Solver for a Magnetic Equivalent Circuit and Modeling the Inrush Current of a 3-Phase Transformer

Authors: Markus G. Ortner, Christian Magele, Klaus Krischan

Abstract:

Knowledge about the magnetic quantities in a magnetic circuit is always of great interest. On the one hand, this information is needed for the simulation of a transformer. On the other hand, parameter studies are more reliable, if the magnetic quantities are derived from a well established model. One possibility to model the 3-phase transformer is by using a magnetic equivalent circuit (MEC). Though this is a well known system, it is often not an easy task to set up such a model for a large number of lumped elements which additionally includes the nonlinear characteristic of the magnetic material. Here we show the setup of a solver for a MEC and the results of the calculation in comparison to measurements taken. The equations of the MEC are based on a rearranged system of the nodal analysis. Thus it is possible to achieve a minimum number of equations, and a clear and simple structure. Hence, it is uncomplicated in its handling and it supports the iteration process. Additional helpful tasks are implemented within the solver to enhance the performance. The electric circuit is described by an electric equivalent circuit (EEC). Our results for the 3-phase transformer demonstrate the computational efficiency of the solver, and show the benefit of the application of a MEC.

Keywords: Inrush current, magnetic equivalent circuit, nonlinear behavior, transformer.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082335

References:

[1] S.G. Abdulsalam, W. Xu and V. Dinavahi, "Modelling and simulation of three-phase transformers for inrush current studies," IEE Proc.- Gener. Transm. Distrib., vol. 152, No. 3, pp. 328-333, May 2005.
[2] J. Arrillaga, W. Enright, N.R. Watson and A.R. Wood, "Improved simulation of HVDC converter transformers in electromagnetic transient programs," IEE Proc.-Gener. Transm. Distrib., vol. 144, No. 2, pp. 100-106, March 1997.
[3] A. Delale, L. Albert, L. Gerbaud and F. Wurtz, "Automatic generation of sizing models for the optimization of electromagnetic devices using reluctance networks," IEEE Trans. Magn., vol. 40, No. 2, pp. 830-833, March 2004.
[4] J. Turowski, M. Turowski and M. Kopec, "Method of three-dimensional network solution of leakage field of three-phase transformers," IEEE Trans. Magn., vol. 26, No. 5, pp. 2911-2919, September 1990.
[5] A. Medina and J. Arrillaga, "Simulation of multilimb power transformers in the harmonic domain," IEE Proc.-C, vol. 139, No. 3, pp. 269-276, May 1992.
[6] M. Amrhein and P.T. Krein, "Magnetic equivalent circuit simulations of electrical machines for design purposes," IEEE Electric Ship Technologies Symposium, 2007, pp. 254-260, May 2007.
[7] V. Ostović, "A method for evaluation of transient steady state performance in saturated squirrel cage induction machines," IEEE Trans. Energy Conversion, vol. EC-1, No. 3, pp. 190-197, September 1986.
[8] C.B. Rasmussen and E. Ritchie, "A equivalent circuit approach for predicting PM motor performance," IEEE Ind. Applicat. Society Conference, pp. 10-17, October 1997.
[9] L.O. Chua, C.A. Desoer and E.S. Kuh, "Linear and nonlinear Circuits," McGraw-Hill series in electrical engineering, Singapore: McGraw-Hill, 1987, pp. 214-232.
[10] V. Ostović, "Dynamics of saturated electric machines," New York: Springer Verlag New York, 1989, pp. 50-74, pp. 86-90, pp. 226-247.
[11] B. Peikari, "Fundamentals of network analysis and synthesis," in Prentice-Hall network series, New York: Prentice-Hall, 1974, pp. 91- 147, pp. 303-314.
[12] H. Köfler, "Bemessung und Konstruktion elektrischer Maschinen," Graz: Institut f├╝r elektrische Antriebstechnik und Maschinen, 2007, pp. 71-72.
[13] J. Otto, "Berechnung linearer und nichtlinearer Netzwerke. Eine Einf├╝hrung in die numerische Modellierung mit PSPICE," Leipzig, Köln: Fachbuchverlag Leipzig, 1994, pp. 42-49.
[14] R. Unbehauen, " Elektrische Netzwerke, Eine Einf├╝hrung in die Analyse," 3. neu bearbeitete und erweiterte Auflage, Berlin: Springer Verlag, 1987, pp. 91-127.
[15] IEC 60404-4: 1995 + A1: 2000, Magnetic materials - Part 4: Methods of measurement of d.c. magnetic properties of magnetically soft materials.