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

2. 2 Outline –Introduction –Measurements –Comparison with models –Discussion and conclusion

3. 3 Motivation for measurements Relay testing Transient based fault location Insulation coordination Power line carrier

4. 4 Decouple 3-phase line 3-phase line has one ground mode and two aerial modes. Focus on ground mode.

5. 5 Task 1: Measure impedance vs frequency for 1500 meter wire with ground return Scope ChA 1 2 3 4 6 1500 m 5 ChB Task 2: Compare with models

6. 6 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.

7. 7 TEFYMA model – Impedance vs Frequency

8. 8 Measurement setup Scope ChA 1 2 3 4 6 1500 m 5 ChB

9. 9 Measurement execution

10. 10 Measured and expected result

11. 11 Transmission line theory References: Hallén, E., Elektricitetslära, Almqvist & Wiksells, 1953. Claesson, I., et al, Analoga kretsar och signaler, Studentlitteratur, 1993.

12. 12 Transmission line theory cont. Re-write and let Calculation using Laplace gives where

13. 13 Transmission line with load Line model

14. 14 Transmission line model with fixed parameters

15. 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. 16 Model with Carson’s frequency dependent parameters

17. 17 Frequency dependence by Carson and ad-hoc grounding model

18. 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.

19. 19 Relevance for typical transmission line? Height=15 m, area=500mm2, length=300 km, R_flt=5 ohm

20. 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