A computational method for the calculation of the feasibility boundary and clustering in differential-algebraic systems

A clustering approach is presented to calculate the limits of parametric stability for a stable equilibrium of the power systems modeled by differential algebraic equations (DAEs) , the so-called "feasibility boundary." The underlying algorithm for calculation is based on the sensitivities of the eigenvalues of the DA system. The procedure is illustrated with several examples based on the standard nine-bus system and test beds formed by connecting sets of two and four nine-bus systems together.

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

[2]  I. Dobson.  Observations on the geometry of saddle node bifurcation and voltage collapse in electrical power systems , 1992 .

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

[4]  Robert A. Schlueter,et al.  Justification of the voltage stability security assessment and diagnostic procedure using a bifurcation subsystem method , 2000 .

[5]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[6]  I. A. Hiskens,et al.  Systematic Modeling and Symbolically Assisted Simulation of Power Systems , 2001, IEEE Power Engineering Review.

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

[8]  G. Verghese,et al.  Selective Modal Analysis With Applications to Electric Power Systems, Part II: The Dynamic Stability Problem , 1982, IEEE Transactions on Power Apparatus and Systems.

[9]  H. Schättler,et al.  Fast time-varying phasor analysis in the balanced three-phase large electric power system , 1995, IEEE Trans. Autom. Control..

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

[11]  H. Schattler,et al.  On the calculation of the feasibility boundary for differential-algebraic systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  A. Zecevic,et al.  A partitioning algorithm for the parallel solution of differential-algebraic equations by waveform relaxation , 1999 .

[13]  Thierry Van Cutsem,et al.  Voltage Stability of Electric Power Systems , 1998 .

[14]  I. Hiskens,et al.  Exploring the Power Flow Solution Space Boundary , 2001, IEEE Power Engineering Review.

[15]  Thomas Kailath,et al.  Linear Systems , 1980 .

[16]  Dragoslav D. Siljak,et al.  Nested ε-decompositions and clustering of complex systems , 1986, Autom..

[17]  Heinz Schättler,et al.  Methods for calculating oscillations in large power systems , 1997 .

[18]  F. Alvarado,et al.  Sensitivity of Hopf bifurcations to power system parameters , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[19]  H. Kwatny,et al.  Singular sets and surfaces and their implications in power systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[20]  R. A. Schlueter,et al.  An approach for determining the subsystem experiencing and producing a bifurcation in a power system dynamic model , 2000 .

[21]  D. Hill,et al.  Stability theory for differential/algebraic systems with application to power systems , 1990 .

[22]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[23]  S. Wiggins.  Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[24]  Kendall E. Atkinson.  An introduction to numerical analysis , 1978 .

[25]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[26]  D. Hill,et al.  Computation of Bifurcation Boundaries for Power Systems: a New , 2000 .

[27]  Ernst Hairer,et al.  The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .

[28]  H. Schättler,et al.  Local bifurcations and feasibility regions in differential-algebraic systems , 1995, IEEE Trans. Autom. Control..