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The finite element method application to the slot impedance calculation

Anwendung der Methode der finiten Elemente in der Nut Impedanzen Berechnung

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Contents

The aim of this paper is to determine, by means of the finite element method, the impedance of the bar filling the semi-closed slot of an electric machine. As an example the slot of complex shape was chosen for calculations. The analysis of that case by means exact methods would have been totally impossible. An accuracy of the method has been evaluated on the basis of published data. The two-dimensional skin effect was taken into considerations.

Übersicht

Der Beitrag behandelt, mit Hilfe der Methode der finiten Elemente, die Bestimmung der Impedanzen von Leitern in der halbgeschlossenen Nut elektrischer Maschinen für den Fall kompliziert geformter Querschnitte, bei denen eine geschlossene analytische Berechnung unmöglich ist. Das Verfahren und die erreichbare Genauigkeit wird an einem Beispiel gezeigt, wobei die Stromverdrängung mit berücksichtigt wird.

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Abbreviations

A :

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

B t :

tangential component of induction

I=|I| ej0 :

complex value of current, |I|=r.m.s. value

\(j = \sqrt { - 1}\) :

imaginary unit

|z|,z * :

modulus of complex numberz and complex conjugate ofz

Re [z], Jm [z]:

real and imaginary part of complex numberz

α:

angle of slot opening

R o :

d.c. resistance

μ:

magnetic permeability

γ:

conductivity

∇2 :

scalar Laplacian

∂/∂n :

derivative in normal external direction

Ω:

cross section area

S :

boundary of area Ω

H :

Hilbert's space

H−∇2 :

energetic space of a positive definite ∇2

Ωh :

region under triangulation

l h :

boundary of Ωh

W 12 (Ω):

Sobolev's space

S h :

subspace ofW 12 (Ω)

ω:

pulsation

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Authors and Affiliations

  1. Department of Electrical Engineering, Polytechnic of Białystok, Grunwaldzka st. 11/15, PL-15-950, Białystok, Poland

    W. Peterson

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Peterson, W. The finite element method application to the slot impedance calculation. Archiv f. Elektrotechnik 67, 203–209 (1984). https://doi.org/10.1007/BF01584525

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  • DOI: https://doi.org/10.1007/BF01584525

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