Research ArticleOpen AccessGoogle Scholar indexed
Singular Hopf Bifurcations in DAE Models of Power Systems
- 1
- 2
Energy and Power Engineering·Volume 03 (2011)·Pages 1–8·Published 25 February 2011·DOI10.4236/epe.2011.31001
Copy link · social · email
Abstract
We investigate an important relationship that exists between the Hopf bifurcation in the singularly perturbed nonlinear power systems and the singularity induced bifurcations (SIBs) in the corresponding different- tial-algebraic equations (DAEs). In a generic case, the SIB phenomenon in a system of DAEs signals Hopf bifurcation in the singularly perturbed systems of ODEs. The analysis is based on the linear matrix pencil theory and polynomials with parameter dependent coefficients. A few numerical examples are included.
KeywordsPower SystemsSingularly Perturbed SystemsDAEsBifurcationsMatrix Pencils
- W. Marszalek and Z.W. Trzaska, “Singularity-Induced Bifurcations in Electrical Power Systems,” IEEE Transactions on Power Systems, Vol. 20, No. 1, 2005, pp. 312- 320. doi:10.1109/TPWRS.2004.841244
- H. G. Kwatny, R. F. Fischl and C. O. Nwankpa, “Local Bifurcation in Power Systems: Theory, Computation, and Applications,” Proceeding of IEEE, Vol. 83, No. 11, 1995, pp. 1456-1483. doi:10.1109/5.481630
- H. G. Kwatny, A. K. Pasrija and L. Y. Bahar, “Static Bifurcations in Electric Power Networks: Loss of Steady- state Stability and Voltage Collapse,” IEEE Transactions on Circuits and Systems, Vol. CAS-33, No. 10, 1986, pp. 981-991.
- H. G. Kwatny and X.-M. Yu, “Energy Analysis of Load-Induced Flutter Instability in Classical Models of Electric Power Networks,” IEEE Transactions on Cir- cuits and Systems, Vol.36, No.12, 1989, pp. 1544-1557.
- S. Ayasun, C. O. Nwankpa and G. G. Kwatny, “Compu- tation of Singular and Singularly Induced Bifurcation Points of Differential-Algebraic Power System Model,” IEEE Transactions on Circuits and Systems I, Vol. 51, No. 8, 2004, pp. 15251538.
- D. J. Hill and I. M. Y. Mareels, “Stability Theory for Dif- ferential/Algebraic Systems with Application to Power System,” IEEE Transactions on Circuits and Systems, Vol. CAS-37, No. 11, 1990, pp. 1416-1423. doi:10.1109/ 31.62415
- C. A. Canizares, N. Mithulananthan, F. Milano and J. Reeve, “Linear Performance Indices to Predict Oscilla- tory Stability Problems in Power Systems,” IEEE Trans- actions on Power System, Vol. 19, No. 2, 2004, pp. 1104- 1114. doi:10.1109/TPWRS.2003.821460
- I. Dobson, J. Zhang, S. Greene, H. Engdahl and P. W. Sauer, “Is Strong Modal Resonance a Precursor to Power System Oscillations?” IEEE Transactions on Circuits and Systems, Vol. 48, No. 3, 2001, pp. 340-349.
- V. Vekatasubrumanian, H. Schattler and J. Zaborszky, “A Stability Theory of Large Differential Algebraic Systems: A Taxonomy,” Report SSM 9201 — Part I, Washington University, St. Louis, 1992.
- V. Vekatasubrumanian, H. Schattler and J. Zaborszky, “Analysis of Local Bifurcation Mechanisms in Large Dif- ferential-Algebraic Systems such as the Power System,” Proceedings of 32nd Conference on Decision and Con- trol, San Antonio, December 1993, pp. 3727-3733.
- R. E. Beardmore and R. Laister, “The Flow of a Differen- tial-Algebraic Equation near a Singular Equilibrium,” SIAM Journal on Matrix Analysis, Vol. 24, No. 1, 2002, pp. 106-120. doi:10.1137/S0895479800378660