Interval Load Flow Models for Islanded AC and Hybrid AC/DC Microgrids with Load Uncertainties

The islanded mode of AC and hybrid AC/DC microgrids enhances the reliability and resiliency of distribution systems by enabling the use of local distributed generators (DGs) during abnormal conditions such as grid faults, weather events, and cyber attacks. Islanded AC microgrids (IMGs) and islanded hybrid AC/DC microgrids (IHMGs) require a specialized modeling approach compared to grid-connected microgrids due to the implementation of droop control for DGs, where active power is regulated through frequency ($\omega$) and reactive power through bus voltage (V). In IHMGs, power sharing among DGs in the DC microgrid is controlled through their respective bus voltages, while the power exchange between AC and DC microgrids is managed using interlining converter (IC). The IC droop control uses the AC microgrid frequency and DC bus voltages for power balance in IHMG. This droop control is modeled using droop equations for system studies. This article presents interval load flow models that account for the unique features of droop control and islanded operation. The integration of renewable energy sources, electric vehicles, storage, and power electronic loads introduces uncertainty in the load demands of IMGs and IHMGs, which are treated as interval quantities, with load flow models solved as optimization problems. The solutions of the interval load flow models for IMGs and IHMGs are validated by comparing them with results from Monte Carlo Simulation studies (MCS). Through various case studies on IMGs and IHMGs, we highlight the scalability and efficacy of the interval approach for managing load uncertainty in these microgrids.