Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31105
A NonLinear Observer of an Electrical Transformer: A Bond Graph Approach

Authors: Gilberto Gonzalez-A , Israel Nuñez


A bond graph model of an electrical transformer including the nonlinear saturation is presented. A nonlinear observer for the transformer based on multivariable circle criterion in the physical domain is proposed. In order to show the saturation and hysteresis effects on the electrical transformer, simulation results are obtained. Finally, the paper describes that convergence of the estimates to the true states is achieved.

Keywords: bond graph, nonlinear observer, nonlinear saturation, electrical transformer

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1237


[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] C. Pichardo-Almarza, A. Rahmani, G. Dauphin-Tanguy, M. Delgado, "High gain observers for non-linear systems modelled by bond graphs", Proc. IMechE Part I: J. Systems and Control Engineering, 219(2005) pp. 477-497.
[5] Gilberto Gonzalez-A, R. Galindo, "Direct Control in Bond Graph by State Estimated Feedback for MIMO LTI Estimated", Proceedings of the 2002 IEEE International Conference on Control Applications, Scotland, pp. 1183-1188.
[6] Cesar Pichardo-Almarza, A. Rahmani, G. Dauphin-Tanguy, M. Delgado, "Using the Bicausality concept to build reduced order observers in linear invariant systems modelled by bond graph",
[7] Peter J. Gawthrop, "Physical Model-based Control: A Bond Graph Approach", Journal of the Franklin Institute, 332B(3), pp. 285-305, 1995.
[8] Rafael Martinez-Guerra, J. De Leon-Morales, "On Nonlinear Observers", Proceedings of the 1997 IEEE International Conference on Control Applications, pp. 324-328, 1997.
[9] Xingzhe Fan, M. Arcak, "Observer design for systems with multivariable monotone nonlinearities", Systems & Control Letters, 50(2003) pp. 319- 330.
[10] Xingzhe Fan, M. Arcak, "Nonlinear Observer Design for Systems with Multivariable Monotone Nonlinearities", Proceedings of the 41st IEEE Conference on Decision and Control, pp. 684-688, 2002.
[11] 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.
[12] Chee-Mun Ong, Dynamic Simulation of Electric Machinery Using MatLab/Simulink, Prentice-Hall, 1998.
[13] 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.
[14] 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.
[15] 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.
[16] M. Arcak, P. Kokotovic, Nonlinear observers: a circle criterion design and robustness, Automatica 37(12) (2001) 1923-1930. World Academy of Science, Engineering and Technology 34 2009