Modelling and Stability Analysis of Wind Power Plants Connected to Weak Grids

Esmaeil Ebrahimzadeh, Frede Blaabjerg, Torsten Lund*, John Godsk Nielsen, Philip Richard Jacobsen Carne Kjær

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

6 Citations (Scopus)
94 Downloads (Pure)


It is important to develop modelling tools to predict unstable situations resulting from the interactions between the wind power plant and the weak power system. This paper presents a unified methodology to model and analyse a wind power plant connected to weak grids in the frequency-domain by considering the dynamics of the phase lock loop (PLL) and controller delays, which have been neglected in most of the previous research into modelling of wind power plants to simplify modelling. The presented approach combines both dq and positive/negative sequence domain modelling, where a single wind turbine is modelled in the dq domain but the whole wind power plant connected to the weak grid is analysed in the positive/negative sequence domain. As the proposed modelling of the wind power plant is systematic and modular and based on the decoupled positive/negative sequence impedances, the application of the proposed methodology is relevant for transmission system operators (TSOs) to assess stability easily with a very low compactional burden. In addition, as the analytical dq impedance models of the single wind turbine are provided, the proposed methodology is an optimization design tool permitting wind turbine manufacturers to tune their converter control. As a case study, a 108 MW wind power plant connected to a weak grid was used to study its sensitivity to variations in network short-circuit level, X/R ratio and line series capacitor compensation (Xc/Xg).
Original languageEnglish
Article number4695
JournalApplied Sciences
Issue number21
Number of pages15
Publication statusPublished - 1 Nov 2019


  • Wind power plants
  • Wind turbines
  • Weak grids
  • Impedance-based modelling
  • Small-signal stability
  • impedance-based modelling
  • weak grids
  • small-signal stability
  • wind turbines
  • wind power plants


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