Modulated Oscillations of Synchronous Machine Nonlinear Dynamics with Saturation

Dan Wu, Petr Vorobev, Samuel C. Chevalier, Konstantin Turitsyn

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


This paper discusses a potential mechanism from bifurcation analysis to explain the occurrence of modulated oscillations (which are observed from real PMU measurements) in synchronous machine nonlinear dynamics. We show that in special system configurations synchronous machine dynamics can be very sensitive to sustained low frequency oscillations which are amplified to a great extent by nonlinear effects. A comprehensive bifurcation analysis illustrates that a small sustained oscillation evolves into a torus through the Neimark-Sacker bifurcation, creating a modulated oscillation with a higher amplitude and a much slower but new oscillatory frequency. The analysis further predicts a new bifurcation type, the Chenciner bifurcation, that has never been reported in power engineering. The Chenciner bifurcation introduces much more complex dynamical behaviors including co-existence of two stable attractors and chaos. It can be a potential reason for the sudden appearance of a benign modulated oscillation without any system configuration change. We use a detailed synchronous machine infinite bus system with an automatic voltage regulator and a steam turbine to demonstrate the phenomenon and to study the bifurcation. Then, we perform a model order reduction to establish the main states responsible for nonlinear effects and show a potential critical role of the exciter saturation for the investigated bifurcation.

Original languageEnglish
Article number8930066
Pages (from-to)2915-2925
Number of pages11
JournalIEEE Transactions on Power Systems
Issue number4
Publication statusPublished - Jul 2020


  • Chenciner bifurcation
  • Neimark-Sacker bifurcation
  • sustained oscillation
  • Synchronous machine


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