Chaos in a simple power system

Chaotic behavior has been observed in computer simulations for a simple power system over a range of loading conditions. The existence of the chaos, also called a strange attractor, is confirmed by calculation of its Lyapunov exponents and by its broad-band spectrum. Some implications of this analysis are discussed. >

[1]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[2]  I. Shimada,et al.  A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems , 1979 .

[3]  N. Kopell,et al.  Chaotic motions in the two-degree-of-freedom swing equations , 1982 .

[4]  L. Young.  Entropy, Lyapunov exponents, and Hausdorff dimension in differentiable dynamical systems , 1983 .

[5]  Hermann Haken,et al.  At least one Lyapunov exponent vanishes if the trajectory of an attractor does not contain a fixed point , 1983 .

[6]  P. Varaiya,et al.  Nonlinear oscillations in power systems , 1984 .

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

[8]  L. Chua,et al.  Chaos: A tutorial for engineers , 1987, Proceedings of the IEEE.

[9]  I. Dobson,et al.  A model of voltage collapse in electric power systems , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[10]  R. Boyd,et al.  INSTABILITIES, DYNAMICS AND CHAOS IN NONLINEAR OPTICAL SYSTEMS , 1988 .

[11]  R.J. Thomas,et al.  On voltage collapse in electric power systems , 1989, Conference Papers Power Industry Computer Application Conference.

[12]  Peter W. Sauer,et al.  Analysis of voltage control systems exhibiting Hopf bifurcation , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

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

[14]  S. A. Naqavi,et al.  Load flow fractals , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[15]  Eyad H. Abed,et al.  On bifurcations in power system models and voltage collapse , 1990, 29th IEEE Conference on Decision and Control.

[16]  Ali H. Nayfeh,et al.  Chaos and instability in a power system — Primary resonant case , 1990 .

[17]  Venkataramana Ajjarapu,et al.  Nonlinear oscillations and voltage collapse phenomenon in electrical power system , 1990, Proceedings of the Twenty-Second Annual North American Power Symposium.

[18]  C. Kieny,et al.  Ferroresonance study using Galerkin method with pseudo-arclength continuation method , 1991 .

[19]  V. Ajjarapu,et al.  Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system , 1991 .

[20]  C. Kieny.  Application of the bifurcation theory in studying and understanding the global behavior of a ferroresonant electric power circuit , 1991 .

[21]  L. Lai,et al.  Chaotic phenomena in power systems , 1991 .

[22]  Venkataramana Ajjarapu,et al.  Observation of bistable behavior in an electrical power system , 1991, [1991] Proceedings of the 34th Midwest Symposium on Circuits and Systems.