Comparison of BR and QR eigenvalue algorithms for power system small signal stability analysis

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Original languageEnglish
Pages (from-to)1848-1855
Journal / PublicationIEEE Transactions on Power Systems
Issue number4
Publication statusPublished - Nov 2006
Externally publishedYes


The BR algorithm is a novel and efficient method to find all eigenvalues of upper Hessenberg matrices and has never been applied to eigenanalysis for power system small signal stability. This paper analyzes differences between the BR and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and storage requirement. The BR algorithm utilizes accelerating strategies to improve its performance when computing eigenvalues of narrowly banded, nearly tridiagonal upper Hessenberg matrices. These strategies significantly reduce the computation time at a reasonable level of precision. Compared with the QR algorithm, the BR algorithm requires fewer iteration steps and less storage space without depriving of appropriate precision in solving eigenvalue problems of large-scale power systems. Numerical examples demonstrate the efficiency of the BR algorithm in pursuing eigenanalysis tasks of 39-, 68-, 115-, 300-, and 600-bus systems. Experiment results suggest that the BR algorithm is a more efficient algorithm for large-scale power system small signal stability eigenanalysis. © 2006 IEEE.

Research Area(s)

  • BR algorithm, CPU time, Eigenvalue calculation, Power systems, QR algorithm, Small signal stability, Stopping criteria, Upper Hessenberg matrix

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