Modeling and Control of AC Microgrids Under Unbalanced Utility Grid Voltage Using the Invariant-Ellipsoid Method

The increasing penetration of renewable microgrids (MGs) into utility grids (UGs) has introduced new stability and power quality challenges, especially under the unbalanced voltage of the utility grid. This paper presents a novel approach for modelling and controlling AC microgrids (MGs) influenced by unbalanced utility grid voltages, emphasizing inverter-based resources (IBRs). The proposed control design is based on the application of the invariant-ellipsoid method for disturbance rejection. In the presence of asymmetrical power exchange between the microgrid and utility grid, a negative-sequence rejection strategy is applied to ensure that the power transactions remain balanced. This study investigates two operational modes: 1) the MG feeds power to the UG (grid forming), and 2) the opposite mode (grid feeding). A simulation verification was conducted to assess the performance of the invariant-ellipsoid disturbance rejection method. Additionally, a comparison between the proposed invariant-ellipsoid tracker and a traditional H $\infty $ control strategy highlights the efficacy of the former in mitigating UG unbalanced voltage issues while reducing computational complexity. The results demonstrate that the invariant-ellipsoid approach provides robust performance under various unbalanced scenarios with improved dynamic response and reduced oscillations in the delivered power.