Analyzing dynamic performance of power systems over parameter space using normal forms of vector fields - Part I: Identification of vulnerable regions

Songzhe Zhu, Vijay Vittal, Wolfgang Kliemann

Research output: Contribution to journalArticle

34 Scopus citations


This is the first part of a two-part paper discussing the dynamic performance of power systems over parameter space using the method of normal forms. A new normal form transformation is derived under the second order resonance condition. By using the resonance condition as a guide to indicate detrimental system dynamic performance, the authors propose a computationally efficient method to study the system under varying parameters. An approach to determine the resonance and near-resonance region in the parameter space is developed. For the resonance case, conclusions are drawn by simply examining the analytic solutions. For the near-resonance case, the machine states showing poor performance can be found by tracing the dominant nonlinear modal interaction and mode-machine interaction. The method is tested on the IEEE 50-generator system. The results reveal many interesting characteristics of the system related to resonance and near-resonance, which validates the effectiveness of the method as a useful ana lytical tool for system operation and design. Further work on quantifying the effect of the modal interactions on the machine states is presented in Part II.

Original languageEnglish (US)
Pages (from-to)444-450
Number of pages7
JournalIEEE Transactions on Power Systems
Issue number3
StatePublished - Aug 1 2001



  • Nonlinear analysis
  • Normal forms
  • Power system dynamics

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering

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