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Low-frequency dispersion characteristics of a multilayered coaxial cable
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.ORCID iD: 0000-0002-7018-6248
Linnaeus University, Faculty of Technology, Department of Mathematics.
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.
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2013 (English)In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 83, no 1, 169-184 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer Netherlands, 2013. Vol. 83, no 1, 169-184 p.
National Category
Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Physics, Waves and Signals
Identifiers
URN: urn:nbn:se:lnu:diva-25989DOI: 10.1007/s10665-012-9616-3ISI: 000327855300009OAI: oai:DiVA.org:lnu-25989DiVA: diva2:624466
Available from: 2013-05-31 Created: 2013-05-31 Last updated: 2017-01-10Bibliographically approved
In thesis
1. Electromagnetic dispersion modeling and analysis for HVDC power cables
Open this publication in new window or tab >>Electromagnetic dispersion modeling and analysis for HVDC power cables
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Derivation of an electromagnetic model, regarding the wave propagation in a very long (10 km or more) High Voltage Direct Current (HVDC) power cable, is the central part of this thesis. With an existing “perfect” electromagnetic model there are potentially a wide range of applications.The electromagnetic model is focused on frequencies between 0 and 100 kHz since higher frequencies essentially will be attenuated. An exact dispersion relation is formulated and the propagation constant is computed numerically. The dominating mode is the first Transversal Magnetic (TM) mode of order zero, denoted TM01, which is also referred to as the quasi-TEM mode. A comparison is made with the second propagating TM mode of order zero denoted TM02. The electromagnetic model is verified against real time data from Time Domain Reflection (TDR) measurements on a HVDC power cable. A mismatch calibration procedure is performed due to matching difficulties between the TDR measurement equipment and the power cable regarding the single-mode transmission line model.An example of power cable length measurements is addressed, which reveals that with a “perfect” model the length of an 80 km long power cable could be estimated to an accuracy of a few centimeters. With the present model the accuracy can be estimated to approximately 100 m.In order to understand the low-frequency wave propagation characteristics, an exact asymptotic analysis is performed. It is shown that the behavior of the propagation constant is governed by a square root of the complex frequency in the lowfrequency domain. This thesis also focuses on an analysis regarding the sensitivity of the propagation constant with respect to some of the electric parameters in the model. Variables of interest when performing the parameter sensitivity study are the real relative permittivityand the conductivity.

Place, publisher, year, edition, pages
Växjö: , 2012. 10 p.
Keyword
HVDC power cables, electromagnetic model, TDR measurement, sensitivity analysis, dispersion relation, propagation constant, low-frequency asymptotics
National Category
Other Physics Topics
Identifiers
urn:nbn:se:lnu:diva-32525 (URN)
Presentation
2012-12-11, D1136, Växjö, 13:15 (English)
Opponent
Supervisors
Available from: 2014-08-19 Created: 2014-02-27 Last updated: 2014-08-19Bibliographically approved
2. Electromagnetic Dispersion Modeling and Analysis for Power Cables
Open this publication in new window or tab >>Electromagnetic Dispersion Modeling and Analysis for Power Cables
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis addresses electromagnetic wave propagation in power cables. It consists of five papers, where the three first papers are based on one and the same model, and the last two papers are based on a similar but slightly different model. The first model considers electromagnetic modeling in connection with basic transmission line theory with a mismatch calibration of the scattering parameters, while the second model is based on a magnetic frill generator with calibration on the input current.

The two models describe the dispersion characteristics of an 82 km long High Voltage Direct Current (HVDC) power cable, and the results are validated with Time Domain Reflectometry (TDR) measurements. In both models the relevant bandwidth is 100 kHz, with the result that the fields inside the metallic layers must be calculated due to a large skin-depth. The present study is concerned with Transversal Magnetic (TM) modes of order zero. Higher order TM modes, including the Transversal Electric (TE) modes, will essentially be cut-off in this low-frequency regime.

An asymptotic analysis regarding the low-frequency dispersion characteristics is provided in Paper I. Comparing the result with a numerical solution shows that the low-frequency characteristics of the power cable is complicated, and an asymptotic solution is only valid at frequencies below 1 Hz.

Paper II presents a sensitivity analysis of the propagation constant. It is concluded that some of the electrical parameters of the metallic layers, and of the insulating layer, have a large impact on the model, while other parameters do not perturb the model in any substantial way.

In Paper III a general framework for the electromagnetic modeling is provided. The paper addresses sensitivity analysis, computation, and measurements regarding wave propagation characteristics in power cables.

The asymptotic behavior of the non-discrete radiating mode, the branch-cut, is presented in Paper IV. The result is compared with the first and second propagating Transversal Magnetic (TM) mode.

Finally, Paper V addresses the numerical problems associated with large arguments in the Bessel functions, which are due to the large conductivity parameters of the metallic layers. The introduction of a perfect electric conductor (PEC) and a short illustration of an inverse problem are also discussed in the paper. At the end an analysis is presented regarding uncertainties in the model parameters, which shows that temperature is an important parameter to consider.

 

Place, publisher, year, edition, pages
Växjö: Linnaeus University Press, 2014
Series
Linnaeus University Dissertations, 182/2014
Keyword
power cable, electromagnetic model, dispersion relation, asymptotic analysis, sensitivity analysis
National Category
Physical Sciences
Identifiers
urn:nbn:se:lnu:diva-40651 (URN)978-91-87925-07-8 (ISBN)
Public defence
2014-10-23, D1136, Växjö, 10:00 (English)
Opponent
Supervisors
Available from: 2015-04-28 Created: 2015-03-07 Last updated: 2015-04-28Bibliographically approved

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