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 the network and to properly share the 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 which 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 which 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 the typical oscillator model which is not able to predict the possible instability of the droop controlled system. Numerical and experimental results demonstrate the validity of the proposed models.