corresponding to a quotient of the distance dividend and the distance divisor; and
provide the distance to the fault during the pole-open condition by utilizing the at least two sequence networks of the three-phase transmission system to compensate for a voltage potential across an open pole of the three-phase transmission system.
2. The system of claim 1 , wherein the prefault sequence current value, IXL pref , comprises a prefault zero-sequence current value I0L pref , and wherein the sequence fault current value, IXL, comprises a zero-sequence current value I0L, such that the incremental value of the sequence current, ΔIXL, comprises an incremental value of the zero-sequence current ΔI0L, and the current distribution factor phase angle, e −jψx , is a zero-sequence current distribution factor phase angle, e −jψ0 .
3. The system of claim 1 , wherein the prefault sequence current value, IXL pref , comprises a prefault positive-sequence current value I1L pref , and wherein the sequence fault current value, IXL, comprises a positive-sequence current value I1L, such that the incremental value of the sequence current, ΔIXL, comprises an incremental value of the positive-sequence current ΔI1L, and the current distribution factor phase angle, e −jψx , is the positive-sequence current distribution factor phase angle, e −jψ1 .
4. The system of claim 1 , wherein the prefault sequence current value, IXL pref , comprises a prefault negative-sequence current value I2L pref , and wherein the sequence fault current value, IXL, comprises a negative-sequence current value I2L, such that the incremental value of the sequence current, ΔIXL, comprises an incremental value of the negative-sequence current ΔI2L, and the current distribution factor phase angle, e −jψx , is the negative-sequence current distribution factor phase angle, e −jψ2 .
5. The system of claim 1 , wherein the current distribution factor phase angle, e −jψx , is based on impedance values of a positive-sequence network of the three-phase transmission system and a zero-sequence network of the three-phase transmission system.
6. The system of claim 1 , wherein the current distribution factor phase angle, e −jψx , is based on impedance values of a negative-sequence network of the three-phase transmission system and a zero-sequence network of the three-phase transmission system.
7. The system of claim 1 , wherein the current distribution factor phase angle, e −jψx , is based on impedance values of a negative-sequence network of the three-phase transmission system and a positive-sequence network of the three-phase transmission system.
8. The system of claim 1 , wherein the current distribution factor phase angle, e −jψx , is further made a function of the distance, d, to the fault and wherein the distance, d, is solved through an iterative polynomial curve-fitting algorithm.
9. The system of claim 1 , wherein the voltage of the faulted loop, VAL, is measured using a voltage meter.
10. A method, comprising:
determining, via at least one current sensor, a fault current value, I AG , of a faulted loop during a fault;
calculating a prefault sequence current value, IXL pref , of a three-phase transmission system during a pole-open condition, and
calculating a sequence fault current value, IXL, during a fault,
calculating an incremental value of the sequence current, ΔIXL, corresponding to the difference between the prefault sequence current value, IXL pref , and the sequence fault current value, IXL;
identifying a current distribution factor phase angle, e −jψx , based on impedance values of at least two sequence networks selected from the group of sequence networks consisting of a positive-sequence network, a negative-sequence network, and a zero-sequence network;
calculating a tilt value corresponding to a conjugate of a product of the incremental value of the sequence current, ΔIXL, and the current distribution factor phase angle, e −jψx ;
determining a distance to the fault based on the quotient of (a) an imaginary part of a product of the voltage of the faulted loop, VAL, and the tilt value divided by (b) an imaginary part of a product of a positive-sequence impedance, ZL1, the fault current value, I AG , and the tilt value; and
provide the distance to the fault during the pole-open condition, wherein the provided distance to the fault utilizes the impedance values of the at least two sequence networks to compensate for a voltage potential across an open pole of the three-phase transmission system.
11. The method of claim 10 , wherein phase B is in a pole-open condition during the fault such that a is equal to 1∠120°.
12. The method of claim 10 , further comprising:
reporting the calculated distance to the fault as a range based on an estimated error percentage.
13. A method, comprising:
identifying which one of three phases of a three-phase transmission system was in a pole-open condition during a fault between a first relay and a second relay;
selecting a corresponding complex operator, α, where the complex operator, α, is equal to 1 for a phase A open-pole, 1∠120° for a phase B open-pole, and (1∠120°) 2 for a phase C open-pole;
determining an impedance value ZL1 between the first relay and the second relay;
calculating a difference between a negative-sequence voltage, V2L, at the first relay and a negative-sequence voltage, V2R, at the second relay;
calculating a difference between a negative-sequence current, I2R, at the second relay and a positive-sequence current, I1R, at the second relay;
calculating a difference between a positive-sequence voltage, V1L, at the first relay and a positive-sequence voltage, V1R, at the second relay;
calculating a sum of a negative-sequence current, I2L, at the first relay and a negative-sequence current, I2R, at the second relay;
calculating a sum of the positive-sequence current, I1L, at the first relay and a positive-sequence current, I1R, at the second relay;
determining a distance to the fault by implementing an algorithm that at least approximately satisfies at least one of two distance equations:
d
=
(
V
2
L
-
V
2
R
)
+
ZL
1
(
I
2
R
-
α
I
1
R
)
-
α
(
V
1
L
-
VIR
)
ZL
1
(
I
2
L
+
I
2
R
)
-
α
ZL
1
(
I
1
L
+
I
1
R
)
,
and
(
1
)
d
=
(
Δ
V
2
L
-
Δ
V
2
R
)
+
ZL
1
(
Δ
I
2
R
-
αΔ
I
1
R
)
-
α
(
Δ
V
1
L
-
Δ
VIR
)
ZL
1
(
Δ
I
2
L
+
Δ
I
2
R
)
-
α
ZL
1
(
Δ
I
1
L
+
Δ
I
1
R
)
;
(
2
)
and
providing an indication of where the fault occurred during the pole-open condition, wherein the distance to the fault utilizes at least two sequence networks to compensate for a voltage potential across an open pole of the three-phase transmission system.
14. A non-transitory computer-readable medium with instructions stored thereon that, when executed by a processor, cause an intelligent electronic device (IED) to perform operations comprising:
receiving data from at least one of a first relay and a second relay indicating which one of three phases was in a pole-open condition during a fault between the first relay and the second relay;
selecting a corresponding complex operator, α, where the complex operator, α, is equal to 1 for a phase A open-pole, 1∠120° for a phase B open-pole, and (1∠120°) 2 for a phase C open-pole;
identifying an impedance value ZL1 between the first relay and the second relay;
calculating a difference between a negative-sequence voltage, V2L, at the first relay and a negative-sequence voltage, V2R, at the second relay;
calculating a difference between a negative-sequence current, I2R, at the second relay and a positive-sequence current, I1R, at the second relay;
calculating a difference between a positive-sequence voltage, V1L, at the first relay and a positive-sequence voltage, V1R, at the second relay;
calculating a sum of a negative-sequence current, I2L, at the first relay and a negative-sequence current, I2R, at the second relay;
calculating a sum of the positive-sequence current, I1L, at the first relay and a positive-sequence current, I1R, at the second relay;
determining a distance to the fault by implementing an algorithm that at least approximately satisfies at least one of two distance equations:
d
=
(
V
2
L
-
V
2
R
)
+
ZL
1
(
I
2
R
-
α
I
1
R
)
-
α
(
V
1
L
-
VIR
)
ZL
1
(
I
2
L
+
I
2
R
)
-
α
ZL
1
(
I
1
L
+
I
1
R
)
,
and
(
1
)
d
=
(
Δ
V
2
L
-
Δ
V
2
R
)
+
ZL
1
(
Δ
I
2
R
-
αΔ
I
1
R
)
-
α
(
Δ
V
1
L
-
Δ
VIR
)
ZL
1
(
Δ
I
2
L
+
Δ
I
2
R
)
-
α
ZL
1
(
Δ
I
1
L
+
Δ
I
1
R
)
;
(
2
)
and
providing the distance to the fault during the pole-open condition by utilizing at least two sequence networks of the three-phase transmission system to compensate for a voltage potential across an open pole of the one of the three phases in the pole-open condition.
15. An intelligent electronic device, comprising
a pole-open identification module to identify which one of three phases was in a pole-open condition during a fault between the first relay and the second relay;
a complex operator determination module to identify a complex operator, α, corresponding to the pole-open phase, where the complex operator, α, is equal to 1 for a phase A open-pole, 1∠120° for a phase B open-pole, and (1∠120°) 2 for a phase C open-pole;
an impedance module to determine an impedance, ZL1, between the first relay and the second relay;
a processing unit to:
calculate a difference between a negative-sequence voltage, V2L, at the first relay and a negative-sequence voltage, V2R, at the second relay;
calculate a difference between a negative-sequence current, I2R, at the second relay and a positive-sequence current, I1R, at the second relay;
calculate a difference between a positive-sequence voltage, V1L, at the first relay and a positive-sequence voltage, V1R, at the second relay;
calculate a sum of a negative-sequence current, I2L, at the first relay and a negative-sequence current, I2R, at the second relay;
calculate a sum of the positive-sequence current, I1L, at the first relay and a positive-sequence current, I1R, at the second relay;
determine a distance to the fault by implementing an algorithm that at least approximately satisfies at least one of two distance equations:
d
=
(
V
2
L
-
V
2
R
)
+
ZL
1
(
I
2
R
-
α
I
1
R
)
-
α
(
V
1
L
-
VIR
)
ZL
1
(
I
2
L
+
I
2
R
)
-
α
ZL
1
(
I
1
L
+
I
1
R
)
,
and
(
1
)
d
=
(
Δ
V
2
L
-
Δ
V
2
R
)
+
ZL
1
(
Δ
I
2
R
-
αΔ
I
1
R
)
-
α
(
Δ
V
1
L
-
Δ
VIR
)
ZL
1
(
Δ
I
2
L
+
Δ
I
2
R
)
-
α
ZL
1
(
Δ
I
1
L
+
Δ
I
1
R
)
;
(
2
)
and
provide the distance to the fault during the pole-open condition by utilizing at least two sequence networks of the three-phase transmission system to compensate for a voltage potential across an open pole of the one of the three phases in the pole-open condition.
16. The system of claim 15 , wherein the pole identification module comprises a sensor configured to measure one of a voltage, a resistance, and a current to measure which of the three phases is in a pole-open condition.
17. The system of claim 15 , wherein the impedance module is configured to measure the impedance, ZL1, between the first relay and the second relay.
18. The system of claim 15 , wherein the impedance module is configured to calculate the impedance, ZL1, between the first relay and the second relay based on stored information regarding the three-phase transmission system.
19. The system of claim 15 , wherein the processing unit is further configured to calculate the voltage across the open pole of the phase in the open-pole condition.
20. The system of claim 15 , wherein phase C is in an open-pole condition such that the complex operator, α, is equal to (1∠120°) 2 .
21. The system of claim 15 , wherein the implemented algorithm satisfies the distance equation
d
=
(
Δ
V
2
L
-
Δ
V
2
R
)
+
ZL
1
(
Δ
I
2
R
-
αΔ
I
1
R
)
-
α
(
Δ
V
1
L
-
Δ
VIR
)
ZL
1
(
Δ
I
2
L
+
Δ
I
2
R
)
-
α
ZL
1
(
Δ
I
1
L
+
Δ
I
1
R
)
,
and wherein each delta (Δ) value represents an incremental difference between a fault value and a pre-fault value.