Validating Transmission Line
Impedances Using Known Event Data
Ariana Amberg, Alex Rangel, and Greg Smelich
Schweitzer Engineering Laboratories, Inc.
Copyright © SEL 2012
Why Are Line Impedances Important?
•
Used in distance element operation
ρ = Z
0L
= k0 = Z
APP
•
Can cause overreach or underreach
1

Solving for Line Impedances
Traditional Method Is Prone to Errors
Can be complex and tedious z aa z bb z cc
  r a
 r d
 j k ln
D e
D sa
  r b
 r d
 j k ln
D e
D sb
  r c
 r d
 j k ln
D e
D sc

/ mile

/ mile

/ mile z ab r d j k ln
D e
D ab

/ mile z bc r j k ln
D e
D bc

/ mile z ac r j k ln
D e
D ca

/ mile where:
2

Software Tools Improve Analysis
•
• Number and type of phase and ground conductors
(databases included)
Distances
• Ground resistivity
• Bundling • Line segment models
Test Equipment Measures Impedances
Test Set Test Set
V
1
2
3
V
1
2
3
Single-Phase-to-Ground Test Phase-to-Phase Test
Test Set
V
1
2
3
Three-Phase-to-Ground Test
•
7 tests
(no mutual coupling)
• 21 tests
(mutual coupling)
3

Ground Resistivity ( ρ) Depends on
Soil Moisture and Temperature
Courtesy of the FCC Encyclopedia
Utility Survey Results
•
10 to 200
Ω-m
•
Various methods
♦ Use single ρ value everywhere
♦
♦
Measure areas of system and use generalized
ρ values across those areas
Measure average across system and use everywhere
♦ Measure at new stations or along right of way
4

Measure ρ: Wenner Four-Point Method
V Ground x x x x
Probes
• Outer probes generate known current
• Voltage is measured between inner probes
• ρ is calculated from resistance as well as spacing and depth of probes
+
Each modeled with:
– Continuous ground wire
– Segmented ground wire
– No ground wire
How Important Is ρ?
• 1 ≤ ρ ≤ 100
•
No change in Z
1L
•
Big change in Z
0L
♦ Resistance 148%
♦ Reactance 144%
•
More effect on lines with segmented or no ground wires
5

Validate Impedances Using Event Data
Data Needed After Line-to-Ground Fault
• Voltages and currents from both ends
• Known fault location
Bus S Bus R m
S R
E
1S
Z
1S
Solve for Z
2L
and Z
0L
N1 m • Z
1L
(1 – m) • Z
1L
E
1R
Z
1R
I
2S Z
2S
–
V
2S
+ m • Z
2L
N2
V
2F
(1
– m) • Z
2L
–
V
2R
+ Z
2R
I
2R
3R f
I
0S
–
Z
0S
V
0S
+ m • Z
0L
N0
V
0F
(1 – m) • Z
0L
–
V
0R
+ Z
0R
I
0R
6

Zero-Sequence Mutual Coupling Error
S
Relay
Location Line A m
Z
0M
Line B
Z
0S
S
I
0A
Relay
Location mZ
0L
F
0
I
0
(1
– m)Z
0L
I
0B mZ
0M
Z
0L
(1
– m)Z
0M
R
Z
0R
R
N
0
Zero-Sequence Mutual Coupling Error
Z
0S
S
I
0A
Relay
Location mZ
0L
F
0
I
0
(1 – m)Z
0L
I
0B mZ
0M
Z
0L
(1
– m)Z
0M
R
Z
0R
N
0
• Relay only sees I
0A
, not I
0B
• Voltage measurement includes mutual coupling
• Method does not account for mutual coupling – errors expected
7

Verify Method Through Simulation
• Create model with known data
♦ Transmission line impedances
♦ Fault location
•
Use negative- and zero-sequence voltages, currents, and fault location ( m ) to calculate
Z
2L
and Z
0L
•
Compare results to impedances in model
Calculating Error – Traditional Method
7.832
7.757
jX
Actual = 7.8
Ð
84
°
Calculated = 7.9
Ð
82
°
Misleading in rectangular form and degrees
0.815
1.099
35% Error
R
1
° 2
°
100% Error
Calculated
Actual
8

Calculating Error – Best Choice
• Polar form is more accurate
♦ Percent error for magnitude
♦ Degree difference for angle
•
Previous example shows
♦ Magnitude error = 1.28%
♦ Degree error = 2°
Simulation Results (Partial)
• Low errors in Z
2L
• Low errors in Z
0L
with no mutual coupling
• High errors in Z
0L
in most cases of mutual coupling (expected)
9

Three Outliers
•
Line length
• Number, areas, and percentage of lines coupled
New Fault Locations
•
Z
0L
error increases
• Interplay between currents may lead to good results despite mutual coupling
10

Conclusions From Simulations
Reliable  Z
2L
Reliable  Z
0L
with no mutual coupling
Not Reliable X Z
0L
with mutual coupling
Using Event Data
11

Event 1
• Accurate Z
2L
• Error in Z
0L
(due to mutual coupling)
Event 2
• Accurate Z
2L
• Accurate Z
0L
(no mutual coupling)
12

Event 3
Fast breaker clearing results in
Z
2L
and Z
0L
errors
Line Impedance Calculator
13

Phenomena That Can Affect Results
Nontransposed Lines
•
Transposition assumed in symmetrical component domain
• Errors can occur when line is not transposed
• Nontransposed lines have coupling between sequence networks
14

Nontransposed Lines
• Three-phase fault on nontransposed line generates negative- and zerosequence currents
•
Faults make transposed lines nonhomogeneous
Problems Obtaining Stable Data
•
Fast breakers
•
CT saturation
•
CVT transients
• Evolving faults
• Changing fault resistance
•
CVTs + fast breakers
15

Fast Breakers
• Stable voltage and current difficult to find
• Time alignment and high sampling rate important
Future Considerations
16

V
S
I
S
Use External Fault Data
I
R
V
R m
Z
L
• Trigger events on Zone 2 forward or
Zone 3 reverse
•
Do not need fault location
•
Immune to nonhomogeneity
Unstable Data With Low Sampling Rates
How to Align Data Points
• Use synchrophasor measurements
• Align prefault data, calculate time shift, and resample at higher resolution
17

Improve Mutual Coupling Results
• Error in Z
0L
when lines are coupled
• Incorporation of coupled-line current
•
Complications from
♦
♦
♦
Multiple coupled lines
Coupling for a fraction of line length
Terminations of coupled lines at different locations than original line
Conclusions
•
Incorrect Z
2L
and Z
0L
can cause misoperations
• Event reports after a line-to-ground fault help to validate impedances
• Investigate any error in Z
2L
•
Investigate any error in Z
0L
for lines without coupling
18

19
Questions?