Phasor Analysis of a Synchronous Generator: A Bond Graph Approach

This paper presents the use of phasor bond graphs to
obtain the steady-state behavior of a synchronous generator. The
phasor bond graph elements are built using 2D multibonds, which
represent the real and imaginary part of the phasor. The dynamic
bond graph model of a salient-pole synchronous generator is showed,
and verified viz. a sudden short-circuit test. The reduction of the
dynamic model into a phasor representation is described. The
previous test is executed on the phasor bond graph model, and its
steady-state values are compared with the dynamic response. Besides,
the widely used power (torque)-angle curves are obtained by means
of the phasor bond graph model, to test the usefulness of this model.

• Israel Núñez-Hernández
• Peter C. Breedveld
• Paul B. T. Weustink
• Gilberto Gonzalez-A

• Bond graphs
• complex power
• phasors
• synchronous generator
• short-circuit
• open-circuit
• power-angle curve.

[1] P.C. Krause, O. Wasynczuk, and S.D. Sudhoff, Analysis of Electric
Machinery and Drive Systems, IEEE Press, Wiley, New York, 2nd
edition, 2002.
[2] Ion Boldea, The Electric Generators Handbook: Synchronous
Generators, Taylor & Francis Group, USA, 2006.
[3] D. Das, Electrical Power Systems, New Age International (P) Limited,
New Delhi, 2006.
[4] Gilbert M. Masters, Renewable and Efficient Electric Power Systems,
John Wiley & Sons, USA, 2004.
[5] Israel Núñez-Hernández, Peter C. Breedveld, Paul B. T. Weustink,
Gilberto Gonzalez-A, "Analysis of Electrical Networks Using Phasors:
A Bond Graph Approach”, Paper presented at the International
Conference on Electric Machines and Drive Systems, 18-19 July, 2014,
Oslo. (in press).
[6] R. H. Park, "Two-Reaction Theory of Synchronous Machines-
Generalized Method of Analysis”, Part I, AIEE Transactions, Vol. 48,
July 1929, pp. 716-727.
[7] P. M. Anderson, A. A. Fouad, Power System Control and Stability, 2nd
edition, John Wiley & Sons, USA, 2003.
[8] D. Karnopp, "Power-conserving transformation: Physical interpretations
and applications using bond graphs”, J. Franklin Inst., Vol. 288 (Sept.
1969), pp. 175–201
[9] IEEE Std 1110-2002(R2007), IEEE Guide for Synchronous Generator
Modeling Practices and Applications In Power System Stability
Analyses, IEEE Power Engineering Society, 2007.
[10] D. Sahm, "A Two-Axis, Bond Graph Model of the Dynamics of
Synchronous Electrical Machines”, Journal of the Franklin Institute,
1979, vol. 308, No. 3, pp. 205-218.
[11] Wolfgang Borutzky, Bond Graphs: A Methodology for Modelling
Multidisciplinary Dynamic Systems, Springer, London, 2010.
[12] Abdallah Barakat, Slim Tnani, Gérard Champenois, Emile Mouni,
"Analysis of synchronous machine modeling for simulation and
industrial applications”, Elsevier, Simulation Modelling Practice and
Theory 18, 2010, pp. 1382–1396.
[13] Junco, S., Diéguez, G., Ramírez, F., "On commutation modeling in
Bond Graphs”, Proc. Int. Conf. on Bond Graph Modeling and
Simulation, San Diego, 2007, pp. 12-19.
[14] A. C. Umarikar and L. Umanand. 2005, "Modelling of switching
systems in bond graphs using the concept of switched power junctions”,
Journal of The Franklin Institute, 342, pp 131-147.
[15] S. Junco. "Real- and complex-power bond graph modeling of the
induction motor”. In Proceeding of the International Conference on
Bond Graph Modeling and Simulation, pages 323–328, San Francisco,
1999.
[16] Jan Machowski, Janusz W. Bialek, James R. Bumby, Power System
Dynamics: Stability and Control, 2nd edition, John Wiley & Sons, Great
Britain, 2008.
[17] IEEE Std 115™-2009, IEEE Guide for Test Procedures for Synchronous
Machines, IEEE Power Engineering Society, 2009.
[18] Stephen J. Chapman, Electric Machinery Fundamentals, 4th edition,
McGraw-Hill, New York, 2005.
[19] Mohamed E. El-Hawary, Electrical Power Systems, John Wiley & Sons,
New York, 1995.