Skip to main content
SpringerLink
Log in

Steady state analysis of the magnetic fields and eddy currents in the rotating screen of a superconducting alternator

  • Published:
Archiv für Elektrotechnik Aims and scope Submit manuscript

Contents

The steady state behaviour of the rotating screen surrounding the inductor winding of the three-phase alternator with superconducting field winding is considered.

The armature positive and negative sequence magnetic fields, rotating with different velocities relative to the screen and present during steady state running due to unbalanced currents and armature reaction, are considered.

A calculation procedure to determine the radial and tangential components of the magnetic field in the screen, the current density and the power losses is described.

Through the calculation of the attenuation factor, the capacity of the screen to reduce the intensity of the magnetic field in the region occupied by the inductor winding is shown. Finally a numerical example is given.

Übersicht

Untersucht wird das stationäre Verhalten eines rotierenden Abschirmzylinders, der die supraleitende Erregerwicklung eines Drehstromgenerators umgibt. Betrachtet werden die mitlaufenden und inversen Drehfelder, die, durch Unsymmetrien hervorgerufen, relativ zum Abschirmzylinder mit verschiedenen Geschwindigkeiten umlaufen. Angegeben wird ein Rechenverfahren, mit dem das radiale und tangentiale magnetische Feld, die Stromdichte und Verluste im Abschirmzylinder bestimmt werden können. Durch Berechnung des Dämpfungsfaktors wird die Schirmwicklung auf den Raum erfaßt, in dem sich die Erregerwicklung befindet. Abschließend wird ein praktisches Beispiel durchgerechnet.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

⋆:

vector Laplacian operator

★:

scalar Laplacian operator

Re |.|:

real part of the argument in brackets

Λ:

potential vector

A* :

phasor notation of the potential vector when time-dependent

a 1,a 2,b 1,b 2,c 1,c 2,d 1,d 2,e 1,e 2,f 2 :

real integration constants

C :

attenuation factor

E * :

phasor notation of imposed electric field

G :

current density vector

G * :

phasor notation of the current density vector when time dependent

g, g′ :

real constants relating to the particular solution of the “Poisson-like” equation

II :

magnetic field vector

II * :

phasor notation of the magnetic field vector when timedependent

H (1) :

Hankel function of the first kind

h 1,h 2 :

real integration constants

J :

Bessel function of the first kind

K :

modified Bessel function of the second kind

Ker, Kei:

real and imaginary parts ofK

Ker′, Kei′:

first derivatives of Ker and Kei

i, in :

complex constants

M :

magnitude of the functionJ

N :

magnitude of the functionK

P :

power losses in the screen per unit length along the axis

\(\dot p,\dot q,\dot s\) :

complex integration constants

p, q :

magnitude ofp and\(\dot q\)

r :

radial coordinate

r 1,r 2,...,r 6 :

radii of the parts of the machine indicated in fig. 3

t :

time variable

\(\dot u\) :

complex variable

v :

screen periferal velocity vector

x :

\(\begin{array}{*{20}c} {\sqrt 2 } \\ {\delta ^v } \\\end{array}\)

x 1 :

value ofx whenr=r 1

x 2 :

value ofx whenr=r 2

w :

real integration constant

z :

axial coordinate

α, β:

arguments of\(\dot p\) and\(\dot q\) respectively

δ:

depth of current penetration in the screen

η:

argument of the functionK

ϑ:

angular coordinate

μ:

absolute permeability

μ0 :

vacuum permeability

σ:

electrical conductivity of the screen

φ:

angle of phase displacement

ψ:

argument of the functionJ

ω:

angular velocity, rotational speed

4:

number indicating the armature region

i :

number indicating region of the machine (excluding the armature region)

m :

rotor subscript

n :

harmonic number, number of the order of Bessel function

r :

radial subscript

z :

axial subscript

ϑ:

angular subscript

References

  1. Einstein, T. H.: Excitation requirements and dynamic performance of a superconducting alternator for electric utility power generation Sc. D. Thesis. Dept. of Mechanical Engineering M.I.T. January 1971

  2. Luck, D. L.: Electromechanical and thermal effects of faults upon superconducting generators. Ph. D. Thesis, Dept of Electrical Engineering, M.I.T. June 1971

  3. Luck, D. L., Thullen, P.: Double shielded superconducting winding. U.S. Patent 3764835, October 1973

  4. Einstein, T. H.: System performance characteristics of superconducting alternators for electric utility power generation. IEEE PAS Summer Meeting, Anaheim, Calif., July 14–19 1974, Paper T 74-486-7

  5. Furuyama, M., Kirtley, J. L. Jr: Transient stability of superconducting alternators. IEEE PAS Summer Meeting, Anaheim, Calif., July 14–19 1974, Paper T 74-485-9

  6. Kirtley, J. L. jr., Furuyama, M.: A design concept for large superconducting alternators. IEEE PAS Winter Meeting, New York, N.Y., January 26–31, 1975

  7. Keim, T. A.: Transient heating of superconducting alternator rotors due to field current changes. IEEE PAS Winter Meeting, New York, N.Y., January 27 February 1, 1974

  8. Monti, C., Morini, A., Pasotti, G., Veca, G.: Determinazione della distribuzione di corrente negli induttori di turboalternatori con avvolgimenti superconduttivi. Atti e memorie dell'Accademia Patavina di Scienze, Lettere ed Arti, vol. LXXXVI (1973–74), parte II: Classe di Scienze Matematiche e Naturali, 97–112

  9. Watson, G. N.: A treatise on the theory of Bessel functions. Cambridge University Press 1966

  10. Mc Lachlan, N. W.: Bessel functions for engneers. Oxford University Press 1948

  11. Monti, C., Morini, A.: Determinazione dei campi di induttore e d'indotto in turboalternatori con avvolgimento di eccitazione superconduttore e schermo magnetico esterno. Rapporto interno UPee 74/10-Luglio 1974

  12. Minnich, S. H., Fox, G. R.: Cryogenic power transmission. Annexe 1969-1 Bull I.I.R., London 1969. 43–67

Download references

Author information

Authors and Affiliations

  1. Instiute of Electrical and Electronic Engineering, Padua University, Via Gradenigo 6/A, Padua, Italy

    C. Monti,  A. Morini &  B. Verde

Authors
  1. C. Monti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Morini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Verde
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work has been carried out with the financial support of CNR

Rights and permissions

Reprints and permissions

About this article

Cite this article

Monti, C., Morini, A. & Verde, B. Steady state analysis of the magnetic fields and eddy currents in the rotating screen of a superconducting alternator. Archiv f. Elektrotechnik 57, 319–327 (1976). https://doi.org/10.1007/BF01575746

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01575746

Keywords

Search

Navigation