Electrical and Magnetic Modelling of a Power Transformer: A Bond Graph Approach

Bond graph models of an electrical transformer including the nonlinear saturation are presented. The transformer using electrical and magnetic circuits are modelled. These models determine the relation between self and mutual inductances, and the leakage and magnetizing inductances of power transformers with two windings using the properties of a bond graph. The equivalence between electrical and magnetic variables is given. The modelling and analysis using this methodology to three phase power transformers can be extended.

Authors:

• Gilberto Gonzalez-A
• Dunia Nuñez-P

Keywords:

• Bond graph
• electrical transformer
• magnetic circuits
• nonlinear saturation.

References:

[1] George McPerson and Robert D. Laramore, An Introduction to Electrical
Machines and Transformers, John, Wiley & Sons, 1990.
[2] Dean C. Karnopp, Donald L. Margolis and Ronald C. Rosenberg, System
Dynamics Modeling and Simulation of Mechatronic Systems, Wiley, John
& Sons, 2000.
[3] P. E. Wellstead, Physical System Modelling, Academic Press, London,
1979.
[4] Z. Q. Wu, G. H. Shirkoohi, J. Z. Cao, "Simple dynamic hysteresis
modelling of three phase power transformer", Journal of Magnetism and
Magnetic Materials 160(1996) pp.79-80.
[5] Chee-Mun Ong, Dynamic Simulation of Electric Machinery Using Mat-
Lab/Simulink, Prentice-Hall, 1998.
[6] H. Fraisse, J. P. Masson, F. Marthouret and H. Morel, "Modeling od a
Non-Linear Conductive Magnetic Circuit. Part 2: Bond Graph Formulation",
IEEE Transactions on Magnetics Vol. 31, No. 6, November 1995.
[7] C. Sueur and G. Dauphin-Tanguy, "Bond graph approach for structural
analysis of MIMO linear systems", Journal of the Franklin Institute, Vol.
328, No. 1, pp. 55-70, 1991.
[8] David C. Hamill, "Lumped Equivalent Circuits of Magnetic Components:
The Gyrator-Capacitor Approach", IEEE Transactions on Power Electronics,
Vol. 8, No. 2, April 1993.
[9] S. Garcia, A. Medina and C. Perez, "A state space single-phase transformer
model incorporating nonlinear phenomena of magnetic saturation
and hysteresis for transient and period steady-state analysis", IEEE Power
Engineering Society Summer Meeting, Vol. 4, pp. 2417-2421, July 2000.