Generation of Bifurcation Diagrams for Ferroresonance Characterization Using Parallel Computing

Yıl 2017, Cilt: 5 Sayı: 2, 77 - 85, 01.09.2017

Javier A. Corea-araujo Gerardo Guerra Juan A. Martınez-velasco Francisco Gonzales-molına

https://doi.org/10.17694/bajece.337936

Cited By: 1

Öz

Ferroresonance is a
complex phenomenon that involves the association of nonlinear magnetizing
inductances and capacitances. This nonlinear phenomenon can be initiated in
many different ways, which makes its characterization very difficult. Some
recent works have shown how bifurcation diagrams can be advantageously used for
predicting the phenomenon at its different stages and finding safety zones for
parameter selection. The present work expands the scope of some tools
originally developed for assessing ferroresonance behavior by means of 3D
bifurcation diagrams. The main goal of this work is to propose the application
of parallel computing to speed up the generation of bifurcation diagrams.

Anahtar Kelimeler

Bifurcation Diagram, EMTP, Ferroresonance, MATLAB, Modeling, Non-linear dynamics, Parallel computing, Parametric study

Kaynakça

• REFERENCES [1] M.R. Iravani, A.K.S. Chaudhary, W.J. Giewbrecht, I.E. Hassan, A.J.F. Keri, K.C. Lee, J.A. Martinez, A.S. Morched, B.A. Mork, M. Parniani, A. Sarshar, D. Shirmohammadi, R.A. Walling, and D.A. Woodford, “Modeling and analysis guidelines for slow transients: Part III: The study of ferroresonance,” IEEE Trans. on Power Delivery, vol. 15, no. 1, pp. 255-265, January 2000.
• [2] J. A. Corea-Araujo, F. González-Molina, J. A. Martínez, J. A. Barrado-Rodrigo, and L. Guasch-Pesquer, “Tools for characterization and assessment of ferroresonance using 3-D bifurcation diagrams,” IEEE Trans. on Power Delivery, vol. 29, no. 6, pp. 2543-2551, December 2014.
• [3] C. Kieny, “Application of the bifurcation theory in studying and understanding the global behavior of a ferroresonant electric power circuit,” IEEE Trans. on Power Delivery, vol. 6, no. 2, pp. 866-872, April 1991.
• [4] P.S. Bodger, G.D. Irwin, D.A. Woodford, and A.M. Gole, “Bifurcation route to chaos for a ferroresonant circuit using an electromagnetic transients program,” IEE Proc. Gener. Transm Distrib., vol 143, no. 3, pp. 238-242, May 1996.
• [5] A. Ben-Tal, D. Shein, and S. Zissu, “Studying ferroresonance in actual power systems by bifurcation diagram,” Electric Power Systems Research, vol. 49, no. 3, pp. 175-183, April 1999.
• [6] D.A.N. Jacobson, P.W. Lehn, and R.W. Menzies, “Stability domain calculations of period-1 ferroresonance in a nonlinear resonant circuit,” IEEE Trans. on Power Delivery, vol. 17, no.3, pp. 865-871, 2002.
• [7] F. Wörnle, D.K. Harrison, and C. Zhou, “Analysis of a ferroresonant circuit using bifurcation theory and continuation techniques,” IEEE Trans. on Power Delivery, vol. 20, no. 1, pp. 191-196, January 2005.
• [8] M. Val Escudero, I. Dudurych, and M.A. Redfern, “Characterization of ferroresonant modes in HV substation with CB grading capacitor,” Electric Power Systems Research, vol. 77, no. 1, pp. 1506-1513, 2010.
• [9] F. Ben Amar and R. Dhifaoui, “Study of the periodic ferroresonance in the electrical power networks by bifurcation diagrams,” Electrical Power and Energy Systems, vol. 33, pp. 61-85, 2011.
• [10] P. Ferracci, Ferroresonance, Cahier Technique no. 190, Groupe Schneider, 1998.
• [11] R. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. New York: Oxford University Press, 2001.
• [12] S. Jazebi, A. Farazmand, B. Perinkolam Murali, and F. de León, “Comparative study on π and T equivalent models for the analysis of transformer ferroresonance,” IEEE Trans. on Power Delivery, vol. 28, no. 1, pp. 526-528, January 2013.
• [13] J.A. Martinez, R. Walling, B. Mork, J. Martin-Arnedo, and D. Durbak, “Parameter determination for modeling systems transients. Part III: Transformers,” IEEE Trans. on Power Delivery, vol. 20, no. 3, pp. 2051-2062, July 2005.
• [14] B.A. Mork, F. Gonzalez, D. Ishchenko, D.L. Stuehm, and J. Mitra, “Hybrid transformer model for transient simulation-Part I: Development and parameters,” IEEE Trans. on Power Delivery, vol. 22, no. 1, pp. 248-255, January 2007.
• [15] F. de León, P. Gómez, J.A. Martinez-Velasco, and M. Rioual, “Transformers,” Chapter 4 of Power System Transients. Parameter Determination, J.A. Martinez-Velasco (ed.), CRC Press, 2009.
• [16] S.E. Zirka, Y.I. Moroz, C.M. Arturi, N. Chiesa, and H.K. Høidalen, “Topology-correct reversible transformer model,” IEEE Trans. on Power Delivery, vol. 27, no. 4, pp. 2037-2045, October 2012.
• [17] A. Rezaei-Zare, R. Iravani, and M. Sanaye-Pasand, “Impacts of transformer core hysteresis formation on stability domain of ferroresonance modes,” IEEE Trans. on Power Delivery, vol. 24, no. 1, pp. 177-186, January 2009.
• [18] A. Rezaei-Zare, R. Iravani, M. Sanaye-Pasand, H. Mohseni, and S. Farhangi, “An accurate hysteresis model for ferrorresonance analysis of a transformer,” IEEE Trans. on Power Delivery, vol. 23, no. 3, pp. 1448-1456, July 2008.
• [19] P. Moses, M.A.S. Masoum, and H.A. Toliyat, “Impact of hysteresis and magnetic couplings on the stability domain of ferrorresonance in asymmetric three-phase three-leg transformers,” IEEE Trans. on Power Delivery, vol. 26, no. 2, pp. 581-592, 2011.
• [20] H.W. Dommel, EMTP Theory Book, Bonneville Power Admin., Portland, August 1986.
• [21] K. Miličević and Z. Emin, “Impact of initial conditions on the initiation of ferroresonance,” Int. J. of Electrical Power and Energy Systems, vol. 31, pp. 146-152, 2009.
• [22] K. Miličević, D. Vinko, and Z. Emin, “Identifying ferroresonance initiation for a range of initial conditions and parameters,” Nonlinear Dynamics, vol. 66, pp.755-762, 2011.
• [23] J.A. Corea-Araujo, F. Gonzalez-Molina, J.A. Martinez-Velasco, J.A. Barrado-Rodrigo, and L. Guasch-Pesquer, “An EMTP-based analysis of the switching shift angle effect during energization/de-energization in the final ferroresonance state,” IPST, Vancouver, July 2013.
• [24] T.S. Parker and L.O. Chua, Practical Numerical Algorithms for Chaotic Systems, Springer, 1989.
• [25] J.A. Martinez-Velasco and J.R. Martí, Electromagnetic Transients Analysis, Chapter 12 in Electric Energy Systems: Analysis and Operation, A. Gomez-Exposito, A. Conejo, and C. Cañizares (Eds.), CRC Press, Boca Raton, 2008.
• [26] D.D. Mairs, D.L. Stuehm, and B.A. Mork, “Overvoltages on five-legged core transformers on rural electric systems,” IEEE Trans. on Industry Applications, vol. 25, no. 2, pp. 366-370, March/April 1989.
• [27] D.L. Stuehm, B.A. Mork, and D.D. Mairs, “Five-legged core transformer equivalent circuit,” IEEE Trans. on Power Delivery, vol. 4, no. 3, pp. 1786-1793, July 1989.
• [28] D.L. Stuehm, B.A. Mork, and D.D. Mairs, “Ferroresonance with three-phase five-legged core transformers,” Minnesota Power Systems Conference, Minneapolis, MN, October 3, 1988.
• [29] B.A. Mork, “Ferroresonance and Chaos - Observation and Simulation of Ferroresonance in a Five Legged Core Distribution Transformer,” Ph.D. Thesis, North Dakota State University, 1992.
• [30] J.A. Corea-Araujo, J.A. Martinez-Velasco, F. González-Molina, J.A. Barrado-Rodrigo, L. Guasch-Pesquer, and F. Castro-Aranda, “Validation of single-phase transformer model for ferroresonance analysis,” Accepted for publication in Electrical Engineering.