Singularity-induced bifurcations in electrical power systems

IEEE Transactions on Power Systems

Volumn 20, Issue 1, 2005, Pages 312-320

  Marszalek, Wieslaw ^a   Trzaska, Zdzislaw W ^b  

^a DEVRY UNIVERSITY   (United States)

^b WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Bifurcations; Differential algebraic equations; Power systems; Stability

Indexed keywords

BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRIC LOAD FLOW; MATHEMATICAL MODELS; MATRIX ALGEBRA; SYSTEM STABILITY; THEOREM PROVING;

DIFFERENTIAL ALGEBRAIC EQUATIONS; HOPF BIFURCATIONS; SINGULARITY INDUCED BIFURCATION;

ELECTRIC POWER SYSTEMS;

EID: 13844315888     PISSN: 08858950     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPWRS.2004.841244     Document Type: Article

References (30)

1. S. Ayasun, C. O. Nwankpa, and H. G. Kwatny, Computation of singular and singularity induced bifurcation points of differential-algebraic power system model, , 2003. preprint.
2. H. G. Kwamy, R. E Fischl, and C. O. Nwankpa, "Local bifurcation in power systems: Theory, computation, and applications," Proc. IEEE vol. 83, no. 11, pp. 1456-1483, Nov. 1995.
3. H. G. Kwatny, A. K. Pasrija, and L. Y. Babar, "Static bifurcations in electric power networks: Loss of steady-state stability and voltage collapse," IEEE Trans. Circuits Syst., vol. CAS-33, no. 10, pp. 981-991, Oct. 1986.
4. K. E. Brenan, S. L. Campbell, and L. R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Philadelphia, PA: SIAM, 1996.
5. S. L. Campbell and W. Marszalek, "Index of infinite dimensional differential algebraic equations," Mathemat. Comput. Modeling of Dynamical Syst., vol. 5, pp. 18-42, 1999.
6. S. L. Campbell and W. Marszalek, "ODE/DAE integrators and MOL problems," Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), no. 4, pp. 251-254, 1996.
7. S. L. Campbell and W. Marszalek, "Mixed symbolic-numerical computations with general DAEs: An applications case study," Numer. Algorithms vol. 19, pp. 85-94, 1998.
8. S. L. Campbell and W. Marszalek, "DAE's arising from traveling wave solutions of PDE's I," J. Comp. Appl. Math., vol. 82, pp. 41-58, 1997.
9. E. Griepentrog and R. März, "Differential-algebraic equations and their numerical treatment," Treubner-Texte zur Mathematik, 1986. Band 88.
10. D. J. Hill and I. M. Y. Mareels, "Stability theory for differential/algebraic systems with application to power system," IEEE Trans. Circuits Syst., vol. 37. no. 11, pp. 1416-1423, Nov. 1990.
11. W. A. Bamett and Y. He, "Bifurcations in macroeconomic models," in Innovations in Macrodynamics, S. Dowrick and R. Pitchford, Eds. London, U.K.: Cambridge Univ. Press. 2004.
12. A. A. P. Lerm, C. A. Canizares, F. A. B. Lemos, and A. S. eSilva, "Multi-parameter bifurcation analysis of power systems," in Proc. North American Power Symp. (NAPS), Cleveland, OH, Oct. 1998.
13. K. L. Praprost and K. A. Loparo, "An energy function method for determining voltage collapse during a power system transient," IEEE Trans. Circuits Syst., vol. CAS-41. no. 10, pp. 635-651, Oct. 1994.
14. M. M. Begovic and A. G. Phadke, "Voltage stability assessment through measurements of a reduced state vector," IEEE Trans. Power Syst., vol. 5, no. 1, pp. 198-203, Feb. 1990.
15. I. Dobson, J. Zhang, S. Greene, H. Engdahl, and P. W. Sauer, "Is strong modal resonance a precursor to power system oscillations?," IEEE Trans. Circuits Syst. I, vol. CAS-48, no. 3, pp. 340-349, Mar. 2001.
16. C. L. DeMarco, "Identifying swing mode bifurcations and associated limits on available transfer capability," in Proc. 1998 American Control Conf., Philadelphia, PA. 1998, pp. 2980-2985.
17. V. Vekatasubmmanian, H. Schattler, and J. Zaborszky, "A Stability Theory of Large Differential Algebraic Systems: A Taxonomy," Dept. Systems Sci. and Mathemat., Washington Uni., St. Louis, MS, Report SSM 9201 - Part I, 1992.
18. R. E. Beardmore and R. Laister, "The flow of a differential-algebraic equation near a singular equilibrium," SIAM J. Matrix Anal., vol. 24. no. 1, pp. 106-120, 2002.
19. Y. Lijun and T. Yun, "An improved version of the singularity induced bifurcation theorem," IEEE Trans. Automat. Contr., vol. AC-46, no. 9, pp. 1483-1486, Sep. 2001.
20. R. E. Beardmore, "Double singularity-induced bifurcation points and singular Hopf bifurcations," Dynamics and Stability of Syst., vol. 15, no. 4, pp. 319-342, 2000.
21. J. Casti, Alternate Realities: Mathematical Models of Nature and Man New York: Wiley, 1988.
22. E. C. Zeeman, "On the unstable behavior of stock exchangers," J. Math. Econom., vol. 1, pp. 39-49, 1974.
23. R. E. Beardmore, "The singularity-induced bifurcation and its Kronecker normal form," in SIAM J. Matrix Anal., 2001, pp. 1-12.
24. R. Riaza, S. L. Campbell, and W. Marszalek, "On singular equilibria of index-1 DAE's," Circuits Syst. Signal Process., vol. 19, pp. 131-157, 2000.
25. R. Riaza, "On the singularity-induced bifurcation theorem," IEEE Trans. Automat. Contr., vol. AC-47, no. 9, pp. 1520-1523, Sep. 2002.
26. R. Riaza, "Double SIB points in differential-algebraic systems," IEEE Trans. Automat. Contr., vol. AC-48, no. 9, pp. 1625-1629, Sep. 2003.
27. 3," preprint, 2004.
28. W. Marszalek and S. L. Campbell, "DAE's arising from traveling wave solutions of PDE's II," Comp. Math. Appl., vol. 37, pp. 15-34, 1999.
29. Z. W. Trzaska and W. Marszalek, "Singular distributed parameter systems," in Proc. Inst. Elect. Eng. D, vol. 140, 1993, pp. 305-308.
30. P. Lancaster and M. Tismenetsky, The Theory of Matrices. London. U.K.: Academic, 1985.