Skip to main content
SpringerLink
Log in

Model representing the nonlinear behaviour of three-phase transformers

Modell zur Nachbildung des nichtlinearen Verhaltens von Drehstromtransformatoren

  • Published:
Archiv für Elektrotechnik Aims and scope Submit manuscript

Contents

This paper deals with the problem of modelling the nonlinear behaviour of transformers for simulating transients. Many approaches have been published to this end. Implemented into transient programs computing time increases, a disadvantage when simulating large systems. The object of this paper is to present a simple method with fairly accurate results. It is based on the approach to substitute the hysteresis characteristic of transformers by a piecewise linear saturation curve including remanence. This method allows to implement the modelling of three-phase transformers into a transient program.

Übersicht

Dieser Beitrag beschäftigt sich mit dem Problem der Modellbildung des nichtlinearen Verhaltens von Transformatoren zur Simulation transienter Vorgänge. Viele Vorschläge wurden hierzu bereits veröffentlicht. Ihre Anwendung führt allerdings zur Erhöhung der Rechenzeiten, ein Nachteil bei der Simulation größerer Systeme. Inhalt dieses Beitrags ist es, eine einfache und dabei ausreichend genaue Methode vorzustellen. Sie basiert auf dem Vorschlag, die Hysteresecharakteristik von Transformatoren durch eine stückweise lineare Sättigungskennlinie unter Berücksichtigung der Remanenz zu ersetzen. Diese Methode erlaubt die Modellbildung von Drehstromtransformatoren für ein transientes Programm.

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

B :

magnetic flux density

H :

magnetizing field strength

i :

current

L :

inductance

R :

resistance

V :

voltage

w :

turns of winding

X :

reactance

Ψ:

flux

E(H 1,H 2):

Everett function

ΔB(H 1,H 2):

change of magnetizing flux density

C :

coercivity

fe :

core losses

HV :

high voltage side

init:

initial

LV :

low voltage side

m :

magnetizing

rem:

remanence

rem, max:

maximum remanence

rev:

reversible

S :

saturation

References

  1. Sequenz, H.: Beiträge zur Gleichung der Hystereseschleife. Arch. Elektrotech. 29 (1935) 387–394

    Google Scholar 

  2. Fischer, J.; Moser, H.: Die Nachbildung von Magnetisierungskurven durch einfache algebraische oder transzendente Funktionen. Arch. Elektrotech. 42 (1956) 286–299

    Google Scholar 

  3. Chua, L. O.; Bass, S. C.: A generalized hysteresis model. IEEE Trans. CT-19 (1972) 36–48

    Google Scholar 

  4. Charap, S. H.: Magnetic hysteresis model. IEEE Trans. MAG-10 (1974) 1091–1096

    Google Scholar 

  5. Teape, J. W.; Simpson, R. R. S.; Slater, R. D.; Wood, W. S.: Representation of magnetic characteristic, including hysteresis, by exponential series. IEE Proc. Vol. 121 (1974) 1019–1020

    Google Scholar 

  6. Yamashita, H.; Nakamae, E.; Hammam, M. S. A. A.; Wakisho, K.: A program to analyze transient phenomena of circuits including precisely represented transformers. IEEE PES Summer Meeting San Francisco, Calif. (1975) A 75 403–6

  7. Talukdar, S. N.; Bailey, J. R.: Hysteresis models for system studies. IEEE Trans. PAS-95 (1976) 1429–1434

    Google Scholar 

  8. Del Vecchio, R. M.: An efficient procedure for modeling complex hysteresis processes in ferromagnetic materials. IEEE Trans. MAG-16 (1980) 809–811

    Google Scholar 

  9. Rivas, J.; Zamarro, J. M.; Martin, E.; Pereira, C.: Simple approximation for magnetization curves and hysteresis loops. IEEE Trans. MAG-17 (1981) 1498–1502

    Google Scholar 

  10. Dick, E. P.; Watson, W.: Transformer models for transient studies based on field measurements. IEEE Trans. PAS-100 (1981) 409–419

    Google Scholar 

  11. DelVecchio, R. M.: The inclusion of hysteresis processes in a special class of electromagnetic finite element calculations. IEEE Trans. MAG-18 (1982) 275–284

    Google Scholar 

  12. Avila-Rosales, J.; Alvarado, F. L.: Nonlinear frequency dependent transformer model for electromagnetic transient studies in power systems. IEEE Trans. PAS-101 (1982) 4281–4288

    Google Scholar 

  13. Udpa, S. S.; Lord, W.: A fourier descriptor model of hysteresis loop phenomena. IEEE Trans. MAG-21 (1985) 2370–2373

    Google Scholar 

  14. Happoldt, H.; Oeding, D.: Elektrische Kraftwerke und Netze. Springer, Berlin/Heidelberg/New York 5th ed. 1978

    Google Scholar 

  15. Yacamini, R.; Abu-Nasser, A.: The calculation of inrush current in three-phase transformers. IEE Proc. Vol. 133 (1986) 31–40

    Google Scholar 

  16. Dommel, H. W.: Electromagnetic transients program reference manual (EMTP theory book). Bonneville Power Administration 1986

  17. Alternative transients program rule book. K. U. Leuven EMTP Center

  18. Stenzel, J.: Simultaneous simulation of electric power systems and control functions. 7th Symposium on Control and Automation of Electric Power Systems 1991, Ljubljana, Slovenia

Download references

Author information

Authors and Affiliations

  1. Institut für Elektrische Energieversorgung, Technische Hochschule Darmstadt, Landgraf-Georg-Straße 4, D-64283, Darmstadt, Deutschland

    J. Stenzel & Th Weber

Authors
  1. J. Stenzel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Th Weber
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stenzel, J., Weber, T. Model representing the nonlinear behaviour of three-phase transformers. Archiv f. Elektrotechnik 77, 143–150 (1994). https://doi.org/10.1007/BF01578537

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01578537

Keywords

Search

Navigation