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Transient skin effect in a rectangular conductor placed in a semi-closed slot

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Contents

It is demonstrated that the Bubnow-Galrekin method can be applied for the analysis of the non-steady state in conductors. The Joule power losses in a rectangular conductor placed in a semi-closed slot and the electrodynamic force acting on this conductor are calculated. The equivalent circuit of the impedance of the conductor is also considered. The investigations are made by using the Bubnow-Galerkin method for the parabolic equation.

Übersicht

Es wird gezeigt, daß man die Methode von Bubnow-Galerkin zur Analyse der nichtstationären Vorgänge in den Leitern anwenden kann. Es werden die Stromwärmeverluste für den rechteckigen Leiter in der halbgeschlossenen Nut einer elektrischen Maschine und die auf den Leiter wirkende Kraft berechnet. Die Ersatzschaltungen für die Impedanz einer Maschinennut werden weiter betrachtet. Zur Analyse der parabolischen Differentialgleichung wird die Methode von Bubnow-Galerkin angewandt.

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Abbreviations

B :

the magnetic induction

B x ,B y :

Components of the magnetic induction

C :

Operator in a Hilbert space

E :

z-component of the electric field

F :

Electrodynamic force

F x ,F y :

Components of the electrodynamic force

H :

Hilbert space

H C :

Energetic space of a positive definite operatorC

I :

Current

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

Imaginary unit

L :

Inductance

ℒ:

Laplace transform

P :

Power

R :

Resistance

Z :

Impedance

z * :

Dimension coupled with complex dimensionz

Rez, Imz, |z|:

Real part, imaginary part and modulus of complex numberz

μ:

Magnetic permeability

γ:

Conductance

ω:

Pulsation

∇2 :

Scalar Laplacian

1 x , 1 y :

Unit vectors

(x/y):

Scalar product of elementsx,y of Hilbert spaceH

\(\left\| \chi \right\| = \sqrt {(\chi |\chi )} \) :

Norm of elementx of Hilbert spaceH

\(\delta _{n_0 } \) :

\(\left\{ {\begin{array}{*{20}c} 1 & {at} & {n = 0} \\ 0 & {at} & {n \ne 0} \\\end{array}} \right.\)

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Authors and Affiliations

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

    P. Rolicz

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  1. P. Rolicz
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Rolicz, P. Transient skin effect in a rectangular conductor placed in a semi-closed slot. Archiv f. Elektrotechnik 57, 329–338 (1976). https://doi.org/10.1007/BF01575747

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  • DOI: https://doi.org/10.1007/BF01575747

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