Bifurcation Analysis on a Multimachine Power System Model

In this article bifurcation analysis of the 9 bus power system model corresponding to the Western Systems Coordinating Council is performed. In order to use standard continuation packages like MATCONT, a full ordinary differential equations model, including the corresponding dynamics of the control loops and the transmission lines, is derived. Different loading conditions are studied by using the load demands as bifurcation parameters. For variations of one of the loads, it is shown that the equilibrium point undergoes Hopf and saddle-node bifurcations. Furthermore, the bifurcation analysis varying two loads simultaneously reveals the existence of a pair of double Hopf and a zero-Hopf bifurcations, acting as organizing centers of the dynamics. Finally, a power system stabilizer has been added in order to modify the location of a Hopf bifurcation curve.

[1]  Leon Y. Bahar,et al.  Static bifurcations in electric power networks: Loss of steady-state stability and voltage collapse , 1986 .

[2]  M. Pai,et al.  Static and dynamic nonlinear loads and structural stability in power systems , 1995 .

[3]  Federico Milano,et al.  Equivalency of Continuation and Optimization Methods to Determine Saddle-Node and Limit-Induced Bifurcations in Power Systems , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  Zhaosheng Feng,et al.  Double Hopf bifurcation for van der Pol-Duffing oscillator with parametric delay feedback control☆ , 2008 .

[5]  J. L. Moiola,et al.  Bifurcation analysis on a detailed multimachine power system model , 2008, 2008 40th North American Power Symposium.

[6]  Eyad H. Abed,et al.  Bifurcations, chaos, and crises in voltage collapse of a model power system , 1994 .

[7]  P. Kundur,et al.  Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions , 2004, IEEE Transactions on Power Systems.

[8]  Peter W. Sauer,et al.  Power System Dynamics and Stability , 1997 .

[9]  C. W. Taylor,et al.  Standard load models for power flow and dynamic performance simulation , 1995 .

[10]  J. P. Wilson,et al.  Bogdanov-Takens bifurcation points and Sil'nikov homoclinicity in a simple power-system model of voltage collapse , 2002 .

[11]  V. Venkatasubramanian,et al.  Dynamics of a minimal power system: invariant tori and quasi-periodic motions , 1995 .

[12]  Jianhua Xie,et al.  Hopf–Hopf bifurcation and invariant torus of a vibro-impact system , 2005 .

[13]  S. C. Srivastava,et al.  Elimination of dynamic bifurcation and chaos in power systems using FACTS devices , 1998 .

[14]  Martin Golubitsky,et al.  Classification and Unfoldings of Degenerate Hopf Bifurcations , 1981 .

[15]  C.A. Canizares,et al.  Elimination of algebraic constraints in power system studies , 1998, Conference Proceedings. IEEE Canadian Conference on Electrical and Computer Engineering (Cat. No.98TH8341).

[16]  Pei Yu,et al.  Analysis on Double Hopf Bifurcation Using Computer Algebra with the Aid of Multiple Scales , 2002 .

[17]  B. D. Coller,et al.  A study of double flutter , 2004 .

[18]  M. Golubitsky,et al.  Singularities and groups in bifurcation theory , 1985 .

[19]  Y. Kuznetsov.  Elements of applied bifurcation theory (2nd ed.) , 1998 .

[20]  Peter W. Sauer,et al.  Is strong modal resonance a precursor to power system oscillations , 2001 .

[21]  P. Yu,et al.  SYMBOLIC COMPUTATION OF NORMAL FORMS FOR RESONANT DOUBLE HOPF BIFURCATIONS USING A PERTURBATION TECHNIQUE , 2001 .

[22]  R. Fischl,et al.  Local bifurcation in power systems: theory, computation, and application , 1995, Proc. IEEE.

[23]  Marija D. Ilic,et al.  Preventing Future Blackouts by Means of Enhanced Electric Power Systems Control: From Complexity to Order , 2005, Proceedings of the IEEE.

[24]  Thomas F. Fairgrieve,et al.  AUTO 2000 : CONTINUATION AND BIFURCATION SOFTWARE FOR ORDINARY DIFFERENTIAL EQUATIONS (with HomCont) , 1997 .

[25]  V. Venkatasubramanian,et al.  Correction to "Dynamics of a Minimal Power System Invariant Tori and Quasi-Periodic Motions" , 1996 .

[26]  Chika O. Nwankpa,et al.  Computation of singular and singularity induced bifurcation points of differential-algebraic power system model , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Ian A. Hiskens,et al.  Analysis tools for power systems-contending with nonlinearities , 1995, Proc. IEEE.

[28]  H. Schättler,et al.  Dynamics of large constrained nonlinear systems-a taxonomy theory [power system stability] , 1995, Proc. IEEE.

[29]  Hsiao-Dong Chiang,et al.  Application of Bifurcation Analysis to Power Systems , 2003 .

[30]  Guanrong Chen,et al.  Hopf Bifurcation Analysis: A Frequency Domain Approach , 1996 .

[31]  Ian Dobson,et al.  Towards a theory of voltage collapse in electric power systems , 1989 .

[32]  A. Zecevic,et al.  The effects of generation redispatch on Hopf bifurcations in electric power systems , 2002 .

[33]  S. C. Srivastava,et al.  Application of Hopf bifurcation theory for determining critical value of a generator control or load parameter , 1995 .

[34]  D. Kosterev,et al.  An Interim Dynamic Induction Motor Model for Stability Studies in the WSCC , 2002, IEEE Power Engineering Review.

[35]  Sue Ann Campbell,et al.  Multistability and stable asynchronous periodic oscillations in a multiple-delayed neural system , 2006 .

[36]  Frank Schilder,et al.  Continuation of Quasi-periodic Invariant Tori , 2005, SIAM J. Appl. Dyn. Syst..

[37]  David J. Hill,et al.  Continuation of local bifurcations for power system differential-algebraic equation stability model , 2005 .

[38]  Jorge L. Moiola,et al.  A Gallery of oscillations in a Resonant Electric Circuit: Hopf-Hopf and fold-flip Interactions , 2008, Int. J. Bifurc. Chaos.

[39]  Felix F. Wu,et al.  Bifurcation, chaos, and voltage collapse in power systems , 1995, Proc. IEEE.

[40]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[41]  Carson W. Taylor,et al.  Definition and Classification of Power System Stability , 2004 .

[42]  Yixin Ni,et al.  Global power system control using generator excitation, PSS, FACTS devices and capacitor switching , 2005 .

[43]  Claudio A. Canizares,et al.  Bifurcation analysis of various power system models , 1999 .

[44]  Claudio A. Canizares,et al.  Multiparameter bifurcation analysis of the south Brazilian power system , 2003 .

[45]  P. Kundur,et al.  Power system stability and control , 1994 .

[46]  H. Happ.  Power system control and stability , 1979, Proceedings of the IEEE.