Domain of Attraction`s Estimation for Grid Connected Converters with Phase-Locked Loop

Ziqian Zhang*, Robert Schürhuber, Lothar Fickert, Katrin Friedl, Guochu Chen, Yongming Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A large number of non-linear hardware and control units exists in power electronic system used in grid connected devices. The analytical transient stability analysis of grid-connected converters presents numerous difficulties. A common method to tackle this problem is the stability analysis using Lyapunovs method. By applying this method, difficulties arise not only from finding a suitable Lyapunov function, but also from checking the constraint of Lyapunov stability. If the appropriate Lyapunov function is a high-order polynomial, it is very challenging to test if it meets the constraints of Lyapunov stability in certain regions. In this paper, the sum-of-squares programming method is used to obtain the estimation of a converters domain of attraction with a relatively small number of iterations compared to classically applied methods, such as the Monte Carlo method. The estimation of the domain of attraction are verified by time-domain simulations and StarSims controller hardware-in-the-loop tests in this paper.
Original languageEnglish
Pages (from-to)1351 - 1362
Number of pages12
JournalIEEE Transactions on Power Systems
Issue number2
Publication statusPublished - 2022


  • Converter stability
  • phase-locked loop
  • transient stability
  • Lyapunov method
  • domain of attraction
  • sum-ofsquares
  • controller hardware-in-the-loop
  • Direction-of-arrival estimation
  • Estimation
  • Power system stability
  • Phase locked loops
  • Analytical models
  • Mathematical model
  • Transient analysis
  • sum-of-squares

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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