Direct-Quadrature Sequence Models for Energy-Function Based Transient Stability Analysis of Unbalanced Inverter-Based Microgrids

The reliability of supply in distribution networks can be improved by islanding (parts of) the network as autonomous microgrids in case of a contingency. Microgrids are commonly fed by inverter-based distributed energy resources, which causes transient stability challenges due to the lack of inertia and strongly coupled dynamics. The transient stability of inverter-based microgrids is conventionally analyzed by time-domain analysis. However, energy-function based transient stability analysis has advantages over time-domain analysis, as it provides a stability result for all initial conditions and allows uncertainty to be taken into account with the domain of attraction. Microgrids are generally unbalanced, however models for unbalanced energy-function based transient stability analysis are lacking in the literature. In this paper, coupled sequence components models of distributed energy resources and load devices in the dq reference frame are proposed, and experimentally validated with unbalanced voltage transients. The validated models are used for energy-function based transient stability analysis of an unbalanced inverter-based case study microgrid. Finally, the impact of unbalanced connection of devices on transient stability is analyzed. The results indicate that the proposed models accurately represent the behavior of physical devices and that the unbalanced connection of devices significantly impacts the transient stability of inverter-based microgrids.