Analytical calculation of power system trajectory eigenvalues and its error analysis

Xueping Pan, Yusheng Xue, Xiaoming Zhang, Chiyung Chung, Kitpo Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

30 Citations (Scopus)


Requiring quite wide sliding windows, signal processing techniques for extracting oscillation-mode information are applicable for neither fast time-varying systems nor strong nonlinear systems. To overcome the shortcomings, a method to calculate time-varying eigenvalues series is proposed based on the piecewise-linearized system models along the disturbed trajectories. Eigenvalue calculation is performed at the beginning of every time step for numerical integration. Furthermore, the piecewise-linearized dynamic equations are mapped into a series of time-varying one machine infinite bus (OMIB) systems and the oscillation mode within each integration-step can be identified with analytical formulas of extended equal-area criterion (EEAC). This makes the estimation of trajectory eigenvalues not only quickly but also accurately. The method is applied to a 3-machine 9-node test system and the effects of nonlinear non-autonomous factors on the eigenvalues are investigated.

Original languageEnglish
Pages (from-to)10-14
Number of pages5
JournalDianli Xitong Zidonghua/Automation of Electric Power Systems
Issue number19
Publication statusPublished - 10 Oct 2008


  • Eigenvalue analysis
  • Low frequency oscillation
  • Oscillation mode
  • Strong nonlinear systems
  • Trajectory eigenvalues of time-varying system

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Energy Engineering and Power Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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