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An efficient algorithm for small signal stability analysis using the Arnoldi and S‐matrix methods
Author(s) -
Ishikawa Fumio,
Sasaki Hiroshi,
Kubokawa Junji,
Terasako Hiroaki
Publication year - 1997
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/(sici)1520-6416(199712)121:4<38::aid-eej5>3.0.co;2-w
Subject(s) - eigenvalues and eigenvectors , arnoldi iteration , transformation (genetics) , algorithm , stability (learning theory) , power iteration , matrix (chemical analysis) , mathematics , signal (programming language) , scale (ratio) , transformation matrix , computer science , iterative method , physics , biochemistry , chemistry , materials science , kinematics , quantum mechanics , classical mechanics , machine learning , composite material , gene , programming language
This paper proposes an efficient algorithm for small signal stability analysis by means of the Arnoldi method with an S‐matrix transformation. In the proposed algorithm, the Arnoldi method evaluates several eigenpairs of large‐scale matrices with less execution time. The S‐matrix transformation constructs dominant eigenvalues corresponding to low damped oscillation modes. The combined use of these techniques enables us to calculate exclusively the critical eigenvalues of large‐scale power systems efficiently. The Arnoldi method has the specific feature that it can obtain eigenvalues successively from the outer part of their distribution. By making use of this characteristic, the spectral transformation can be simplified, thus improving calculation efficiency. The proposed method is also useful in understanding the shape of the spectrum by investigating all of the eigenvalues obtained, including nonconverged eigenvalues. The algorithm has been successfully applied to a large‐scale power system which has 220 generating units and 3000 state variables. © 1998 Scripta Technica. Electr Eng Jpn, 121(4): 38–47, 1997