TRANSCRITICAL AND HOPF BIFURCATIONS IN AC / DC SYSTEMS

This paper illustrates transcritical and Hopf bifurcations in a realistic ac/dc power system model. These bifurcations are thoroughly analyzed based on bifurcation theory to understand and characterize their e ect on the dynamic behavior of the system, particularly on voltage stability. A new technique to trace transcritical bifurcations diagrams is proposed, based on the generic characteristic of saddle-node bifurcations for constant P load changes, as demonstrated in the paper. Control mechanisms for avoiding the bifurcations are also presented. Finally, the paper discusses the computational requirements for studying possible chaotic behavior due to bifurcations on the system limit cycles.

[1]  Wilfred Kaplan,et al.  Advanced mathematics for engineers , 1981 .

[2]  Dirk Roose,et al.  An algorithm for the computation of Hopf bifurcation points in comparison with other methods , 1985 .

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

[4]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[5]  Felix F. Wu,et al.  Stability of nonlinear systems described by a second-order vector differential equation , 1988 .

[6]  A.G. Phadke,et al.  Dynamic simulation of voltage collapse , 1989, Conference Papers Power Industry Computer Application Conference.

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

[8]  F. L. Alvarado,et al.  Bifurcations in nonlinear systems-computational issues , 1990, IEEE International Symposium on Circuits and Systems.

[9]  V. Ajjarapu,et al.  Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system , 1991, [Proceedings] Conference Papers 1991 Power Industry Computer Application Conference.

[10]  Thomas J. Overbye,et al.  Voltage security enhancement using energy based sensitivities , 1991 .

[11]  F. Alvarado,et al.  Point of collapse methods applied to AC/DC power systems , 1992 .

[12]  D. Hill,et al.  Fast calculation of a voltage stability index , 1992 .

[13]  Ian Dobson,et al.  Voltage collapse precipitated by the immediate change in stability when generator reactive power limits are encountered , 1992 .

[14]  B. Gao,et al.  Voltage Stability Evaluation Using Modal Analysis , 1992, IEEE Power Engineering Review.

[15]  Claudio A. Canizares,et al.  Point of collapse and continuation methods for large AC/DC systems , 1993 .

[16]  J. Deuse,et al.  Simulation of voltage collapse , 1993 .

[17]  Felix F. Wu,et al.  Chaos in a simple power system , 1993 .

[18]  P. Kundur,et al.  Voltage stability analysis using static and dynamic approaches , 1993 .

[19]  Claudio Adrián,et al.  Saddle-node bifurcations in power systems , 1993 .

[20]  J. Deuse,et al.  Dynamic simulation of voltage collapses , 1993 .