Model Order Reductions for Stability Analysis of Islanded Microgrids With Droop Control

Three-phase inverters subject to droop control are widely used in islanded microgrids to interface distributed energy resources to a network and to properly share loads among different units. In this paper, a mathematical model for islanded microgrids with linear loads and inverters under frequency and voltage droop control is proposed. The model is constructed by introducing a suitable state-space transformation that allows to write the closed-loop model in an explicit state-space form. Then, the singular perturbations technique is used to obtain reduced order models that reproduce the stability properties of the original closed-loop model. The analysis shows that the currents' dynamics influence the stability of the microgrid, particularly for high values of the frequency droop control parameters. It is also shown that a further reduction of the model order leads to a typical oscillator model that is not able to predict the possible instability of the droop-controlled system. Numerical and experimental results demonstrate the validity of the proposed models.