This paper proposed a probabilistic framework that could be used for the sensitivity assessment of grid-connected voltage source converters (VSCs), where uncertainties in the grid short circuit ratio (SCR) and operating point conditions, as well as control-loop interactions, were considered. The proposed method tried to broaden the available knowledge on the small-signal stability analysis of VSCs and provide a probabilistic point of view of this subject. It considered the probability of different operational conditions in order to obtain less conservatism and more accurate results. Based on uncertain inputs and the employed stability model, the proposed model produced statistical distributions of the critical mode and its damping factor and ratio, which were not accessible by existing deterministic methods. Crucial statistical information measures how much system stability and performance are maintained or changed over the system uncertainties and disturbances, as well as provides a clear insight into the system stability problem. For instance, as concluded in this paper, for the conventional control system design, fast dynamic parts of a VSC, such as the current controller and control delay, significantly impact the minimum damping ratio. Furthermore, slow dynamic parts, such as outer voltage control loops and the synchronization block, influence the maximum damping factor. For strong grids, the AC voltage magnitude controller (AVC) significantly impacts the maximum damping factor due to its lower bandwidth among all control loops. For weak grids, the damping factor of the critical mode is highly affected by interactions between the VSC, the power grid, and different control loops due to the synchronization mechanism. The other contributions of this paper were the introduction of robust stability and performance definitions and indices; explanations of the pros and cons of probabilistic assessment methods and their applicability; interpretation of the obtained results; and, finally, a link was provided between system stability and reliability, which will be crucial for future power system design
Original languageEnglish
Article number7375
JournalApplied Sciences (Switzerland)
Issue number15
Publication statusPublished - 22 Jul 2022


  • voltage source converters (VSCs)
  • grid-connected VSC
  • weak grids
  • probabilistic stability analysis
  • Monte Carlo simulations
  • Robustness Analysis


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