Nonlinear transient stability analysis of Phased-Locked Loop based grid-following Voltage Source Converters using Lyapunov's direct method

Milad Zarif Mansour, Si Phu Me, Sajjad Hadavi, Babak Badrazadeh, Alireza Karimi, Behrooz Bahrani

Research output: Contribution to journalArticleResearchpeer-review


In this paper, using Lyapunov’s stability theorem,

the transient stability conditions for a grid-following Voltage

Source Converter (VSC) are found. These conditions take into

account both the grid specifications and the VSC’s dynamics. The

derived conditions are based on a well-known nonlinear model

of the VSC’s Phase-Locked Loop. To evaluate the stability of the

nonlinear system, Lyapunov’s direct method is employed. To this

end, a new Lyapunov function is proposed, and its characteristics

are analysed. Using this Lyapunov function, the domain

of attraction of the system’s equilibrium point is calculated.

Additionally, a novel system strength index based on the domain

of attraction of the system is proposed. The privilege of this index

over the conventional indices are absoluteness, VSC’s dynamics

consideration, and comparability of different VSCs with each

other from a stability point of view. In the end, the correctness

of the proposed stability analysis is validated via simulation in

Matlab/PLECS and experiment.

Original languageEnglish
Number of pages11
JournalIEEE Journal of Emerging and Selected Topics in Power Electronics
Publication statusAccepted/In press - 8 Feb 2021


  • Circuit stability
  • Domain of Attraction
  • Indexes
  • Lyapunov methods
  • Lyapunov’s Stability Theorem
  • Nonlinear Modeling
  • Phase locked loops
  • Phase-Locked Loop
  • Power system stability
  • Stability
  • Stability criteria
  • Transient analysis
  • Voltage Source Converter
  • Weak Grid

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