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

Three-phase inverters subject to droop control arewidely used in islanded microgrids to interface distributed energyresources to the network and to properly share the loads amongdifferent units. In this paper, a mathematical model for islandedmicrogrids with linear loads and inverters under frequency andvoltage droop control is proposed. The model is constructed byintroducing a suitable state space transformation which allows towrite the closed loop model in an explicit state space form. Then,the singular perturbations technique is used to obtain reducedorder models which reproduce the stability properties of theoriginal closed loop model. The analysis shows that the currentsdynamics influence the stability of the microgrid particularlyfor high values of the frequency droop control parameters. Itis also shown that a further reduction of the model order leadsto the typical oscillator model which is not able to predict thepossible instability of the droop controlled system. Numerical andexperimental results demonstrate the validity of the proposedmodels.