Nonlinear dynamic singularity analysis of two interconnected synchronous generator system with 1:3 internal resonance and parametric principal resonance
- 112 Downloads
The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus voltage are considered to maintain two fluctuations in the amplitude and phase angle. The case of 1:3 internal resonance between the two modes in the presence of parametric principal resonance is considered and examined. The method of multiple scales is used to obtain the bifurcation equations of this system. Then, by employing the singularity method, the transition sets determining different bifurcation patterns of the system are obtained and analyzed, which reveal the effects of the infinite-bus voltage amplitude and phase fluctuations on bifurcation patterns of this system. Finally, the bifurcation patterns are all examined by bifurcation diagrams. The results obtained in this paper will contribute to a better understanding of the complex nonlinear dynamic behaviors in a two-machine infinite-bus (TMIB) power system.
Keywordsparametric principal resonance internal resonance singularity method bifurcation
Chinese Library ClassificationO322
2010 Mathematics Subject Classification70K50
Unable to display preview. Download preview PDF.
- Chiang, H. D. Direct Methods for Stability Analysis of Electric Power Systems: Theoretical Foundation, BCU Methodologies, and Applications, John Wiley, New York (2011)Google Scholar
- Moon, F. C. Chaos Vibrations, an Introduction for Applied Scientists and Engineers, Wiley-InterScience, New York (1987)Google Scholar
- Amano, H., Kumano T., Inoue, T., and Taniguchi, H. Proposal of nonlinear stability indices of power swing oscillation in a multi-machine power system. Electrical Enginerring in Japan, 151(4), 215–221 (2005)Google Scholar
- Thapar, J., Vittal, V., Kliemann, W., and Fouad, A. A. Application of normal form of vector fields to predict inter-area separation in power systems. IEEE Transactions on Power Systems, 12(2), 844–850 ( 1997)Google Scholar
- Deng, J. X. and Zhao, L. L. Study on the second order non-linear interaction of the critical inertial modes (in Chinese). Proceeding of the CSEE, 25(7), 75–80 (2005)Google Scholar
- Yuan, B. and Sun, Q. H. Chaos in the multi-machine power system (in Chinese). Automation of Electric Power System, 19(2), 26–31 (1995)Google Scholar
- Chen, Y. S. Nonlinear Vibration (in Chinese), Higher Education Press, Beijing (2002)Google Scholar
- Golubitsky, M. and Schaeffer, D. G. Singluarities and Groups in Bifurcation Theory-I, Springer-Verlag, New York (1984)Google Scholar