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Current reconstruction from magnetic field using spherical harmonic expansion to reduce impact of disturbance fields
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.ORCID iD: 0000-0002-9665-8557
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.ORCID iD: 0000-0001-9241-8030
2016 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, 1-15 p.Article in journal (Refereed) Published
Abstract [en]

A current reconstruction method, for determining currents in a set of parallel infinitely long conductors located above the ground from measured magnetic field, is developed. The method is designed to work even if three-dimensional external disturbance fields from external sources are present. The external field is written as an expansion in spherical harmonics. Therefore, the field in the different measurement points is regarded as a linear combination of the expansion coefficients and the currents to be determined. A linear equation system is formed with the currents and the expansion coefficients as the unknowns. The currents are reconstructed by solving the equation system using least squares method and Tikhonov regularization. If the characteristics of the ground below the conductors are known with sufficient precision, the ground effect can also be included into the model. Results of various simulations show that the method works well and noise in the measured magnetic field can be handled.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2016. 1-15 p.
Keyword [en]
Current reconstruction, inverse source problem, power line measurements, spherical harmonics, Tikhonov regularization, Ground effect, Inverse problems, Least squares approximations, Linear equations, Magnetic field measurement, Magnetic fields, Magnetism, Spheres, Power lines, Harmonic analysis
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-197209DOI: 10.1080/17415977.2016.1201661ISI: 000399465600002Scopus ID: 2-s2.0-84976254217OAI: oai:DiVA.org:kth-197209DiVA: diva2:1055352
Note

QC 20161212

Available from: 2016-12-12 Created: 2016-11-30 Last updated: 2017-06-02Bibliographically approved
In thesis
1. Remote contact-free reconstruction of currents in two-dimensional parallel conductors
Open this publication in new window or tab >>Remote contact-free reconstruction of currents in two-dimensional parallel conductors
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, the theory of the remote contact-free reconstruction of currents in two-dimensional parallel conductors is investigated. The motivation of this study is finding a complement technique to measurement transformers which are the well-established devices to measure currents in power transmission lines. This technique would provide the possibility of measuring currents at different locations of a power system, as well as, at different frequencies.

 

Remote contact-free determination of currents is an electromagnetic inverse source problem in which the currents are reconstructed from the magnetic field data collected by a set of sensors located in the vicinity of the conductors. Since the sensors are not too close to the conductors, the main challenge is the effect of the disturbance fields produced by the external sources in the measurement.

 

In the case that the external sources produce three-dimensional disturbance fields, the magnetic field due to the external sources is expressed as a truncated expansion of the spherical harmonics and both the currents in the conductors and the expansion coefficients are determined by applying the least square method. To overcome the ill-posedness of the problem, the functional to be minimized is augmented by a Tikhonov regularization term that penalizes unphysical solutions introduced by the expansion coefficients.

 

Finally, the problem of selecting a limited number of optimal sensor positions among a set of predetermined sensor positions is considered. Using the relaxation method, this optimization problem is changed to a convex optimization problem which can be readily solved using the CVX package.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. 35 p.
Series
TRITA-EE, ISSN 1653-5146 ; 2016:196
National Category
Engineering and Technology
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-199635 (URN)978-91-7729-240-1 (ISBN)
Presentation
2017-01-26, V3, Teknikringen 72, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20170116

Available from: 2017-01-16 Created: 2017-01-11 Last updated: 2017-01-16Bibliographically approved

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