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Non-symmetrical shaped conductors located in a time-harmonic TM field

Die in einem senkrechten harmonischen Magnetfeld (TM-Feld) lokalisierten nicht symmetrischen Profilleiter

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Contents

In the work the method providing to determinate the power losses of long conductor of an arbitrary polygonal cross-section, placed in a time-harmonic transverse magnetic (TM) field. This method rests on the connection of the Bubnov-Galerkin method in its numerical version performed by means of finite element method for internal region with the method of division of variables for external region. — On the basis of theoretical considerations the numerical calculations were performed for several chosen cases of shaped conductors, on the basis of which the plots of Joule power losses in those conductors were made.

Übersicht

Im Beitrag wurde eine Methode zur Ermittlung der Leistungsverluste in einem langen Leiter mit einem beliebigen vielblätterigen Querschnitt angegeben. Der Leiter befindet sich in einem harmonischen senkrechten Magnetfeld (TM-Feld). Die Methode verbindet die Bubnov-Galerkin-Methode (es geht hier um nummerische Realisierung dieser Methode unter Verwendung der Methode finiter Elemente für den inneren Bereich) und die Variablentrennung-Methode (für den äußeren Bereich). — Auf der Grundlage theoretischer Erwägungen hat man numerische Berechnungen für einige gewählte Leiterprofile durchgeführt und die Joule-Diagramme der Leistungsverluste erhalten.

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Abbreviations

A :

z-component of the vector potentialA (complex r.m.s. value)

B :

magnetic induction vector (complex r.m.s. value)

B t =∂A/∂n :

tangential component of the magnetic induction vector (complexs r.m.s. value)

E :

electric field vector (complex r.m.s. value)

i, j, k :

numbers of vertices of the considered finite element

H :

magnetic field intensity vector (complex r.m.s. value)

\(\begin{gathered} j = \sqrt { - 1} \hfill \\ k = \sqrt {\omega \gamma \mu } \hfill \\ \end{gathered} \) :

Imaginary unit

l :

boundary of the region II

l h :

boundary of the region II approximated by broken line

P :

complex Poynting vector

P :

Joule's power losses

r 0 :

radius

S :

boundary of the region

x, y, z :

rectangular coordinates

r, φ,z :

cylindrical coordinates

π=3.141593:

...

z * :

conjugate complex number ofz

φ:

basis function

μ:

magnetic permeability

ω:

pulsation

N i ,N j ,N k :

function of finite element shape

γ:

conductivity

Ω:

region

Ωh :

region approximating the region Ω

Ωe :

finite element region

∇ 2 :

scalar Laplacian

Δ:

finite element area

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Authors and Affiliations

  1. Department of Electrical Engineering, Polytechnic of Częstochowa, 17 Zawadzki St., PL-42-200, Częstochowa, Poland

    A. K. Gąsiorski

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  1. A. K. Gąsiorski
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Gąsiorski, A.K. Non-symmetrical shaped conductors located in a time-harmonic TM field. Archiv f. Elektrotechnik 69, 1–9 (1986). https://doi.org/10.1007/BF01573975

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  • DOI: https://doi.org/10.1007/BF01573975

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