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In this paper, we develop an observer-based fault detection mechanism forgrid-forming inverters operating in islanded droop-controlled AC microgrids.The detection scheme uses linear matrix inequalities as constraints with$\mathcal{H}_{-}/\mathcal{H}_{\infty}$ optimization to achieve sensitivity tofaults and robustness against disturbances or parametric uncertainties. Weexplore a nonlinear inverter model formulation based on the less-restrictiveone-sided Lipschitz and quadratic inner-boundedness conditions instead of thestate-of-the-art formulation based on the Lipschitz condition. In this sense,we aim to overcome the sensitivity of observer-based schemes to the Lipschitzconstant. The relation between these two formulations for fault detection isanalyzed theoretically. We find the deterministic matrix expressions ofdifferent internal faults, including busbar, actuator, and inverter bridgefaults. The performance of the proposed detection method is tested on anislanded AC microgrid with four grid-forming inverters and compared against thestate-of-the-art nonlinear detection based on the Lipschitz condition. Mostimportantly, this method requires no additional sensors, a crucial advantageover many proposed solutions in the literature.

Fault Detection for Grid-Forming Inverters in Islanded Droop-Controlled AC Microgrids