Improved methodologies for the calculation of critical eigenvalues in small signal stability analysis

This paper presents improved and new methodologies for the calculation of critical eigenvalues in the small-signal stability analysis of large electric power systems. They augment the robustness and efficiency of existing methods and provide new alternatives. The procedures are implementations of Newton's method, inverse power and Rayleigh quotient iterations, equipped with implicit deflation, and restarted Arnoldi with a locking mechanism and either shift-invert or semi-complex Cayley preconditioning. The various algorithms are compared and evaluated regarding convergence, performance and applicability.

[1]  D. S. Kirschen,et al.  Eigenvalue analysis of very large power systems , 1988 .

[2]  F. Schweppe,et al.  Selective Modal Analysis with Applications to Electric Power Systems, PART I: Heuristic Introduction , 1982, IEEE Transactions on Power Apparatus and Systems.

[3]  Nelson Martins,et al.  Efficient methods for finding transfer function zeros of power systems. Discussion , 1991 .

[4]  R. Bennon,et al.  Eigenvalue Analysis of Synchronizing Power Flow Oscillations in Large Electric Power Systems , 1982, IEEE Transactions on Power Apparatus and Systems.

[5]  M. G. Lauby,et al.  A comprehensive computer program package for small signal stability analysis of power systems , 1990 .

[6]  Djalma M. Falcao,et al.  An efficient and robust eigenvalue method for small-signal stability assessment in parallel computers , 1995 .

[7]  L. Wang,et al.  Sequential computation of the complete eigensystem for the study zone in small signal stability analysis of large power systems , 1988 .

[8]  N. Martins.  Efficient Eigenvalue and Frequency Response Methods Applied to Power System Small-Signal Stability Studies , 1986, IEEE Transactions on Power Systems.

[9]  Ignacio J. Pérez-Arriaga,et al.  Selective modal analysis of power system oscillatory instability , 1988 .

[10]  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.

[11]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[12]  N. Martins,et al.  New methods for fast small-signal stability assessment of large scale power systems , 1995 .

[13]  A. Spence,et al.  Shift-invert and Cayley transforms for detection of rightmost eigenvalues of nonsymmetric matrices , 1994 .

[14]  L. Wang,et al.  Application of sparse eigenvalue techniques to the small signal stability analysis of large power systems , 1989, Conference Papers Power Industry Computer Application Conference.

[15]  A. Semlyen,et al.  Efficient calculation of critical eigenvalue clusters in the small signal stability analysis of large power systems , 1995 .

[16]  P. Kundur,et al.  Eigenvalue analysis of very large power systems , 1988 .

[17]  J. M. Campagnolo,et al.  Refactored bi-iteration: a high performance eigensolution method for large power system matrices , 1996 .

[18]  N. Uchida,et al.  A new eigen-analysis method of steady-state stability studies for large power systems: S matrix method , 1988 .