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Reduced-Order Model of Distributed Generators with Internal Loops and Virtual Impedance


Reduced-order converter models have attracted attention in microgrid applications for being less computationally expensive and simpler to analyze. However, most of the models already developed in the literature only include basic control loops, while control additions such as virtual impedances and the effect of internal control loops are typically neglected. Also, the frequency range in which these models are applicable has not been thoroughly studied. In this paper, a low-order reduced-order model of a droop-controlled converter that includes internal control loops and virtual impedances is derived. The validity of the assumptions used to reduce the model is analyzed and a criterion for deciding the frequency range in which the model can be used is proposed. Differences between transient and quasi-stationary virtual impedances are highlighted by using the proposed modelling method. In particular, it is analytically shown that quasi-stationary virtual impedances have a larger stability region compared to transient virtual impedances. Simulation and experimental results based on a 60 kVA converter are used to validate the main contributions of this work


Academic article


  • Research Council of Norway (RCN) / 257626





  • Norwegian University of Science and Technology
  • Spain
  • SINTEF Energy Research / Energisystemer



Published in

IEEE Transactions on Smart Grid



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