Electrical Engineering

, Volume 100, Issue 2, pp 625–632 | Cite as

Single-phase autotransformer modelling and model parameter identification

  • Tin Benšić
  • Ivan Biondić
  • Predrag Marić
Original Paper


This paper proposes a newly formed model for time-domain analysis of single-phase autotransformer based on superposition of collinear vectors. Parameters of the model are determined with parameter identification procedure presented as a step-by-step algorithm using two no-load states. Identification is completed by solving minimization of least squares using genetic algorithm. This procedure also verifies the model and returns the total relative error referred to effective current value under 10%. Saturation is taken into account with nonlinear transcendent functions that are differentiable in whole domain, while the hysteresis is neglected.


Autotransformer Parameter identification Time-domain modelling No-load state Magnetization curve 



The authors would like to thank Marinko Barukčić, PhD for his support in making of this paper.


  1. 1.
    Pereira ALM, Belchior FN, de Abreu JPG (2010) Performance analysis of auto-transformer adz through the software ATP. In: Transmission and distribution conference and exposition: Latin America (T&D-LA), 2010 IEEE/PES, pp 516–521, November 2010Google Scholar
  2. 2.
    Volčko V, Eleschova A, Belan Z, Janiga P, Cintula B, Heretk P (2014)Verification of steady state model of power autotransformer. In: Proceedings of the 2014 15th international scientific conference on electric power engineering (EPE)Google Scholar
  3. 3.
    Holenarsipur PSS, Mohan N, Albertson VD, Cristofersen J (1999) Avoiding the use of negative inductances and resistances in modeling three-winding transformers for computer simulations. In: IEEE power engineering society 1999 winter meeting, vol 2, pp 1025–1030, January/February 1999Google Scholar
  4. 4.
    Neisius H-T, Dzafic I, Henselmeyer S, Ablakovic D, Lecek N (2012) Modeling of auto-transformers for load flow calculations. In: 3rd IEEE PES international conference and exhibition on innovative smart grid technologies (ISGT Europe), pp 1–6, October 2012Google Scholar
  5. 5.
    Degeneff RC, Gutierrez MR, Vakilian M (1995) Nonlinear, lumped parameter transformer model reduction technique. IEEE Trans Power Deliv 10(2):862–868CrossRefGoogle Scholar
  6. 6.
    Vakilian Mehdi, Degeneff RC (1994) A method for modeling nonlinear core characteristic of transformers during transients. IEEE Trans Power Deliv 9(4):1916–1925CrossRefGoogle Scholar
  7. 7.
    Delfino Federico, Procopio Renato, Ross Mansueto (2011) High-frequency EHV/HV autotransformer model identification from LEMP test data. IEEE Trans Power Deliv 26(2):714–724CrossRefGoogle Scholar
  8. 8.
    Colla L, Iuliani V, Palone F, Rebolini M, Taricone C (2010) EHV/HV autotransformers modeling for electromagnetic transients simulation of power systems. In: XIX international conference on electrical machines (ICEM), pp 1–6, September 2010Google Scholar
  9. 9.
    Rezaei-Zare Afshin, Iravani Reza (2010) On the transformer core dynamic behavior during electromagnetic transient. IEEE Trans Power Deliv 25(3):1606–1619CrossRefGoogle Scholar
  10. 10.
    Radmanesh H, Fathi H, Mosazade SU, Hosseinian H (2012) Harmonics analysis in autotransformers ferroresonance circuit. In: 20th Iranian conference on electrical engineering, (ICEE2012), pp 354–357, May 2012Google Scholar
  11. 11.
    Zeng L, Lin X, Huang J, Bo Z (2009) Modeling of UHV power transformer and analysis of electromagnetic transient. In: IEEE power & energy society general meeting, pp 1–5, July 2009Google Scholar
  12. 12.
    Gutierrez M, Degeneff RC (1995) Linear, lumped parameter transformer model reduction technique. IEEE Trans Power Deliv 10(2):853–861CrossRefGoogle Scholar
  13. 13.
    Horton R, Dugan RC, Wallace K, Hallmark D (2012) Improved autotransformer model for transient recovery voltage (TRV) studies. IEEE Trans Power Deliv 27(2):895–901CrossRefGoogle Scholar
  14. 14.
    Degeneff RC (1977) A general method for determining resonances in transformer windings. IEEE Trans Power Appar Syst 96(2):423–430CrossRefGoogle Scholar
  15. 15.
    Sofian DM, Wang Z, Li J (2010) Interpretation of transformer fra responsespart II: influence of transformer structure. IEEE Trans Power Deliv 25(4):2582–2589CrossRefGoogle Scholar
  16. 16.
    Abeywickrama N, Serdyuk VY, Gubanski SM (2008) Effect of core magnetization on frequency response analysis (FRA) of power transformers. IEEE Trans Power Deliv 23(3):1432–1438CrossRefGoogle Scholar
  17. 17.
    Donoxia L, Zanji W, Xiucheng L (2001) Modeling and simulation of magnetizing inrush current of large power transformers. In: Proceedings of the fifth international conference on electrical machines and systems, vol. 1, pp 440–443 August 2001Google Scholar
  18. 18.
    Lin X, Weng H, Liu P, Wang B, Bo Zhiqian (2008) Analysis of a sort of unusual mal-operation of transformer differential protection due to removal of external fault. IEEE Trans Power Deliv 23(3):1374–1379CrossRefGoogle Scholar
  19. 19.
    Lin X, Huang J, Zeng ZQ, Bo L (2010) Analysis of electromagnetic transient and adaptability of second-harmonic restraint based differential protection of uhv power transformer. IEEE Trans Power Deliv 25(4):2299–2307CrossRefGoogle Scholar
  20. 20.
    Scitovski R, Ungar Š, Jukić D, Crnjac Mi (1995) Moving total least squares for parameter identification in mathematical model. In: Operations research proceedings, pp 196–201, September 1995Google Scholar
  21. 21.
    Nyarko Emmanuel Karlo, Scitovski Rudolf (2004) Solving the parameter identification problem of mathematical models using genetic algorithms. Appl Math Comput 153(13):651–658MathSciNetzbMATHGoogle Scholar
  22. 22.
    Galić R, Scitovski R, Marošević T, Jukić D (1995) The problem of optimal initial conditions in a mathematical model/problem optimalnih početnih uvjeta u matematičkom modelu. In: Zbornik radova V. konferencije iz operacijskih istraživanja, pp 62–71, October 1995Google Scholar
  23. 23.
    Montgomery Douglas C, Runger George C (2003) Applied statistics and probability for engineers. Wiley, New YorkzbMATHGoogle Scholar
  24. 24.
    Miličević K, Flegar I, Pelin D (2009) Flux reflection model of the ferroresonant circuit. Math Probl Eng 2009:693081. doi: 10.1155/2009/693081

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering, Computing and Information Technology OsijekJosip Juraj Strossmayer University OsijekOsijekCroatia

Personalised recommendations