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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=
Z0L =
k0 =
ZAPP
• Can cause overreach or underreach
1
Solving for Line Impedances
Traditional Method Is Prone to Errors
Can be complex
and tedious
zaa   ra  rd   jk ln D e  / mile
D
sa
zbb   rb  rd  
D
jk ln D e
sb
 / mile
zcc   rc  rd   jk ln D e  / mile
D
sc
zab  rd  jk ln D e  / mile
D
ab
zbc  rd 
D
jk ln D e
bc
 / mile
zac  rd  jk ln D e  / mile
D
ca
2
where:
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
1
2
2
V
V
3
Single-Phase-to-Ground Test
Test Set
3
Phase-to-Phase Test
• 7 tests
(no mutual coupling)
1
2
V
1
3
• 21 tests
(mutual coupling)
Three-Phase-to-Ground Test
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
x
x
Probes
Ground
x
x
• Outer probes generate known current
• Voltage is measured between inner probes
• ρ is calculated from resistance as well as
spacing and depth of probes
How Important Is ρ?
• 1 ≤ ρ ≤ 100
• No change in Z1L
+
Each modeled with:
– Continuous ground wire
– Segmented ground wire
• Big change in Z0L
♦
Resistance 148%
♦
Reactance 144%
• More effect on lines
with segmented or
no ground wires
– No ground wire
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
R
S
Solve for Z2L and Z0L
N1
E1S
Z1S
E1R
m • Z1L
(1 – m) • Z1L
Z1R
N2
I2S
–
V2S
Z2S +
I0S
–
V0S
Z0S +
m • Z2L
–
V2R
V2F
(1 – m) • Z2L + Z2R I2R
N0
m • Z0L
–
V0R
V0F
(1 – m) • Z0L + Z0R I0R
6
3Rf
Zero-Sequence Mutual Coupling Error
S
R
Relay
Location
Line A
m
Z0M
Line B
Relay
Location
mZ0L
S
Z0S
F0
I0
(1 – m)Z0L
R
Z0R
I0A
mZ0M
Z0L
(1 – m)Z0M
I0B
N0
Zero-Sequence Mutual Coupling Error
Relay
Location
mZ0L
S
Z0S
F0
I0
(1 – m)Z0L
R
Z0R
I0A
mZ0M
Z0L
(1 – m)Z0M
I0B
N0
• Relay only sees I0A, not I0B
• 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
Z2L and Z0L
• Compare results to impedances in model
Calculating Error – Traditional Method
jX
7.832
7.757
Actual = 7.8Ð84°
Calculated = 7.9Ð82°
Misleading in rectangular
form and degrees
Calculated
1° 2°
100% Error
}
35% Error
0.815 1.099
R
8
Actual
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 Z2L
• Low errors in Z0L with no mutual coupling
• High errors in Z0L in most cases of mutual
coupling (expected)
9
Three Outliers
• Line length
• Number, areas, and percentage of
lines coupled
New Fault Locations
• Z0L error increases
• Interplay between currents may lead to
good results despite mutual coupling
10
Conclusions From Simulations
Reliable  Z2L
Reliable  Z0L with no mutual coupling
Not Reliable X Z0L with mutual coupling
Using Event Data
11
Event 1
• Accurate Z2L
• Error in Z0L
(due to mutual
coupling)
Event 2
• Accurate Z2L
• Accurate Z0L
(no mutual
coupling)
12
Event 3
Fast breaker
clearing results in
Z2L and Z0L 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
Use External Fault Data
VS
IR
IS
VR
m
ZL
• 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 Z0L 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 Z2L and Z0L can cause
misoperations
• Event reports after a line-to-ground
fault help to validate impedances
• Investigate any error in Z2L
• Investigate any error in Z0L for lines
without coupling
18
Questions?
19