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3 Motivation for measurements Relay testing Transient based fault location Insulation coordination Power line carrier
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Measurement of the frequency dependent impedance of a thin
wire with ground return
Magnus Akke2004-04-115
Industriell Elektroteknik och [email protected]
2
Outline
– Introduction – Measurements– Comparison with models– Discussion and
conclusion
3
Motivation for measurements
• Relay testing• Transient based fault location • Insulation coordination• Power line carrier
4
Decouple 3-phase line
333231
232221
131211
phase
lllllllll
L
minus
plus
zero
comp. sym.
000000
ll
lL
321zero3 LLL IIII
3-phase line has one ground mode and two aerial modes. Focus on ground mode.
5
Task 1: Measure impedance vs frequency for 1500 meter wire with ground return
ScopeChA
1
23
4
6
1500 m
5ChB
Task 2: Compare with models
6
What to expect? Quick and dirty, use handbook TEFYMA
ladL r
)ln(
40
Approximate inductance with two lines. Return line is the mirror image. Distance between wire and mirror image is 2 m. Resistance from DC-measurement.
Hz) 50at kmper ohm 1( mH 5m 2 mm; 690 m; 1500
Ld.al
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TEFYMA model – Impedance vs Frequency
8
Measurement setup
ScopeChA
1
23
4
6
1500 m
5ChB
9
Measurement execution
10
Measured and expected result
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Transmission line theory
References: Hallén, E., Elektricitetslära, Almqvist & Wiksells, 1953.
Claesson, I., et al, Analoga kretsar och signaler, Studentlitteratur, 1993.
xx x
),( txi xr xl
),( txv xg xc
),( txxi
),( txxv
),(),(),(),( txxvt
txxixltxxixrtxv
),(),(),(),( txxit
txvxctxvxgtxi
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Transmission line theory cont.Re-write and let 0x
ttxvcvg
xtxi
ttxilir
xtxv
),(),(
),(),(
Calculation using Laplace gives
),0(),0(
),(),(
sIsV
KsxIsxV
)()( lsrcsg
where
)()(
0 csglsrZ
)cosh()sinh()sinh()cosh(
Kwith 0
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xxxZx
DCBA
Z
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Transmission line with load
0x
),0( sI
),0( sV
Line model
DCBA
K
),( sdI
),( sdV
dx
LZ
DZCBZA
sIsVsZ
L
Lin
),0(),0()(
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Transmission line model with fixed parameters
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Frequency dependent parameters
• Fixed parameters works well with metallic return, but fails when ground is used as the current’s return path.
• Carson (1926) used Maxwell’s equation to make a line model where the effect of ground losses and current distribution are embedded in frequency dependent line parameters R and L.
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Model with Carson’s frequency dependent parameters
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Frequency dependence by Carson and ad-hoc grounding model
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Discussion • Model with lumped inductance and
resistance is only valid at
• Transmission line model with fixed parameters is insufficient. Results in poor model and inefficient simulation
• Carson’s model is reasonable up to 100 kHz.
kHz 2581
dcf
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Relevance for typical transmission line?
Height=15 m, area=500mm2, length=300 km, R_flt=5 ohm
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Conclusion• Theory and measurements are needed
to verify and develop models.• Measurement shows un-modeled
dynamics.• Further work
– High frequency modeling of line– Include dynamics of connection between
line and ground, e.g, ground rod or fault– Bounded line length
