Reliable prediction of Hopf bifurcation in power systems

Poria Astero, S. H. Hosseinian, E. Nasr, B. Vahidi

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


In this study, a new index for detection and prediction of oscillatory instabilities associated with HOPF bifurcation (HB) in power systems is proposed. Conventional indices could just predict HB in the heavy load conditions. The proposed index has a wider linear range and therefore prediction of system behavior at a wider range of load changes (even in lightly load condition) is provided. Consequently, the power system operators have more time to make the proper decisions to prevent HB. Conventional indices use critical eigenvalue pair of the state matrix to predict HB. This pair possesses biggest real parts among all eigenvalue pairs. However, sometimes this pair might not reach the imaginary axis before other eigenvalues. Therefore, they are not representative for HB eigenvalues which can lead to HB (This pair of eigenvalues could not be considered as HB eigenvalues). In this study, proposed index uses HB eigenvalue pair of state matrix to predict HB and two criteria are used to recognize HB eigenvalue pair. The first criterion is based on the proximity of the pairs of complex eigenvalue to the imaginary axis and the second criterion is based on the speed and the direction of the eigenvalues' movement towards the imaginary axis. Also, in this study, Matrix Reciprocal Condition Number Estimate (MRCNE) instead of minimum singular value decomposition is used to determine proximity of matrix to singularity. This estimation causes faster calculation without missing considerable accuracy. In order to demonstrate the effectiveness and accuracy of the proposed index, the new method is tested on the IEEE-14 bus and WSCC-9 bus test systems and results are presented. Results indicate that the proposed index has wider linear range and could predict HB in lower load level.

Original languageEnglish
Pages (from-to)61-68
Number of pages8
JournalElectrical Engineering
Issue number2
Publication statusPublished - Aug 2009
MoE publication typeA1 Journal article-refereed


  • Hopf Bifurcation prediction
  • Non-linear system
  • Oscillatory stability prediction
  • Small signal stability


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