A fast algorithm for identification and tracing of voltage and oscillatory stability margin boundaries

Proceedings of the IEEE

Volumn 93, Issue 5, 2005, Pages 934-946

  Zhou, Yuan ^a   Ajjarapu, Venkataramana ^b  

^a GE ENERGY   (United States)

^b Iowa State University of Science and Technology   (United States)

Author keywords

Differential and algebraic equations (DAE); Hopf bifurcation; Load margin; Manifold; Margin boundary tracing; Saddle node bifurcation (SNB); Time domain simulation; Voltage stability

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; ELECTRIC POWER SYSTEMS; NONLINEAR CONTROL SYSTEMS; OPTIMIZATION; OSCILLATIONS;

DIFFERENTIAL AND ALGEBRAIC EQUATIONS (DAE); HOPF BIFURCATION; LOAD MARGIN; MANIFOLD; MARGIN BOUNDARY TRACING; SADDLE NODE BIFURCATION (SNB); TIME-DOMAIN SIMULATION; VOLTAGE STABILITY;

ELECTRIC POTENTIAL;

EID: 21244470397     PISSN: 00189219     EISSN: None     Source Type: Journal    
DOI: 10.1109/JPROC.2005.847254     Document Type: Conference Paper

References (54)

1. Power Syst. Stability Subcomm., "Voltage stability assessment: Concepts, practices and tools," IEEE Power Eng. Soc., Catalog No. SP101PSS, 2002.
2. Power Syst. Dynamic Perform. Subcomm., "Voltage stability of "' power systems: Concepts, analytical tools and industry experience," IEEE Power Eng. Soc., Catalog No. 90TH0358-2-PWR, 1990.
3. IEEE Working Group on Voltage Stability, "Suggested techniques for voltage stability analysis," IEEE Power Eng. Soc., Catalog No. 93TH0620-5-PWR, Y. Mansour, Ed., 1993.
4. C. W. Taylor, Power System Voltage Stability. New York: McGraw-Hill, 1994.
5. P. Kundur, Power System Stability and Control. New York: McGraw-Hill, 1994.
6. T. Van Cutsem and C. Vournas, Voltage Stability of Electric Power Systems. Norwell, MA: Kluwer, 1998.
7. M. Ilic and J. Zaborszky, Dynamics and Contrl of Large Electric Power Systems. New York: Wiley, 2000.
8. Proc. Bulk Power System Voltage Phenomena III, Voltage Stability, Security and Control, L. H. Fink, Ed., Davos, Switzerland, 1994.
9. Proc. Bulk Power System Dynamics and Control IV, Restructuring, L. H. Fink, Ed., Santorini, Greece, 1998.
10. "Proc. of bulk power system dynamics and control-V, security and reliability in a changing environment," presented at the IREP Workshop, Onomichi, Japan, 2001.
11. V. Ajjarapu and B. Lee, "Bibliography on voltage stability," IEEE Trans. Power Syst., vol. 13, no. 1, pp. 115-125, Feb. 1998.
12. V. Ajjarapu. Iowa State University's Web-based voltage stability search engine. [Online]. Available: http://design-2.ee.iastate.edu/biblio/
13. B. D. Hassard, N. D. Kazarinoff, and Y. -H. Wan, Theory and Applications of Hopf Bifurcation. Cambridge, U.K.: Cambridge Univ. Press, 1981.
14. I. Dobson, F. Alvarado, and C. L. DeMarco, "Sensitivity of Hopf bifurcations to power system parameters," in Proc. 31st IEEE Conf. Decision and Control, vol. 3, 1992, pp. 2928-2933.
15. C. D. Vournas, M. A. Pai, and P. W. Sauer, "The effect of automatic voltage regulation on the bifurcation evolution in power systems," IEEE Trans. Power Syst., vol. 11, no. 4, pp. 1683-1688, Nov. 1996.
16. W. Zhu, R. R. Mohler, R. Spee, W. A. Mittelstadt, and D. Maratukulam, "Hopf bifurcations in a SMIB power system with SSR," IEEE Trans. Power Syst., vol. 11, no. 3, pp. 1579-1584, Aug. 1996.
17. V. Ajjarapu and B. Lee, "Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system," IEEE Trans. Power Syst., vol. 7, no. 1, pp. 424-431, Feb. 1992.
18. K. Kim, H. Schattler, V. Venkatasubramanian, J. Zaborszky, and P. Hirsch, "Methods for calculating oscillations in large power systems," IEEE Trans. Power Syst., vol. 12, no. 4, pp. 1639-1648, Nov. 1997.
19. F. Howell and V. Venkatasubramanian, "Transient stability assessment with unstable limit cycle approximation," IEEE Trans. Power Syst., vol. 14, no. 2, pp. 667-677, May 1999.
20. V. Ajjarapu and C. Christy, "The continuation power flow: A tool for steady state voltage stability analysis," IEEE Trans. Power Syst., vol. 7, no. 1, pp. 416-423, Feb. 1992.
21. Z. Feng, V. Ajjarapu, and D. J. Maratukulam, "Identification of voltage collapse through direct equilibrium tracing," IEEE Trans. Power Syst., vol. 15, pp. 342-349, Feb. 2000.
22. C. A. Canizares, A. C. Z. de Souza, and V. H. Quintana, "Comparison of performance indexes for detection of proximity to voltage collapse," IEEE Trans. Power Syst., vol. 11, no. 3, pp. 1441-1450, Aug. 1996.
23. C. A. Canizares and F. L. Alvarado, "Point of collapse and continuation methods for large AC/DC systems," IEEE Trans. Power Syst., vol. 8, no. 1, pp. 1-8, Feb. 1993.
24. A. C. Z. de Souza, C. A. Canizares, and V. H. Quintana, "New techniques to speed up voltage collapse computations using tangent vectors," IEEE Trans. Power Syst., vol. 12, no. 3, pp. 1380-1387, Aug. 1997.
25. A. J. Flueck and J. R. Dondeti, "A new continuation power flow tool for investgating the nonlinear effects of transmission branch parameter variations," IEEE Trans. Power Syst., vol. 15,no. 1, pp. 223-227, Feb. 2000.
26. H. D. Chiang, A. J. Flueck, K. S. Shah, and N. Balu, "CPFLOW: A practical tool for tracing power system steady-state stationary behavior due to load and generation variations," IEEE Trans. Power Syst., vol. 10, no. 2, pp. 623-634, May 1995.
27. I. Dobson and L. Lu, "Computing an optimum direction in control space to avoid saddle bifurcation and voltage collapse in electric power systems," IEEE Trans. Autom. Control, vol. 37, no. 10, pp. 1616-1620, Oct. 1992.
28. S. Greens, I. Dobson, and F. L. Alvarado, "Contingency ranking for voltage collapse via sensitivities from a single nose curve," IEEE Trans. Power Syst., vol. 14, no. 1, pp. 232-240, Feb. 1999.
29. _, "Sensitivity of the loading margin to voltage collapse with respect to arbitrary parameters," IEEE Trans. Power Syst., vol. 12, no. 1, pp. 262-272, Feb. 1997.
30. B. Long and V. Ajjarapu, "The sparse formulation of ISPS and its application to voltage stability margin sensitivity and estimation," IEEE Trans. Power Syst., vol. 14, no. 3, pp. 944-957, Aug. 1999.
31. A. Berizzi, P. Finazzi, D. Dosi, P. Marannino, and s. corsi, "First and second order methods for voltage collapse assessment and security enhancement," presented at the IEEE Power Engineering Soc. Winter Meeting, New York, 1997.
32. J. Barauin, T. Gomez, and F. L. pagola, "Estimating the loading limit margin taking into account voltage collapse areas," IEEE Trans. Power Syst., vol. 10, no. 4, pp. 1952-1962, Nov. 1995.
33. W. C. Rheinboldt, Numerical Analysis of Parameterized Nonlinear Equations. New York: Wiley, 1986.
34. R. Dai and W. C. Rheinboldt, "On the computation of manifolds of foldpoints for paramter-dependent problems," SIAM J. Numer. Anal., vol. 27, no. 2, pp. 437-446, Apr. 1990.
35. P. W. Sauer and M. A. Pai, "Power system steady-state stability and the load flow Jacobian," IEEE Trans. Power Syst., vol. 5, no. 4, pp. 1374-1383, Nov. 1990.
36. V. Ajjarapu, "Identification of steady state voltage stability in power systems," Int. J. Elect. Power Energy Syst., vol. 11, pp. 43-46, 1991.
37. M. Kubicek and M. Marek, "Computational methods in bifurcation theory and dissipative structures," in Springer Series in Computational Physics. New York: Springer-Verlag, 1983.
38. Y. V. Makarov, Z. Y. Dong, and D. J. Hill, "A general method for small signal stability analysis," IEEE Trans. Power Syst., vol. 13, no. 3, pp. 979-985, Aug. 1998.
39. D. J. Hill and Z.-Y. Dong, "Nonlinear computation and control for small disturbance stability," in Proc. IEEE Power Engineering Soc. Summer Meeting, vol. 2, 2000, pp. 836-841.
40. J. M. Campagnolo, N. Martins, J. L. R. Pereira, L. T. G. Lima, H. J. C. P. Pinto, and D. M. Falcao, "Fast small-signal stability assessment using parallel processing," IEEE Trans. Power Syst., vol. 9, no. 2, pp. 949-956, May 1994.
41. G. Angelidis and A. Semlyen, "Efficient calculation of critical eigenvalue clusters in the small signal stability analysis of large power systems," IEEE Trans. Power Syst., vol. 10, no. 1, pp. 427-432, Feb. 1995.
42. P. Kundur, G. J. Rogers, D. Y. Wong, L. Wang, and L. Lauby, "A comprehensive computer program package for small signal stability analysis of power systems," IEEE Trans. Power Syst., vol. 5, no. 4, pp. 1076-1083, Nov. 1990.
43. Y. Zhou and V. Ajjarapu, "Optimal margin boundary tracing with continuation optimal power flow," presented at the 34th North Amer. Power Symp., Tempe, AZ, 2003.
44. _, "A novel approach to trace time domain trajectories of power systems in multiple time scales," IEEE Trans. Power Syst., vol. 20, no. 1, pp. 149-155, Feb. 2005.
45. T. Van. Cutsem, "An approach to corrective control of voltage instability using simulation and sensitivity," IEEE Trans. Power Syst., vol. 10, no. 2, pp. 616-622, May 1995.
46. T. Van Cutsem and C. D. Vournas, "Voltage stability analysis in transient and midterm time scales," IEEE Trans. Power Syst., vol. 11, no. 1, pp. 146-154, Feb. 1996.
47. T. Van Cutsem, "Voltage instability: Phenomena, countermeasures, and analysis methods," Proc. IEEE, vol. 88, no. 2, pp. 208-227, Feb. 2000.
48. T. Van Cutsem, Y. Jacquemart, J.-N. Marquet, and P. Pruvot, "A comprehensive analysis of midterm voltage stability," IEEE Trans. Power Syst., vol. 10, no. 3, pp. 1173-1182, Aug. 1995.
49. L. T. G. Lima, L. H. Bezerra, C. Tomei, and N. Martins, "New method for fast small-signal stability assessment of large scale power systems," IEEE Trans. Power Syst., vol. 10, no. 4, pp. 1979-1985, Nov. 1995.
50. N. Martins, L. T. G. Lima, and J. J. C. P. Pinto, "Computing dominant poles of power system transfer functions," IEEE Trans. Power Syst., vol. 11, no. 1, pp. 162-170, Feb. 1996.
51. J. M. Campagnolo, N. Martins, and D. M. Falcao, "An efficient and robust eigenvalue method for small-signal stability assessment in parallel computers," IEEE Trans. Power Syst., vol. 10, no. 1, pp. 506-511, Feb. 1995.
52. _, "Refactored bi-iteration: A high performance eigensolution method for large power system matrices," IEEE Trans. Power Syst., vol. 11, no. 3, pp. 1228-1235, Aug. 1996.
53. G. Angelidis and A. Semlyen, "Improved methodologies for the calculation of critical eigenvalues in small signal stability analysis," IEEE Trans. Power Syst., vol. 11, no. 3, pp. 1209-1217, Aug. 1996.
54. P. Kundur and L. Wang, "Small signal stability analysis: Experiences, achievements, and challenges," in Proc. Power Con 2002 Int. Conf. Power System Technology, vol. 1, pp. 6-12.