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Low-frequency dispersion characteristics of a multilayered coaxial cable

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Abstract

This paper provides an exact asymptotic analysis regarding the low-frequency dispersion characteristics of a multilayered coaxial cable. A layer-recursive description of the dispersion function is derived that is well suited for asymptotic analysis. The recursion is based on two well-behaved (meromorphic) subdeterminants defined by a perfectly electrically conducting (PEC) and a perfectly magnetically conducting termination, respectively. For an open waveguide structure, the dispersion function is a combination of two such functions, and there is only one branch point that is related to the exterior domain. It is shown that if there is one isolating layer and a PEC outer shield, then the classical Weierstrass preparation theorem can be used to prove that the low-frequency behavior of the propagation constant is governed by the square root of the complex frequency, and an exact analytical expression for the dominating term of the asymptotic expansion is derived. It is furthermore shown that the same asymptotic expansion is valid to its lowest order even if the outer shield has finite conductivity and there is an infinite exterior region with finite nonzero conductivity. As a practical application of the theory, a high-voltage direct current (HVDC) power cable is analyzed and a numerical solution to the dispersion relation is validated by comparisons with the asymptotic analysis. The comparison reveals that the low-frequency dispersion characteristics of the power cable is very complicated and a first-order asymptotic approximation is valid only at extremely low frequencies (below 1 Hz). It is noted that the only way to come to this conclusion is to actually perform the asymptotic analysis. Hence, for practical modeling purposes, such as with fault localization, an accurate numerical solution to the dispersion relation is necessary and the asymptotic analysis is useful as a validation tool.

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Notes

  1. In [10] and [1] the frequency ranges considered are 0 Hz to 600 Hz and 1 Hz to 10 MHZ, respectively.

  2. To make the square root unique, its phase angle is chosen as \(-\pi <\arg \kappa _i\le 0\).

  3. Note that the TE and TM field components are generally coupled via the boundary conditions but are always decoupled for the axial-symmetric \(\mathrm TM _{0n}\) and \(\mathrm TE _{0n}\) modes.

References

  1. Amekawa N, Nagaoka N, Baba Y (2003) Derivation of a semiconducting layer impedance and its effect on wave propagation characteristics on a cable. IEE proceedings on generation, transmission and distribution 150(4):434–441

    Google Scholar 

  2. Boggs S, Pathak A, Walker P (1996) Partial discharge. XXII. High frequency attenuation in shielded solid dielectric power cable and implications thereof for PD location. IEEE Electr Insulation Mag 12(1):9–16

    Article  Google Scholar 

  3. Lundbäck J, Nordebo S, Biro T (2008) A digital directional coupler with applications to partial discharge measurements. IEEE Trans Instrum Meas 57(11):2561–2567

    Article  Google Scholar 

  4. Nordebo S, Nilsson B, Biro T, Cinar G, Gustafsson M, Gustafsson S, Karlsson A, Sjöberg M (2011) Electromagnetic dispersion modeling and measurements for HVDC power cables. Technical Report LUTEDX/(TEAT-7211)/1-32/(2011), Lund University, Department of Electrical and Information Technology, P.O. Box 118, S-221 00 Lund, Sweden. http://www.eit.lth.se

  5. Pommerenke D, Strehl T, Heinrich R, Kalkner W, Schmidt F, Weissenberg W (1999) Discrimination between interal PD and other pulses using directional coupling sensors on HV cable systems. IEEE Trans Dielectr Electr Insulation 6(6):814–824

    Article  Google Scholar 

  6. Steinbrich K (2005) Influence of semiconducting layers on the attenuation behaviour of single-core power cables. IEE proceedings on generation, transmission and distribution 152(2):271–276

    Article  Google Scholar 

  7. Stone GC (2005) Partial discharge diagnostics and electrical equipment insulation condition assessment. IEEE transactions on dielectrics and electrical insulation 12(5):891–905

    Google Scholar 

  8. Veen J (2005) On-line signal analysis of partial discharges in medium-voltage power cables. PhD thesis, Eindhoven University of Technology, The Netherlands

  9. Gardiol FE (1987) Lossy transmission lines. Artech House, Boston

  10. Carson JR, Gilbert JJ (1921) Transmission characteristic of the submarine cable. J Franklin Inst 192(6):705–735

    Article  Google Scholar 

  11. Lundstedt J (1995) Condition for distortionfree transmission lines with a nonuniform characteristic impedance. IEEE Trans Microwave Theory Tech 43(6):1386–1389

    Article  ADS  Google Scholar 

  12. Papazyan R, Pettersson P, Pommerenke D (2007) Wave propagation on power cables with special regard to metallic screen design. IEEE Trans Dielectr Electr Insulation 14(2):409–416

    Article  Google Scholar 

  13. Tai CT (1983) Dyadic Green’s functions for a coaxial line. IEEE Trans Antennas Propagat 31(2):355–358

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Hörmander L (1983) The analysis of linear partial differential operators I. Grundlehren der mathematischen Wissenschaften 256. Springer, Berlin

  15. Collin RE (1991) Field theory of guided waves, 2nd edn. IEEE Press, New York

    MATH  Google Scholar 

  16. Felsen LB, Marcuvitz N (1994) Radiation and scattering of waves. IEEE Press, Piscataway (Originally published by Prentice-Hall in 1973)

  17. Olyslager F (1999) Electromagnetic waveguides and transmission lines. Clarendon Press, Oxford

    MATH  Google Scholar 

  18. Olver FWJ (1997) Asymptotics and special functions. A K Peters, Ltd., Natick

    MATH  Google Scholar 

  19. Olver FWJ, Lozier DW, Boisvert RF, Clark CW (2010) NIST handbook of mathematical functions. Cambridge University Press, New York

    MATH  Google Scholar 

  20. Nilsson B, Cinar G, Nordebo S, Cinar OY (2012) Asymptotic methods for long distance monitoring of power cables. In: The 6th international conference on inverse problems: modeling and simulation, pp 206–207. Antalya, Turkey, May 2012

  21. Jackson JD (1999) Classical electrodynamics, 3rd edn. Wiley, New York

    MATH  Google Scholar 

  22. Pozar DM (2005) Microwave engineering, 3rd edn. Wiley, New York

    Google Scholar 

  23. Boström A, Kristensson G, Ström S (1991) Field representations and introduction to scattering, acoustic, electromagnetic and elastic wave scattering. In: Varadan VV, Lakhtakia A, Varadan VK (eds) Transformation properties of plane, spherical and cylindrical scalar and vector wave functions, Chap. 4. Elsevier Science Publishers, Amsterdam, pp 165–210

    Google Scholar 

Download references

Acknowledgments

This work was supported in part by the Swedish Research Council (VR) and ABB AB. The authors are also grateful to ABB AB for providing the opportunity to perform the cable measurements on their premises.

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Authors and Affiliations

  1. School of Computer Science, Physics and Mathematics, Linnæus University, 351 95 , Växjö, Sweden

    Sven Nordebo, Börje Nilsson & Stefan Gustafsson

  2. School of Engineering, Jönkö** University, 551 11 , Jönkö**, Sweden

    Thomas Biro

  3. Electronics Engineering Department, Gebze Institute of Technology, 414 00 , Gebze, Kocaeli, Turkey

    Gökhan Cinar

  4. Department of Electrical and Information Technology, Lund University, Box 118, 221 00 , Lund, Sweden

    Mats Gustafsson & Anders Karlsson

  5. ABB AB, 371 23 , Karlskrona, Sweden

    Mats Sjöberg

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  1. Sven Nordebo
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Correspondence to Sven Nordebo.

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Nordebo, S., Nilsson, B., Gustafsson, S. et al. Low-frequency dispersion characteristics of a multilayered coaxial cable. J Eng Math 83, 169–184 (2013). https://doi.org/10.1007/s10665-012-9616-3

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