U.S. patent application number 09/752892 was filed with the patent office on 2002-10-17 for systems and methods for locating faults on a transmission line with multiple tapped loads.
Invention is credited to Buettner, Reto, Hart, David, Hu, Yi, Lubkeman, David.
Application Number | 20020149375 09/752892 |
Document ID | / |
Family ID | 25028326 |
Filed Date | 2002-10-17 |
United States Patent
Application |
20020149375 |
Kind Code |
A1 |
Hu, Yi ; et al. |
October 17, 2002 |
SYSTEMS AND METHODS FOR LOCATING FAULTS ON A TRANSMISSION LINE WITH
MULTIPLE TAPPED LOADS
Abstract
A fault is located in a transmission line with a sending end, a
receiving end, and a plurality of tapped nodes, and multiple tapped
loads connected to the transmission line at tap nodes. The sending
end and the receiving end each include a measuring device. The
fault location is determined by obtaining measured circuit
parameters including measured pre-fault and faulted current and
voltage values at the sending end and at the receiving end of the
transmission line. An equivalent tap node location is calculated
using measured pre-fault and faulted current and voltage values at
the sending end and at the receiving end of the transmission line.
The equivalent tap node divides the transmission line into a
sending side and a receiving side. The phase angle difference due
to unsynchronized measurement using the measured pre-fault current
and the measured pre-fault voltage values may be calculated. The
equivalent load impedance of the tapped loads is calculated. A
first fault location is calculated assuming that the fault is
located on the sending side of the equivalent tap node. A second
fault location is calculated assuming that the fault is located on
the receiving side of the equivalent tap node. The fault location
is selected from one of the first fault location and the second
fault location, by selecting the fault location having a value
within a predetermined range representing a full distance between
two nodes.
Inventors: |
Hu, Yi; (Cary, NC) ;
Lubkeman, David; (Raleigh, NC) ; Buettner, Reto;
(Erlenbach, CH) ; Hart, David; (Raleigh,
NC) |
Correspondence
Address: |
Steven B. Samuels, Esq.
Woodcock Washburn Kurtz
Mackiewicz & Norris LLP
One Liberty Place - 46th Floor
Philadelphia
PA
19103
US
|
Family ID: |
25028326 |
Appl. No.: |
09/752892 |
Filed: |
December 29, 2000 |
Current U.S.
Class: |
324/522 |
Current CPC
Class: |
G01R 31/085
20130101 |
Class at
Publication: |
324/522 |
International
Class: |
G01R 031/08 |
Claims
What is claimed is:
1. A method for locating a fault in a transmission line, the
transmission line comprising a sending end and a receiving end, a
plurality of tap loads connected to the transmission line each at a
tap node location, a tap load connected to each of the plurality of
tap nodes, with an equivalent tap node at an equivalent tap node
location, the equivalent tap node dividing the transmission line
into a sending side and a receiving side, the sending end
comprising a measuring device, the receiving end comprising a
measuring device, the method comprising: obtaining measured circuit
parameters including measured pre-fault and faulted current and
voltage values at the sending end and at the receiving end of the
transmission line; calculating the equivalent tap node location
using measured current and voltage values at the sending end and at
the receiving end of the transmission line; calculating an
equivalent load impedance of the tapped loads at the equivalent tap
node; calculating a first fault location assuming that the fault is
located on the sending side of the equivalent tap node; calculating
a second fault location assuming that the fault is located on the
receiving side of the equivalent tap node; and selecting the
calculated fault location from one of either the first fault
location and the second fault location, by selecting the fault
location having a value within a predetermined range.
2. The method of claim 1 further comprising calculating a phase
angle difference due to unsynchronized measurement using the
measured pre-fault current and the measured pre-fault voltage
values.
3. The method of claim 2 wherein the obtaining measured circuit
parameters further comprises obtaining measured circuit parameters
from the sending end measuring device and the receiving end
measuring device.
4. The method of claim 3 wherein the obtaining measured circuit
parameters further comprises obtaining the values, Vp.sub.1.sub.S,
Ip.sup.1.sub.S, T1, Vp.sup.1.sub.R, Ip.sup.1.sub.R, T1,
V.sup.1.sub.S, I.sup.1.sub.S, T1, V.sup.1.sub.R, and
I.sup.1.sub.R,T1 where: Vp.sup.1.sub.S is the positive sequence
pre-fault complex voltage from the sending end to ground,
Ip.sup.1.sub.S, T1 is the positive sequence pre-fault complex
current from the sending end to the equivalent tap node,
Vp.sup.1.sub.R is the positive sequence pre-fault complex voltage
from the receiving end to ground, IP.sup.1.sub.R, T1 is the
positive sequence pre-fault complex current from the receiving end
to the equivalent tap node, V.sup.1.sub.S is the positive sequence
faulted complex voltage from the sending end to ground,
I.sup.1.sub.S,T1 is the positive sequence faulted complex current
from the sending end to the equivalent tap node, V.sup.1.sub.R is
the positive sequence faulted complex voltage from the receiving
end to ground, and I.sup.1.sub.R,T1 is the positive sequence
faulted complex current from the receiving end to the equivalent
tap node, and the transmission line is a three phase transmission
line.
5. The method of claim 4 wherein the calculating an equivalent tap
node location comprises calculating the equivalent tap node
location m.sub.S, T1 from the following quadratic
equation:a(m.sub.S,T1).sup.2+bm.sub.S,T1+-
c=0wherea=.vertline.Z.sub.S,R.sup.1.vertline..sup.2.vertline.I.sub.S,T1.su-
p.1.vertline..sup.2-.vertline.Z.sub.S,R.sup.1.vertline..sup.2.vertline.I.s-
ub.R,T1.sup.1.vertline..sup.2b=-2(C.sub.1R.sub.S,R.sup.1-C.sub.2X.sub.S,R.-
sup.1)-2(C.sub.3R.sub.S,R.sup.1-C.sub.4X.sub.S,R.sup.1)+2.vertline.Z.sub.S-
,R.sup.1.vertline..sup.2.vertline.I.sub.R,T1.sup.1.vertline..sup.2c=.vertl-
ine.Vp.sub.S.sup.1.vertline..sup.2-.vertline.Vp.sub.R.sup.1.vertline..sup.-
2+2(C.sub.3R.sub.S,R.sup.1-C.sub.4X.sub.S,R.sup.1)-.vertline.Z.sub.S,R.sup-
.1.vertline..sup.2.vertline.I.sub.R,T1.sup.1.vertline..sup.2withC.sub.1=Re-
.left brkt-bot.Ip.sub.S,T1.sup.1(Vp.sub.S.sup.1)*.right
brkt-bot.C.sub.2=Im.left
brkt-bot.Ip.sub.S,T1.sup.1(Vp.sub.S.sup.1)*.righ- t
brkt-bot.C.sub.3=Re.left
brkt-bot.Ip.sub.R,T1.sup.1(Vp.sub.R.sup.1)*.rig- ht
brkt-bot.C.sub.4=Im.left
brkt-bot.Ip.sub.R,T1.sup.1(Vp.sub.R.sup.1)*.ri- ght
brkt-bot.R.sub.S,R.sup.1=Re.left brkt-bot.Z.sub.S,R.sup.1.right
brkt-bot.andX.sub.S,R.sup.1=Im.left brkt-bot.Z.sub.S,R.sup.1.right
brkt-bot.whereZ.sup.1.sub.S, R is the positive sequence complex
impedance from the sending end to the receiving end.
6. The method of claim 5 wherein the calculating a phase angle
further comprises calculating the phase angle, .delta., according
to the following equation: 5 e j = Vp S 1 - Z S , T1 1 Ip S , T1 1
Vp R 1 - Z R , T1 1 Ip R , T1 1 where: Z.sup.1.sub.S, T1 is the
positive sequence complex impedance from the sending end to the
equivalent tap node, and Z.sup.1.sub.R, T1 is the positive sequence
complex impedance from the receiving end to the equivalent tap
node.
7. The method of claim 5 wherein the measured data is synchronized
and the phase angle, .delta., is zero.
8. The method of claim 6 wherein the calculating an equivalent tap
load impedance of the tapped loads comprises calculating the
equivalent tap load impedance of the tapped loads according to the
following equation: 6 Z T1 1 = Vp S 1 - Z S , T1 1 Ip S , T1 1 Ip S
, T1 1 + e j Ip R , T1 1 where Z.sup.1.sub.T1 is the positive
sequence complex impedance of the equivalent tap node.
9. The method of claim 8 wherein the calculating a first fault
location comprises calculating a first fault location according to
the following equation: 7 m S , F = V S 1 - e j V R 1 + Z R , T1 1
e j I R , T1 1 + Z S , T1 1 ( e j I R , T1 1 - e j V R 1 - Z R , T1
1 e j I R , T1 1 Z T1 1 ) Z S , T1 1 I S , T1 1 + Z S , T1 1 ( e j
I R , T1 1 - e j V R 1 - Z R , T1 1 e j I R , T1 1 Z T1 1 ) where
m.sub.S, F is the calculated first fault location.
10. The method of claim 9 wherein the calculating a second fault
location comprises calculating a second fault location according to
the following equation: 8 m R , F = e j V R 1 - V S 1 + Z S , T1 1
I S , T1 1 + Z R , T1 1 ( I S , T1 1 - V S 1 - Z S , T1 1 I S , T1
1 Z T1 1 ) Z R , T1 1 e j I R , T1 1 + Z R , T1 1 ( I S , T1 1 - V
S 1 - Z S , T1 1 I S , T1 1 Z T1 1 ) where m.sub.R, F is the
calculated second fault location.
11. The method of claim 10 wherein the selecting the calculated
fault location comprises selecting the calculated fault location
from one of either m.sub.S,F and m.sub.R,F by selecting the one
having a value within a predetermined range representing a full
distance between two nodes.
12. The method of claim 11 wherein the predetermined range is from
zero to one.
13. A system for locating a fault in a transmission line having a
sending end and a receiving end, and a plurality of tap loads
connected to the transmission line each at a tap node location, a
tap load connected to each of the plurality of tap nodes, with an
equivalent tap node at an equivalent tap node location, the
equivalent tap node dividing the transmission line into a sending
side and a receiving side, the system comprising: a processor for
calculating a fault location in the transmission line; a sending
end measuring device connected to the processor for taking
pre-fault and faulted measurements of the sending end of the
transmission line; a receiving end measuring device connected to
the processor for taking pre-fault and faulted measurements of the
receiving end of the transmission line; and wherein the processor
is adapted to obtain measured circuit parameters including measured
pre-fault and faulted current and voltage values from the sending
end measuring device and the receiving end measuring device,
calculate the equivalent tap node location using measured pre-fault
and faulted current and voltage values at the sending end and at
the receiving end of the transmission line, calculate an equivalent
load impedance of the tapped loads, calculate a first fault
location assuming that the fault is located on the sending side of
the equivalent tap node, calculate a second fault location assuming
that the fault is located on the receiving side of the equivalent
tap node, and select the calculated fault location from one of the
first fault location and the second fault location, by selecting
the fault location having a value within a predetermined range
representing a full distance between two nodes.
14. The system of claim 13 wherein the processor is further adapted
to calculate a phase angle difference due to unsynchronized
measurement using the measured pre-fault current and the measured
pre-fault voltage values.
15. The system of claim 14 wherein the sending end measuring device
comprises a voltage sensor.
16. The system of claim 14 wherein the sending end measuring device
comprises a current sensor.
17. The system of claim 14 wherein the receiving end measuring
device comprises a voltage sensor.
18. The system of claim 14 wherein the receiving end measuring
device comprises a current sensor.
19. The system of claim 14 wherein the sending end measuring device
is connected to the processor through a data link.
20. The system of claim 14 wherein the receiving end measuring
device is connected to the processor through a data link.
21. The system of claim 14 wherein the sending end measuring device
comprises a memory for storing pre-fault measurements.
22. The system of claim 14 wherein the receiving end measuring
device comprises a memory for storing pre-fault measurements.
23. The system of claim 14 wherein the processor is adapted to
obtain the values, Vp.sup.1.sub.S, Ip.sup.1.sub.S, T1,
Vp.sup.1.sub.R, Ip.sup.1.sub.R, T1, V.sup.1.sub.S,
I.sup.1.sub.S,T1,V.sup.1.sub.R, and I.sup.1.sub.R, T1 where:
Vp.sup.1.sub.S is the positive sequence pre-fault complex voltage
from the sending end to ground, Ip.sup.1.sub.S, T1 is the positive
sequence pre-fault complex current from the sending end to the
equivalent tap node, Vp.sup.1.sub.R is the positive sequence
pre-fault complex voltage from the receiving end to ground,
Ip.sup.1.sub.R, T1 is the positive sequence pre-fault complex
current from the receiving end to the equivalent tap node,
V.sup.1.sub.S is the positive sequence faulted complex voltage from
the sending end to ground, I.sup.1.sub.S, T1 is the positive
sequence faulted complex current from the sending end to the
equivalent tap node, V.sup.1.sub.R is the positive sequence faulted
complex voltage from the receiving end to ground, and I.sub.R, T1
is the positive sequence faulted complex current from the receiving
end to the equivalent tap node, and the transmission line is a
three phase transmission line.
24. The system of claim 23 wherein the processor is adapted to
calculate the equivalent tap node location MS Tfrom the following
quadratic
equation:a(m.sub.S,T1).sup.2+bm.sub.S,T1+c=0wherea=.vertline.Z.sub.S,R.su-
p.1.vertline..sup.2.vertline.I.sub.S,T1.sup.1.vertline..sup.2-Z.sub.S,R.su-
p.1.vertline..sup.2I.sub.R,T1.sup.1.vertline..sup.2b=-2(C.sub.1R.sub.S,R.s-
up.1-C.sub.2X.sub.S,R.sup.1)-2(C.sub.3R.sub.S,R.sup.1-C.sub.4X.sub.S,R.sup-
.1)+2Z.sub.S,R.sup.1.vertline..sup.2.vertline.I.sub.R,T1.vertline..sup.2c=-
.vertline.Vp.sub.S.sup.1.vertline..sup.2-.vertline.Vp.sub.R.sup.1.vertline-
..sup.2+2(C.sub.3R.sub.S,R.sup.1-C.sub.4X.sub.S,R.sup.1)-.vertline.Z.sub.S-
,R.sup.1.vertline..sup.2.vertline.I.sub.R,T1.sup.1.vertline..sup.2withC.su-
b.1=Re.left brkt-bot.Ip.sub.S,T1.sup.1(Vp.sub.S.sup.1)*.right
brkt-bot.C.sub.2=Im.left
brkt-bot.Ip.sub.S,T1.sup.1(Vp.sub.S.sup.1)*.righ- t
brkt-bot.C.sub.3=Re.left
brkt-bot.Ip.sub.R,T1.sup.1(Vp.sub.R.sup.1)*.rig- ht
brkt-bot.C.sub.4=Im.left
brkt-bot.Ip.sub.R,T1.sup.1(Vp.sub.R.sup.1)*.ri- ght
brkt-bot.R.sub.S,R.sup.1=Re[Z.sub.S,R.sup.1]andX.sub.S,R.sup.1=Im[Z.su-
b.S,R.sup.1]where Z.sup.1.sub.S, R is the positive sequence complex
impedance from the sending end to the receiving end.
25. The system of claim 24 wherein the processor is adapted to
calculate the phase angle, .delta., according to the following
equation: 9 e j = Vp S 1 - Z S , T1 1 Ip S , T1 1 Vp R 1 - Z R , T1
1 Ip R , T1 1 where: Z.sup.1.sub.S, T1 is the positive sequence
complex impedance from the sending end to the equivalent tap node,
and Z.sup.1.sub.R, T1 is the positive sequence complex impedance
from the receiving end to the equivalent tap node.
26. The system of claim 24 wherein the measured data is
synchronized and the phase angle, .delta., is zero.
27. The system of claim 25 wherein the processor is adapted to
calculate the equivalent tap load impedance of the tapped loads
according to the following equation: 10 Z T1 1 = Vp S 1 - Z S , T1
1 Ip S , T1 1 Ip S , T1 1 + e j Ip R , T1 1 where Z.sup.1.sub.T1 is
the positive sequence complex impedance of the equivalent tap
node.
28. The system of claim 27 wherein the processor is adapted to
calculate a first fault location according to the following
equation: 11 m S , F = V S 1 - j V R 1 + Z R , T1 1 j I R , T1 1 +
Z S , T1 1 ( j I R , T1 1 - j V R 1 - Z R , T1 1 j I R , T1 1 Z T1
1 ) Z S , T1 1 I S , T1 1 + Z S , T1 1 ( j I R , T1 1 - j V R 1 - Z
R , T1 1 j I R , T1 1 Z T1 1 ) where m.sub.S, F is the calculated
first fault location.
29. The system of claim 28 wherein the processor is adapted to
calculate a second fault location according to the following
equation: 12 m R , F = j V R 1 - V S 1 + Z S , T1 1 I S , T1 1 + Z
R , T1 1 ( I S , T1 1 - V S 1 - Z S , T1 1 I S , T1 1 Z T1 1 ) Z R
, T1 1 j I R , T1 1 + Z R , T1 1 ( I S , T1 1 - V S 1 - Z S , T1 1
I S , T1 1 Z T1 1 ) where m.sub.R, F is the calculated second fault
location.
30. The system of claim 29 wherein the processor is adapted to
select the calculated fault location from one of either m.sub.S, F
and m.sub.R, F by selecting the one having a value within a
predetermined range representing a full distance between two
nodes.
31. The system of claim 30 wherein the predetermined range is from
zero to one.
32. The system of claim 30 wherein the transmission line is a
single phase transmission line.
33. A computer-readable medium having instructions stored thereon
for locating a fault in a transmission line, the transmission line
comprising a sending end and a receiving end, a plurality of tap
loads connected to the transmission line each at a tap node
location, a tap load connected to each of the plurality of tap
nodes, with an equivalent tap node at an equivalent tap node
location, the equivalent tap node dividing the transmission line
into a sending side and a receiving side, the sending end
comprising a measuring device, the receiving end comprising a
measuring device, the instructions, when executed on a processor,
causing the processor to perform the following: obtaining measured
circuit parameters including measured pre-fault and faulted current
and voltage values at the sending end and at the receiving end of
the transmission line; calculating the equivalent tap node location
using measured current and voltage values at the sending end and at
the receiving end of the transmission line; calculating an
equivalent load impedance of the tapped loads; calculating a first
fault location assuming that the fault is located on the sending
side of the equivalent tap node; calculating a second fault
location assuming that the fault is located on the receiving side
of the equivalent tap node; and selecting the calculated fault
location from one of either the first fault location and the second
fault location, by selecting the fault location having a value
within a predetermined range.
34. The computer-readable medium of claim 33 further comprising
calculating a phase angle difference due to unsynchronized
measurement using the measured pre-fault current and the measured
pre-fault voltage values.
35. The computer-readable medium of claim 33 wherein the obtaining
measured circuit parameters further comprises obtaining measured
circuit parameters from the sending end measuring device and the
receiving end measuring device.
36. The computer-readable medium of claim 35 wherein the obtaining
measured circuit parameters further comprises obtaining the values,
Vp.sup.1.sub.S, Ip.sup.1.sub.S, T1, Vp.sup.1.sub.R, Ip.sup.1.sub.R,
T1, V.sup.1.sub.S, I.sup.1.sub.S,T1, V.sup.1.sub.R, and
I.sup.1.sub.R, T1 where: Vp.sup.1.sub.S is the positive sequence
pre-fault complex voltage from the sending end to ground,
Ip.sup.1.sub.S, T1 is the positive sequence pre-fault complex
current from the sending end to the equivalent tap node,
Vp.sup.1.sub.R is the positive sequence pre-fault complex voltage
from the receiving end to ground, Ip.sup.1.sub.R, T1 is the
positive sequence pre-fault complex current from the receiving end
to the equivalent tap node, V.sup.1.sub.S is the positive sequence
faulted complex voltage from the sending end to ground,
I.sup.1.sub.S, T1 is the positive sequence faulted complex current
from the sending end to the equivalent tap node, V.sup.1.sub.R is
the positive sequence faulted complex voltage from the receiving
end to ground, and I.sup.1.sub.R, T1 is the positive sequence
faulted complex current from the receiving end to the equivalent
tap node, and the transmission line is a three phase transmission
line.
37. The computer-readable medium of claim 36 wherein the
calculating an equivalent tap node location comprises calculating
the equivalent tap node location m.sub.S, T1 from the following
quadratic
equation:a(m.sub.S,T1).sup.2+bm.sub.S,T1+c=0wherea=.vertline.Z.sub.S,R.su-
p.1.vertline..sup.2.vertline.I.sub.S,T1.sup.1.vertline..sup.2-.vertline.Z.-
sub.S,R.sup.2.vertline..sup.2.vertline.I.sub.R,T1.sup.1.vertline..sup.2b=--
2(C.sub.1R.sub.S,R.sup.1-C.sub.2X.sub.S,R.sup.1)-2(C.sub.3R.sub.S,R.sup.1--
C.sub.4X.sub.S,R.sup.1)+2.vertline.Z.sub.S,R.sup.1.vertline..sup.2.vertlin-
e.I.sub.T1,R.sup.1.vertline..sup.2c=.vertline.Vp.sub.S.sup.1.vertline..sup-
.2-.vertline.Vp.sub.R.sup.1.vertline..sup.2+2(C.sub.3R.sub.S,R.sup.1-C.sub-
.4X.sub.S,R.sup.1)-.vertline.Z.sub.S,R.sup.1.vertline..sup.2.vertline.I.su-
b.R,T1.sup.1.vertline..sup.2withC.sub.1=Re.left
brkt-bot.Ip.sub.S,T1.sup.1- (Vp.sub.S.sup.1)*.right
brkt-bot.C.sub.2=Im.left brkt-bot.Ip.sub.S,T1.sup.-
1(Vp.sub.S.sup.1)*.right brkt-bot.C.sub.3=Re.left
brkt-bot.Ip.sub.R,T1.sup- .1(Vp.sub.R.sup.1)*.right
brkt-bot.C.sub.4=Im.left brkt-bot.Ip.sub.R,T1.su-
p.1(Vp.sub.R.sup.1)*.right brkt-bot.R.sub.S,R.sup.1=Re.left
brkt-bot.Z.sub.S,R.sup.1.right brkt-bot.andX.sub.S,R.sup.1=Im.left
brkt-bot.Z.sub.S,R.sup.1.right brkt-bot.where Z.sup.1.sub.S, R is
the positive sequence complex impedance from the sending end to the
receiving end.
38. The computer-readable medium of claim 37 wherein the
calculating a phase angle further comprises calculating the phase
angle, .delta., according to the following equation: 13 j = Vp S 1
- Z S , T1 1 Ip S , T1 1 Vp R 1 - Z R , T1 1 Ip R , T1 1 where:
Z.sub.1.sub.S, T1 is the positive sequence complex impedance from
the sending end to the equivalent tap node, and Z.sup.1.sub.R, T1
is the positive sequence complex impedance from the receiving end
to the equivalent tap node.
39. The computer-readable medium of claim 37 wherein the measured
data is synchronized and the phase angle, .delta., is zero.
40. The computer-readable medium of claim 38 wherein the
calculating an equivalent load impedance of the tapped load
comprises calculating the equivalent load impedance of the
equivalent tapped load according to the following equation: 14 Z T1
1 = Vp S 1 - Z S , T1 1 Ip S , T1 1 Ip S , T1 1 + j Ip R , T1 1
where Z.sup.1.sub.T1 is the positive sequence complex impedance of
the equivalent tap node.
41. The computer-readable medium of claim 40 wherein the
calculating a first fault location comprises calculating a first
fault location according to the following equation: 15 m S , F = V
S 1 - j V R 1 + Z R , T1 1 j I R , T1 1 + Z S , T1 1 ( j I R , T1 1
- j V R 1 - Z R , T1 1 j I R , T1 1 Z T1 1 ) Z S , T1 1 I S , T1 1
+ Z S , T1 1 ( j I R , T1 1 - j V R 1 - Z R , T1 1 j I R , T1 1 Z
T1 1 ) where m.sub.S, F is the calculated first fault location.
42. The computer-readable medium of claim 41 wherein the
calculating a second fault location comprises calculating a second
fault location according to the following equation: 16 m R , F = j
V R 1 - V S 1 + Z S , T1 1 I S , T1 1 + Z R , T1 1 ( I S , T1 1 - V
S 1 - Z S , T1 1 I S , T1 1 Z T1 1 ) Z R , T1 1 j I R , T1 1 + Z R
, T1 1 ( I S , T1 1 - V S 1 - Z S , T1 1 I S , T1 1 Z T1 1 ) where
m.sub.R, F is the calculated second fault location.
43. The computer-readable medium of claim 42 wherein the selecting
the calculated fault location comprises selecting the calculated
fault location from one of either m.sub.S, F and m.sub.R, F by
selecting the one having a value within a predetermined range
representing a full distance between two nodes.
44. The computer-readable medium of claim 43 wherein the
predetermined range is from zero to one.
45. The computer-readable medium of claim 33 wherein the
transmission line is a single phase transmission line.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is related to co-pending and commonly
assigned U.S. patent application Ser. No. ______, filed herewith
entitled "Systems and Methods for Locating Faults on a Transmission
Line with a Single Tapped Load" (Attorney Docket No.:
ABTT-0230/B000570).
FIELD OF THE INVENTION
[0002] The present invention relates to systems and methods for
locating faults in a power transmission system, more particularly,
a power transmission system with multiple tapped loads.
BACKGROUND OF THE INVENTION
[0003] Power transmission lines carry current from generating
sources to electric power users. The power transmission lines are
typically high voltage lines and are typically transformed down to
a lower voltage at a power substation, before being distributed to
individual electric power users (e.g., homes and business
buildings). At many power substations, protective relays are
included and perform the following functions in connection with the
transmission system: (A) substation control and data acquisition
and (B) protection. Data acquisition typically contains the
functionality of (a) monitoring the system to ascertain whether it
is in a normal or abnormal state; (b) metering, which involves
measuring certain electrical quantities for operational control;
and (c) alarming, which provides a warning of some impending
problem. Protection typically involves fast tripping a circuit
breaker in response to the detection of a short-circuit condition
(a fault), typically within a few electrical cycles after a fault
occurs
[0004] The detection of a fault in a protection function involves
measuring critical system parameters and, when a fault occurs,
quickly making a rough estimate of the fault location and of
certain characteristics of the fault so that the faulted line can
be isolated from the power grid as quick as possible. A fault
occurs when a transmission line, typically due to external causes,
diverts electrical current flow from its normal path along the
transmission line.
[0005] The major types and causes of faults are insulation faults,
caused by design defects, manufacturing defects, improper
installation, and aging insulation; electrical faults, caused by
lightning surges, switching surges, and dynamic overvoltages;
mechanical faults, caused by wind, snow, ice, contamination, trees,
and animals; and thermal faults, caused by overcurrent and
overvoltage conditions.
[0006] A transmission line typically includes three phase lines,
however, a transmission line may also contain one phase, or some
other number of phases. With a three-phase transmission line, there
are several types of possible faults. A single-phase fault is a
fault from a single phase to ground (e.g. phase a to ground). A
phase-to-phase fault is a fault from one phase to another phase
(e.g., phase a to phase b). A phase-to-phase-to-ground fault is a
fault that involves two phases and the ground (e.g., phase a and
phase b to ground). A three-phase fault is a fault that involves
all three phases and may or may not involve the ground (e.g., phase
a, phase b, and phase c to ground).
[0007] In addition to protection functions, digital fault recorders
or other processors may be included at a power substation or at a
remote site for calculating fault locations. Fault location does
not have to be as fast as protection function, which may be
calculated after the fault has been handled by the protection
function, but it should estimate the actual fault location more
accurately than a protection function. Accurate fault location
facilitates fast location and isolation of a damaged transmission
line section, and quick restoration of service to utility customers
after repair of the faulted line.
[0008] In addition to supplying power to an electrical user through
a power substation with protective relaying, electrical utilities
may also provide power to electrical users through a tap, referred
to as a tap node. The tap is a connection point to a phase or
phases of the power transmission system. There may be more than one
tap node on a transmission system. The tap is connected to a tap
lateral, which in turn is connected to and supplies power to a
load, referred to as a tapped load. There may be more than one
tapped load on a tap lateral. A tapped load typically does not have
protective relaying, and therefore, does not usually have current
and voltage data being measured/recorded.
[0009] Many fault location calculation systems exist for
determining the location of a fault on a power transmission line.
In these systems, voltage and current are measured at one or both
ends of a segment of the transmission line. In some systems, the
voltage and current measurements at both ends of a segment are
synchronized. In a synchronized system, the voltage and current
readings must have their time clocks synchronized. In some systems,
data acquired before the fault condition is used in the
calculation. Some prior fault location calculations are inaccurate
for transmission lines with a tapped load, because they were
designed for use on transmission lines without tapped loads. Some
fault location calculations are only applicable to certain types of
faults, thus a fault type must be selected before or during the
calculation process, and the accuracy of these systems may be
affected by the fault type selection.
[0010] The prior art does not address calculating fault locations
on a power transmission line with multiple tapped loads, using
synchronized or unsynchronized data from two ends (e.g., two
protective relays providing current and voltage readings). In a
power transmission line with multiple tapped loads, the
calculations used previously yield less accurate estimations of the
fault location. The fault location calculation on transmission
lines with multiple tapped loads must resolve the main problems of
the lack of measurement at the tap nodes, the fact that
measurements at both ends of a tapped line may or may not be
synchronized, and the fact that each tapped load normally is not a
fixed load, but a varying load.
[0011] Therefore, a need exists for a system and method for
calculating a fault location in a transmission line with multiple
tapped loads using synchronized or unsynchronized measured data
from two ends. The present invention satisfies this need.
SUMMARY OF THE PRESENT INVENTION
[0012] The present invention is directed to systems and methods for
calculating a fault location in a transmission line with multiple
tapped loads using synchronized or unsynchronized measured data
from two ends.
[0013] According to an aspect of the invention, a fault is located
in a transmission line with a sending end, a receiving end, and
multiple tapped loads connected to the transmission line at tap
nodes. The fault location is determined by obtaining measured
pre-fault and faulted current and voltage values at the sending end
and at the receiving end of the transmission line. An equivalent
tap node location is calculated using measured pre-fault and
faulted current and voltage values at the sending end and at the
receiving end of the transmission line.
[0014] The equivalent tap node divides the transmission line into a
sending side and a receiving side. The sending end and the
receiving end each include a measuring device. The phase angle
difference due to unsynchronized measurement may be calculated
using the measured pre-fault current and the measured pre-fault
voltage values. The equivalent load impedance of the equivalent
tapped load is calculated. A first fault location is calculated
assuming that the fault is located on the sending side of the
equivalent tap node. A second fault location is calculated assuming
that the fault is located on the receiving side of the equivalent
tap node. The fault location is selected from one of the first
fault location and the second fault location, by selecting the
fault location having a value within a predetermined range
representing a full distance between two nodes.
[0015] According to another aspect of the invention, a fault
location may be calculated for many types of faults.
[0016] According to a further aspect of the invention, a fault
location may be calculated for both single phase and three phase
transmission lines.
[0017] According to another aspect of the invention, the measured
data may be synchronized or unsynchronized.
[0018] These and other features of the present invention will be
more fully set forth hereinafter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] The present invention is further described in the detailed
description that follows, by reference to the noted plurality of
drawings by way of non-limiting examples of exemplary embodiments
of the present invention, in which like reference numerals
represent similar elements throughout the several views of the
drawings, and wherein:
[0020] FIG. 1 is a block diagram of an exemplary transmission line
with multiple tapped loads;
[0021] FIG. 2 is a block diagram of an exemplary equivalent
transmission line with an equivalent single tapped load of the
transmission line of FIG. 1;
[0022] FIG. 3 is a block diagram of the exemplary equivalent
transmission line of FIG. 2 illustrating exemplary pre-fault
conditions;
[0023] FIG. 4a is a block diagram of the exemplary equivalent
transmission line of FIG. 2 illustrating exemplary faulted
conditions;
[0024] FIG. 4b is a block diagram of the exemplary equivalent
transmission line of FIG. 2 illustrating exemplary faulted
conditions with positive sequence values;
[0025] FIG. 5 is a block diagram of an embodiment of the present
invention; and
[0026] FIG. 6 is a flow chart showing further details of an
embodiment of the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0027] The present invention is directed to systems and methods for
calculating a fault location in a transmission line with multiple
tapped loads using synchronized or unsynchronized measured data
from two ends.
[0028] FIG. 1 illustrates an exemplary transmission line with
multiple tapped loads. As shown in FIG. 1, the transmission line 10
line includes a sending end S, a receiving end R, and multiple tap
nodes TA, TB. The transmission line may include any number of tap
nodes. A load node LA is connected to the tap node TA through a tap
lateral. A load node LB is connected to the tap node TB through a
tap lateral.
[0029] In order to describe the invention, the following naming
conventions will be used. Upper case letters, which are not
subscripted or superscripted, designate a physical value according
to Table 1. The values may be measured values, known values, or
calculated values.
1 TABLE 1 V Voltage, a complex value I Current, complex value Z
Impedance, complex value R Resistance, real value, the real part of
impedance Z X Reactance, real value, the imaginary part of
impedance Z
[0030] A lower case letter following a physical value designates
whether the value is a pre-fault value or a faulted value according
to Table 2. The distance to the fault within a transmission line
segment is designated by m.
2 TABLE 2 p pre-fault none faulted (during the fault) m unit
distance to fault within segment, real value
[0031] Typically there are three phases of a fault distinguished in
fault analysis: pre-fault, faulted and post-fault. Pre-fault is
before the instant of the fault, faulted is from the instant of the
fault to the actuation of circuit protection, and post-fault is
after the actuation of circuit protection.
[0032] A superscript designates the phase or the symmetrical
sequence components according to Table 3.
3 TABLE 3 a Phase a b Phase b c Phase c 0 Zero sequence 1 Positive
sequence 2 Negative sequence * Conjugate of complex number
[0033] A subscript designates the node according to Table 4. When
two subscripts are separated by a comma, the subscripts designate
the "from" node and the "to" node, respectively. For example the
subscript S, T1 designates from the sending end S to the tap node
T1. When only one node is designated, it is designated as the
"from" node and the "to" node is ground. For example, the subscript
T1 designates from tap node T1 to ground. Alternately, the "to"
node may be designated as 0 for ground.
4 TABLE 4 S Sending end of transmission line R Receiving end of
transmission line Tx Tap node x Lx Load node x F Fault point,
faulted node, or fault location
[0034] Parenthesis with the following prefixes designate the part
of a complex value according to Table 5. Values raised to a power
are enclosed in parenthesis. Magnitudes raised to a power are
enclosed in absolute value indicators, ".vertline.".
5TABLE 5 Re( ... ) the real part of the value in parenthesis in
Cartesian coordinates lm( ... ) the imaginary part of the value in
parenthesis in Cartesian coordinates (...).sup.a the value in
parenthesis raised to power of a .vertline.....vertline. the
absolute value of the value in parenthesis in polar coordinates
[0035] The following examples illustrate the naming convention.
V.sub.T1.sup.a or V.sub.T1,0.sup.a represents a complex faulted
value of voltage during a fault, of phase a, from tap node T1 to
ground. Ip.sub.T4,R.sup.0 represents a zero sequence complex
pre-fault value of current from tap node T4 to the receiving end R.
(Z.sub.T2,T3.sup.2).sup.- a represents a negative sequence complex
impedance from tap node T2 to tap node T3, raised to the power of
a. Re(I.sub.S,T1.sup.1) represents the real part of a positive
sequence complex value of the faulted current from the sending end
S to the tap node T1.
[0036] As shown in FIG. 1, the impedance from the sending end S to
the tap node TA is Z.sub.S,TA. The impedance from the tap node TA
to the tap node TB is Z.sub.TA,TB. The impedance from the tap node
TB to the receiving end R is Z.sub.TB,R. The impedance from the tap
node TA to the load node LA is Z.sub.TA,LA. The impedance of the
load connected to load node LA is Z.sub.LA. The impedance from the
tap node TA to ground is Z.sub.TA and includes the impedance from
Z.sub.TA,LA and Z.sub.LA. The impedance from the tap node TB to the
load node LB is Z.sub.TB,LB. The impedance of the load connected to
load node LB is Z.sub.LB. The impedance from the tap node TB to
ground is Z.sub.TB and includes the impedance from Z.sub.TB,LB and
Z.sub.LB.
[0037] FIG. 2 illustrates an exemplary equivalent transmission line
with an equivalent single tapped load, equivalent to the
transmission line of FIG. 1. As shown in FIG. 2, the transmission
line 10 includes a sending end S, a receiving end R, and an
equivalent tap T1, also referred to herein as an equivalent tap
node T1, between the sending end S and the receiving end R. An
equivalent tapped load Z.sub.T1 is connected to the equivalent tap
node T1. The equivalent tap node T1 divides the transmission line
into a sending side 11 and a receiving side 12.
[0038] As shown in FIG. 2, the impedance from the sending end S to
the equivalent tap node T1 is Z.sub.S,T1. The impedance from the
equivalent tap node T1 to the receiving end R is Z.sub.T1,R. The
impedance from the equivalent tap node T1 to ground is Z.sub.T1.
The equivalent distance from the sending end S to the equivalent
tap node T1 is m.sub.S,T1.
[0039] FIG. 3 illustrates exemplary pre-fault conditions on the
equivalent transmission line of FIG. 2. As shown in FIG. 3,
Vp.sub.S.sup.1 is a positive sequence pre-fault complex voltage
from the sending end S to ground. IP.sup.1.sub.S,T1 is a positive
sequence pre-fault complex current from the sending end S to the
equivalent tap node T1. Z.sup.1.sub.S,T1 is a positive sequence
complex impedance from the sending end S to the equivalent tap node
T1. VP.sup.I.sub.T1 is a positive sequence pre-fault complex
voltage from the equivalent tap node T1 to ground. Ip.sup.1.sub.T1
is a positive sequence pre-fault complex current from the
equivalent tap node T1 to ground. Z.sup.1.sub.T1 is a positive
sequence complex impedance from the equivalent tap node T1 to
ground (including the load impedance Z.sub.L1). Vp.sup.1.sub.R is a
positive sequence pre-fault complex voltage from the receiving end
R to ground. Ip.sup.1.sub.R,T1 is a positive sequence pre-fault
complex current from the receiving end R to the equivalent tap node
T1. Z.sup.1.sub.T1,R is a positive sequence complex impedance from
the equivalent tap node T1 to the receiving end R.
[0040] The values Vp.sup.1.sub.S, Ip.sup.1.sub.S,T1,
Vp.sup.1.sub.R, and Ip.sup.1.sub.R,T1 are measured values. The
values Z.sup.1S,T1 and Z.sup.1.sub.T1,R are calculated values,
which may be calculated from the distance of the equivalent
transmission line segment and the characteristics of the
transmission line using well known conventional methods.
[0041] FIG. 4a illustrates exemplary faulted conditions on the
transmission line of FIG. 2 with an exemplary fault to the ground.
As shown in FIG. 4a, a fault node F is located on the transmission
line 10. The fault node F is located between the sending end S and
the equivalent tap node T1. As such, the fault provides a path to
ground with impedance Z.sub.F. Z.sup.1.sub.F is an equivalent
positive sequence fault impedance from the fault node F to ground
in the positive sequence network of the line.
[0042] As shown in FIG. 4a, the equivalent tap node T1 divides the
transmission line into the sending side 11 and the receiving side
12. The sending side 11 of the transmission line 10 has an
impedance of Z.sub.S,T1. The receiving side 12 of the transmission
line 10 has an impedance of Z.sub.R,T1.
[0043] The fault node F divides the impedance from sending end S to
tap node T1 into two impedances. The first impedance is
(m*Z.sub.S,T1) and the second impedance is ((1-m)*Z.sub.S,T1). In
one embodiment, for a distance of one from the sending end S to the
tap node T1, the fault node F lies a distance of m away from the
sending end S, and a distance of (1-m) from the tap node T1. For
example, if m is 0.4 and the distance between sending end S and tap
node T1 is ten miles, then the distance from the sending end S to
the fault node F is four miles and the distance from the fault node
F to the tap node T1 is six miles. More generally, the fault lies a
fraction of m between node h and node i, represented by
m.sub.h,F.
[0044] Referring to FIG. 4b, V.sup.1.sub.S is a positive sequence
faulted complex voltage from the sending end S to ground; V.sup.1
.sub.R is a positive sequence faulted complex voltage from the
receiving end R to ground; I.sup.1.sub.S,T1 is a positive sequence
faulted complex current from the sending end S to the equivalent
tap node T1; I.sup.1.sub.R,T1 is a positive sequence faulted
complex current from the receiving end R to the equivalent tap node
T1; Z.sup.1.sub.T1 is a positive sequence complex impedance from
the equivalent tap node T1 to ground (including the tapped load
impedance Z.sub.L1); The values V.sup.1.sub.S, I.sup.1.sub.S,T1,
V.sup.1.sub.R, and I.sup.1.sub.R, T1 are measured values.
[0045] The following assumptions are made: the tapped loads (e.g.,
tapped load LA) are positive sequence impedances which do not
change during the fault; there is only one single fault on the
transmission line; and all transmission line segments between tap
nodes have an approximately uniform impedance.
[0046] The present invention uses pre-fault voltage and current
measurements to find an equivalent tapped load and its proper
location to represent the equivalent impact of all tapped loads on
the line. Using pre-fault measurements, the system may determine
the time difference (or phasor angle difference) of the voltage and
current signals from both ends of a power transmission line to
synchronize the measured signals. If the data is already
synchronized, the phase angle is zero. Using the pre-fault data,
the system also determines the equivalent load impedance of the
equivalent tapped load. The synchronized faulted data and the
calculated equivalent tapped load impedance are used to perform the
initial fault location estimation. One calculation is performed
assuming that the fault is on the sending side 11 of the equivalent
tap node T1. A second calculation is performed assuming that the
fault is on the receiving side 12 of the equivalent tap node T1.
The final fault location is selected from the two calculations.
[0047] FIG. 5 is a block diagram of an exemplary embodiment of a
system in accordance with the present invention. As shown in FIG.
5, the system includes a processor 100, a memory 110, a sending end
measuring device 120, and a receiving end measuring device 130.
[0048] The processor 100 may be any processor suitable for
performing calculations and receiving input data from measuring
devices. For example, the processor 100 may be a protective relay
with oscillographic data capture or a digital fault recorder. The
memory 110 may be used to store data received from the sending end
measuring device 120 and the receiving end measuring device
130.
[0049] The sending end measuring device 120 measures voltage and
current, including both pre-fault and faulted measurements, at the
sending end S of the transmission line 10. The sending end
measuring device 120 may comprise a memory 115 to store pre-fault
measurements. The sending end measuring device 120 may comprise a
voltage sensor 121 and a current sensor 122. The voltage sensor 121
and current sensor 122 may output an analog signal. The sending end
measuring device 120 may convert the analog signal to a digital
signal using known analog to digital techniques before transmission
over data link 135. The sending end measuring device 120 may
further convert the digital signal into vectors representing
current and voltage, Vp.sup.1.sub.S, Ip.sup.1.sub.S,T1,
V.sup.1.sub.S, and I.sup.1.sub.S,T1 at the sending end S.
[0050] The receiving end measuring device 130 measures voltage and
current, including both pre-fault and faulted measurements, at the
receiving end R of the transmission line 10. The receiving end
measuring device 130 may comprise a memory 115 to store pre-fault
measurements. The receiving end measuring device 130 may comprise a
voltage sensor 121 and a current sensor 122. The voltage sensor and
current sensor may output an analog signal. The receiving end
measuring device 130 may convert the analog signal to a digital
signal using known analog to digital techniques before transmission
over data link 135. The receiving end measuring device 130 may
further convert the digital signal into vectors representing
current and voltage, Vp.sup.1.sub.R, Ip.sup.1.sub.R,T1,
V.sup.1.sub.R, and I.sup.1.sub.R,T1 at the receiving end R.
[0051] The measuring devices 120, 130 are connected to the
processor 100 via a data link 135. The data link 135 may be a
modem, a local area network, or any suitable data link.
[0052] FIG. 6 is a flow chart showing further details of the
operation of the system of FIG. 5 and of a method in accordance
with the present invention. As shown in FIG. 6, at step 200, the
measured values are obtained. The pre-fault measured values are
Vp.sup.1.sub.S, Ip.sup.1.sub.S,T1 Vp.sup.1.sub.R, and
Ip.sup.1.sub.R,T1. The faulted measured values are V.sup.1.sub.S,
I.sup.1.sub.S,T1, V.sup.1.sub.R, and I.sub.R,T1.
[0053] At step 205, the equivalent tap location, m.sub.S,T1, of the
equivalent tapped load is calculated. The voltage at equivalent
tapped load location, m.sub.S,T1, is calculated from the
measurements of both ends as follows:
Vp.sub.T1.sup.1=Vp.sub.S.sup.1-m.sub.S,T1Z.sub.S,R.sup.1Ip.sub.S,T1.sup.1
Equation 1
Vp.sub.T1.sup.1=e.sup.j.delta.(Vp.sup.1.sub.R-(1-m.sub.S,T1)Z.sub.S,R1.sup-
.1Ip.sup.1.sub.R,T1) Equation 2
[0054] where .delta. is the phase angle representing a
synchronization error between measurements taken at the sending end
S and the receiving end R of the line, and Z.sup.1.sub.S, R is the
total line impedance between sending end S and the receiving end R.
The magnitudes of the complex voltage at the equivalent tapped load
location, as calculated by both equations, should be equal at the
equivalent tapped load location, which leads to a quadratic
equation of m.sub.S,T1 that can be derived from the above two
equations:
a(m.sub.S,T1).sup.2+bm.sub.S,T1+c+0 Equation 3
[0055] where
a=.vertline.Z.sub.S,R.sup.1.vertline..sup.2.vertline.I.sub.S,T1.sup.1.vert-
line..sup.2-.vertline.Z.sub.S,R.sup.1.vertline..sup.2.vertline.I.sub.R,T1.-
sup.1.vertline..sup.2 Equation 4
b=-2(C.sub.1R.sub.S,R.sup.1-C.sub.2X.sub.S,R.sup.1)-2(C.sub.3R.sub.S,R.sup-
.1-C.sub.4X.sub.S,R.sup.1)+2.vertline.Z.sub.S,R.sup.1.vertline..sup.2.vert-
line.I.sub.R,T1.sup.1.vertline..sup.2 Equation 5
c=.vertline.Vp.sub.S.sup.1.vertline..sup.2-.vertline.Vp.sub.R.sup.1.vertli-
ne..sup.2+2(C.sub.3R.sub.S,R.sup.1-C.sub.4X.sub.S,R.sup.1)-.vertline.Z.sub-
.S,R.sup.1.vertline..sup.2.vertline.I.sub.R,T1.sup.1.vertline..sup.2
Equation 6
[0056] with
C.sub.1=Re.left brkt-bot.Ip.sub.S,T1.sup.1(VP.sub.S.sup.1)*.right
brkt-bot. Equation 7
C.sub.2=Im.left brkt-bot.Ip.sub.S,T1.sup.1(Vp.sub.S.sup.1)*.right
brkt-bot. Equation 8
C.sub.3=Re.left brkt-bot.Ip.sub.R,T1.sup.1(Vp.sub.R.sup.1)*.right
brkt-bot. Equation 9
C.sub.4=Im.left brkt-bot.Ip.sub.R,T1.sup.1(Vp.sub.R.sup.1)*.right
brkt-bot. Equation 10
R.sub.S,R.sup.1=Re.left brkt-bot.Z.sub.S,R.sup.1.right brkt-bot.
Equation 11
[0057] and
X.sub.S,R.sup.1=Im.left brkt-bot.Z.sub.S,R.sup.1.right brkt-bot.
Equation 12
[0058] Solving the quadratic equation of m.sub.S, T1 yields two
solutions. The correct m.sub.S, T1 is the one that satifies the
condition of 0.ltoreq.m.sub.S,T1.ltoreq.1. The equivalent line
impedance on both sides of the equivalent tapped load thus can be
computed from the equivalent tapped load location as
Z.sub.S,T1.sup.1=m.sub.S,T1Z.sub.S,R.sup.1 Equation 13
[0059] and
Z.sub.T1,R.sup.1=(1-m.sub.S,T1)Z.sub.S,R.sup.1 Equation 14
[0060] At step 210, the phase angle difference, .delta., is
calculated as a vector e.sup.J.delta.if the data is unsynchronized,
using pre-fault data according to the following equation. If the
data is synchronized, the phase angle difference is zero. 1 e j =
Vp S 1 - Z S , T1 1 Ip S , T1 1 Vp R 1 - Z R , T1 1 Ip R , T1 1
Equation 15
[0061] At step 220, the equivalent load impedance of equivalent tap
node T1 is calculated using pre-fault data and the phase angle
difference according to the following equation. 2 Z T1 1 = Vp T1 1
Ip S , T1 1 + e j Ip R , T1 1 = Vp S 1 - Z S , T1 1 Ip S , T1 1 Ip
S , T1 1 + e j Ip R , T1 1 Equation 16
[0062] At step 230, a first fault location, m.sub.S, F is
calculated assuming that the fault node F is located on the sending
side 11. The first fault location is calculated from Equation 17. A
universal network is used for all fault types. The fault impedance
is represented in a positive sequence network as a balanced
three-phase impedance network connected at the fault location to
form the universal network. In this manner, a fault location may be
calculated for any types of fault. 3 m S , F = V S 1 - e j V R 1 +
Z R , T1 1 e j I R , T1 1 + Z S , T1 1 ( e j I R , T1 1 - e j V R 1
- Z R , T1 1 e j I R , T1 1 Z T1 1 ) Z S , T1 1 I S , T1 1 + Z S ,
T1 1 ( e j I R , T1 1 - e j V R 1 - Z R , T1 1 e j I R , T1 1 Z T1
1 ) Equation 17
[0063] At step 240, a second fault location, m.sub.R,F is
calculated assuming that the fault node F is located on the
receiving side 12. The second fault location is calculated from
Equation 18. 4 m R , F = e j V R 1 - V S 1 + Z S , T1 1 I S , T1 1
+ Z R , T1 1 ( I S , T1 1 - V S 1 - Z S , T1 1 I S , T1 1 Z T1 1 )
Z R , T1 1 e j I R , T1 1 + Z R , T1 1 ( I S , T1 1 - V S 1 - Z S ,
T1 1 I S , T1 1 Z T1 1 ) Equation 18
[0064] At step 250 the final solution is selected. When a correct
assumption is made, the resulting fault location estimation is
always within some predetermined range, if not, the result will be
outside of the predetermined range. This criterion is used to
select the accurate fault location result from the two estimations.
The predetermined range is a range selected to represent the full
distance between two nodes. In the present embodiment, the
predetermined range is from zero to 1.0, which represent the
distance between the sending node S and the equivalent tap node T1
when assuming that the fault lies between the sending node S and
the equivalent tap node T1. A result outside of the predetermined
range cannot be correct, as it lies at a point outside of the
distance between the two nodes. For example, using a unitary
predetermined value of m, where the range of 0.0 to 1.0 represents
the distance between two nodes, if m.sub.S,T1 is calculated to be
2.4 in step 230 and m.sub.R,T1 is calculated to be 0.4 in step 240,
then m.sub.R,T1 is selected, m=0.4, and the fault node F is on the
receiving side 12. Selecting 2.4 would be contrary to the
assumption that the fault is located on the sending side 11.
[0065] In an alternate embodiment, the phase angle may be
calculated prior to calculating the equivalent tap location.
[0066] In another embodiment, the transmission line is a single
phase transmission line, the equations are the same except that the
references to the positive sequence impedance is removed, and the
equivalent fault impedance is the actual fault impedance.
[0067] As can be appreciated, the above described system and method
meet the aforementioned need for systems and methods for
calculating a fault location in a transmission line with multiple
tapped loads using synchronized or unsynchronized measured data
from two ends.
[0068] Although not required, the present invention may be embodied
in the form of program code (i.e., instructions) stored on a
computer-readable medium, such as a magnetic, electrical, or
optical storage medium, including without limitation a floppy
diskette, CD-ROM, CD-RW, DVD-ROM, DVD-RAM, magnetic tape, flash
memory, hard disk drive, or any other machine-readable storage
medium, wherein, when the program code is loaded into and executed
by a machine, such as a computer, the machine becomes an apparatus
for practicing the invention. The present invention may also be
embodied in the form of program code that is transmitted over some
transmission medium, such as over electrical wiring or cabling,
through fiber optics, over a network, including the Internet or an
intranet, or via any other form of transmission, wherein, when the
program code is received and loaded into and executed by a machine,
such as a computer, the machine becomes an apparatus for practicing
the invention. When implemented on a general-purpose processor, the
program code combines with the processor to provide a unique
apparatus that operates analogously to specific logic circuits.
[0069] It is to be understood that the foregoing examples have been
provided merely for the purpose of explanation and are in no way to
be construed as limiting of the present invention. Where the
invention has been described with reference to embodiments, it is
understood that the words which have been used herein are words of
description and illustration, rather than words of limitation.
Further, although the invention has been described herein with
reference to particular structure, materials and/or embodiments,
the invention is not intended to be limited to the particulars
disclosed herein. Rather, the invention extends to all functionally
equivalent structures, methods and uses, such as are within the
scope of the appended claims. Those skilled in the art, having the
benefit of the teachings of this specification, may effect numerous
modifications thereto and changes may be made without departing
from the scope and spirit of the invention in its aspects.
* * * * *