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Measurement of the frequency dependent impedance of a thin wire with ground return. Magnus Akke 200 4 -0 4 -1 15 Industriell Elektroteknik och Automation magnus.akke@iea.lth.se. Outline. Introduction Measurements Comparison with models Discussion and conclusion. - PowerPoint PPT Presentation
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Measurement of the frequency dependent impedance of a thin
wire with ground return
Magnus Akke
2004-04-115Industriell Elektroteknik och Automation
magnus.akke@iea.lth.se
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
lll
lll
lll
L
minus
plus
zero
comp. sym.
00
00
00
l
l
l
L
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
2
3
4
6
1500 m
5ChB
Task 2: Compare with models
6
What to expect? Quick and dirty, use handbook TEFYMA
la
dL 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 5
m 2 mm; 690 m; 1500
L
d.al
7
TEFYMA model – Impedance vs Frequency
8
Measurement setup
ScopeChA
1
2
3
4
6
1500 m
5ChB
9
Measurement execution
10
Measured and expected result
11
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
12
Transmission line theory cont.
Re-write and let 0x
t
txvcvg
x
txi
t
txilir
x
txv
),(),(
),(),(
Calculation using Laplace gives
),0(
),0(
),(
),(
sI
sVK
sxI
sxV
)()( lsrcsg
where
)(
)(0 csg
lsrZ
)cosh()sinh(
)sinh()cosh(Kwith
0
1
0
xx
xZx
DC
BA
Z
13
Transmission line with load
0x
),0( sI
),0( sV
Line model
DC
BAK
),( sdI
),( sdV
dx
LZ
DZC
BZA
sI
sVsZ
L
Lin
),0(
),0()(
14
Transmission line model with fixed parameters
15
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.
16
Model with Carson’s frequency dependent parameters
17
Frequency dependence by Carson and ad-hoc grounding model
18
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 258
1
d
cf
19
Relevance for typical transmission line?
Height=15 m, area=500mm2, length=300 km, R_flt=5 ohm
20
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
Recommended