Skip to main content
Log in

Single-phase transformer model including magnetic hysteresis and eddy currents

  • Original Paper
  • Published:
Electrical Engineering Aims and scope Submit manuscript

Abstract

In this paper, a single-phase core-type and shell-type transformer model is proposed on the level of state equations. The magnetic hysteresis and the eddy currents effects are successfully included based on the analytical description of the magnetic core topology. Predicted values from simulations are in very good agreement with published measurements and hence, the developed transformer model is a powerful tool for transient and steady-state studies.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Silvester P and Chari MVK (1970). Finite element solution of saturable magnetic field problems. IEEE T Power Ap Syst PAS-89: 1642–1651

    Article  Google Scholar 

  2. Chari MVK, D’angelo J, Palmo MA and Sharma DK (1986). Application of three-dimensional electromagnetic analysis methods to elecrtical machinery and devices. IEEE T Energy Conver EC-1: 145–157

    Article  Google Scholar 

  3. Demerdash NA, Nehl TW, Fuand FA and Mohammed OA (1981). Three dimensional finite element vector potential formulation of magnetic fields in electrical apparatus. IEEE T Power Ap Syst PAS- 100: 4104–4111

    Article  Google Scholar 

  4. Demerdash NA, Nehl TW, Fuand FA and Mohammed OA (1981). Experimental verification and application of the three dimensional finite element magnetic vector potential method in electrical apparatus. IEEE T Power Ap Syst PAS-100: 4112–4122

    Article  Google Scholar 

  5. Arturi CM (1991). Transient simulation of a three phase five limb step-up transformer following an out-of-phase synchronization. IEEE T Power Deliv 6: 196–207

    Article  Google Scholar 

  6. De Leon F and Semlyen A (1994). Complete transformer model for electromagnetic transients. IEEE T Power Deliv 9: 231–239

    Article  Google Scholar 

  7. Narag A and Brierley RH (1994). Topology based magnetic model for steady state and transient studies for three-phase core type transformers. IEEE T Power Syst 9: 1337–1349

    Article  Google Scholar 

  8. Chen X and Venkata SS (1997). A three-phase winding core type transformer model for low frequency transient studies. IEEE T Power Deliv 12: 775–782

    Article  Google Scholar 

  9. Mork BA (1999). Five legged wound core transformer model: derivation, parameters, implementation and evaluation. IEEE T Power Deliv 14: 1519–1525

    Article  Google Scholar 

  10. Nakra HL and Barton TH (1973). Three phase transformer transients. IEEE T Power App Syst 93: 1810–1818

    Article  Google Scholar 

  11. Ewart DN (1986). Digital computer simulation model of a steel core transformer. IEEE T Power Deliv PWRD-1: 174–183

    Article  Google Scholar 

  12. Hatziantoniu C, Galanos GD and Milias-Argitis J (1988). An incremental transformer model for the study of harmonic overvoltages in weak ac/dc systems. IEEE T Power Deliv 3: 1111–1121

    Article  Google Scholar 

  13. Rajakovic N and Semlyen A (1989). Investigation of the inrush phenomenon a quasi-stantionary approach in the harmonic domain. IEEE T Power Deliv 4: 2114–2120

    Article  Google Scholar 

  14. Chen XS and Neudorfer P (1992). Digital model for transient studies of a three-phase five legged transformer. IEE Proc-C 139: 351–358

    Google Scholar 

  15. Dolinar D, Pihler J and Grcar B (1993). Dynamic model of a three-phase power transformer. IEEE T Power Deliv 8: 1811–1819

    Article  Google Scholar 

  16. Yacamini R and Bronzeado H (1994). Transformer inrush calculations using a coupled electromagnetic model. IEE Proc-A 141: 429–498

    Google Scholar 

  17. Hatziargyriou ND, Prousalidis JM and Papadias BC (1993). Generalized transformer model based on the analysis of its magnetic core circuit. IEE Proc-C 140: 269–278

    Google Scholar 

  18. EMTP-ATP rule book, Chapter XIX-C

  19. EMTP-ATP rule book, Chapter IV-E

  20. Henriksen T (2002). How to avoid unstable time domain responses caused by transformer models. IEEE T Power Deliv 17: 516–522

    Article  Google Scholar 

  21. Chen X (2000). Negative inductance and numerical instability of the saturable transformer component in EMTP. IEEE T PowerDeliv 15: 1199–1204

    Google Scholar 

  22. Chen X (1996). A three phase multi legged transformer model in ATP using the directly formed inverse inductance matrix. IEEE T Power Deliv 11: 1554–1562

    Article  Google Scholar 

  23. Chadrasena W, McLaren PG, Annakkage UD and Jayasinghe RP (2004). An improved low-frequency transformer model for use in GIC studies. IEEE T Power Deliv 19: 643–651

    Article  Google Scholar 

  24. Thomas DWP, Paul J, Ozgonenel O and Christopoulos C (2006). Time-domain simulation of non-linear transformers displaying hysteresis. IEEE T Magn 42: 1820–1827

    Article  Google Scholar 

  25. Pedra J, Sainz L, Corcoles F, Lopez R and Salichs M (2004). PSPICE computer model of a nonlinear three phase three legged transformer. IEEE T Power Deliv 19: 200–207

    Article  Google Scholar 

  26. Jiles DC and Atherton DL (1984). Theory of ferromagnetic hysteresis. J Appl Phys 55: 2115–2120

    Article  Google Scholar 

  27. Jiles DC and Thoekle JB (1989). Theory of ferromagnetic hysteresis: determination of model parameters from experimental hysteresis loops. IEEE T Magn 25: 3928–3930

    Article  Google Scholar 

  28. Jiles DC, Thoekle JB and Devine MK (1992). Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis. IEEE T Magn 28: 27–35

    Article  Google Scholar 

  29. Tellinen J (1998). A simple scalar model for magnetic hysteresis. IEEE T Magn 34: 2200–2206

    Article  Google Scholar 

  30. Bertotti G (1988). General properties of power losses in soft ferromagnetic materials. IEEE T Magn 24: 621–630

    Article  Google Scholar 

  31. Bertotti G (1998). Hysteresis in magnetism, 1st edn. Academic, San Diego

    Google Scholar 

  32. Liorzou F, Phelps B and Atherton DL (2000). Macroscopic models of magnetization. IEEE T Magn 36: 418–428

    Article  Google Scholar 

  33. Chen SD, Lin RL and Cheng CK (2005). Magnetizing inrush model of transformers based on structure parameters. IEEE T Power Deliv 20: 1947–1954

    Article  Google Scholar 

  34. Akcay H and Gokhan Ece D (2003). Modeling of hysteresis and power losses in transformer laminations. IEEE T Power Deliv 18: 487–492

    Article  Google Scholar 

  35. Theocharis AD, Menti A, Milias-Argitis J, Zacharias Th (2005) Modeling and simulation of a single-phase residential photovoltaic system. In: Proceedings of the IEEE power tech 2005 conference, St. Petesburg, paper nr. 206

  36. Avila-Rosales J and Alvarado F (1982). Nonlinear frequency dependent transformer model for electromagnetic transient studies in power systems. IEEE T Ap Syst PAS-101: 4281–4288

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. D. Theocharis.

Additional information

This work was supported by the Research Committee of the University of Patras under Grant B106.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Theocharis, A.D., Milias-Argitis, J. & Zacharias, T. Single-phase transformer model including magnetic hysteresis and eddy currents. Electr Eng 90, 229–241 (2008). https://doi.org/10.1007/s00202-007-0071-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00202-007-0071-5

Keywords

Navigation