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Measurement of the frequency dependent impedance
of a thin wire with ground return
Magnus Akke 2004-04-115 Industriell Elektroteknik
och Automation magnus.akke_at_iea.lth.se
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Outline

• Introduction
• Measurements
• Comparison with models
• Discussion and conclusion

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Motivation for measurements

• Relay testing
• Transient based fault location
• Insulation coordination
• Power line carrier

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Decouple 3-phase line
3-phase line has one ground mode and two aerial
modes. Focus on ground mode.
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Task 1 Measure impedance vs frequency for 1500
meter wire with ground return
Task 2 Compare with models
1500 m
ChA
ChB
Scope
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What to expect? Quick and dirty, use handbook
TEFYMA
Approximate inductance with two lines. Return
line is the mirror image. Distance between wire
and mirror image is 2 m. Resistance from
DC-measurement.
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TEFYMA model Impedance vs Frequency
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Measurement setup
1500 m
ChA
ChB
Scope
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Measurement execution
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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.
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Transmission line theory cont.
Re-write and let
Calculation using Laplace gives
where
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Transmission line with load
Line model
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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 currents
  return path.
• Carson (1926) used Maxwells 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 Carsons 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
• Carsons model is reasonable up to 100 kHz.

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Relevance for typical transmission line?
Height15 m, area500mm2, length300 km, R_flt5
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