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Passive approximation and optimization with B-splines
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.
Lund University.
KTH Royal Institute of Technology.
Stockholm University.
Show others and affiliations
2017 (English)Report (Other academic)
Abstract [en]

A passive approximation problem is formulated where the target function is an arbitrary complex valued continuous function defined on an approximation domain consisting of a closed interval of the real axis. The approximating function is any Herglotz function with a generating measure that is absolutely continuous with Hölder continuous density in an arbitrary neighborhood of the approximation domain. The norm used is induced by any of the standard Lp-norms where 1 ≤ p ≤ ∞. The problem of interest is to study the convergence properties of simple Herglotz functions where the generating measures are given by finite B-spline expansions, and where the real part of the approximating functions are obtained via the Hilbert transform. In practice, such approximations are readily obtained as the solution to a finite- dimensional convex optimization problem. A constructive convergence proof is given in the case with linear B-splines, which is valid for all Lp-norms with 1 ≤ p ≤ ∞. A number of useful analytical expressions are provided regarding general B-splines and their Hilbert transforms. A typical physical application example is given regarding the passive approximation of a linear system having metamaterial characteristics. Finally, the flexibility of the optimization approach is illustrated with an example concerning the estimation of dielectric material parameters based on given dispersion data. 

Place, publisher, year, edition, pages
2017. , p. 24
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Physics, Waves and Signals
Identifiers
URN: urn:nbn:se:lnu:diva-63878OAI: oai:DiVA.org:lnu-63878DiVA, id: diva2:1096530
Funder
Swedish Foundation for Strategic Research , AM13-0011Available from: 2017-05-18 Created: 2017-05-18 Last updated: 2017-06-09Bibliographically approved
In thesis
1. Estimation of electromagnetic material properties with application to high-voltage power cables
Open this publication in new window or tab >>Estimation of electromagnetic material properties with application to high-voltage power cables
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Efficient design of high-voltage power cables is important to achieve an economical delivery of electric power from wind farms and power plants over the very long distances as well as the overseas electric power. The main focus of this thesis is the investigation of electromagnetic losses in components of high-voltage power cables. The objective of the ongoing research is to develop the theory and optimization techniques as tools to make material choices and geometry designs to minimize the high-frequency attenuation and dispersion for HVDC power cables and the power losses associated with HVAC cables. Physical limitations, dispersion relationships and the application of sum rules as well as convex optimization will be investigated to obtain adequate physical insight and a priori modeling information for these problems.

For HVAC power cables, the objectives are addressed by performing measurements and estimation of complex valued permeability of cable armour steel in Papers I and II. Efficient analytical solutions for the electromagnetic field generated by helical structures with applications for HVAC power cables have been obtained in Paper III.

For HVDC power cables, estimation of insulation characteristics from dielectric spectroscopy data using Herglotz functions, convex optimization and B-splines, has been investigated in Papers V and VI. The unique solution requirements in waveguide problems have been reviewed in Paper IV.

Place, publisher, year, edition, pages
Linnaeus University Press, 2017. p. 19
Series
Lnu Licentiate ; 2
Keywords
Material losses, power cables, cylindrical multipole expansion, Herglotz functions, convex optimization, sum rules
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Physics, Waves and Signals
Identifiers
urn:nbn:se:lnu:diva-64265 (URN)978-91-88357-77-9 (ISBN)
Presentation
2017-06-14, C1202, Newton, Hus C, Växjö, 10:15 (English)
Opponent
Supervisors
Funder
Swedish Foundation for Strategic Research , AM13-0011
Available from: 2017-06-09 Created: 2017-06-09 Last updated: 2017-09-01Bibliographically approved

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Ivanenko, YevhenNilsson, BörjeNordebo, SvenToft, Joachim

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