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I. INTRODUCTION XTREME natural events in recent years have caused immense losses to power systems and societies. Recent severe power outages caused by extreme natural events such as Superstorm Sandy [1], are powerful reminders that energy infrastructure resilience requires significant enhancement. Resilience is defined as "The ability to prepare for and adapt to changing conditions and withstand and recover rapidly from disruptions" [2]. In power systems, the North American Electric Reliability Corporation (NERC) and the United States Electric Power Research Institute (EPRI) have been actively developing innovative technologies aimed at enhancing resilience. Although the functionary requirements of resilience are very diverse, the ability to adapt unfolding extreme natural events and to restore from an outage are identified. Especially, the survivability of critical loads during extreme natural events has been widely highlighted [2]. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2016.2609603, IEEE Transactions on Smart Grid > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2To meet the requirements of system resilience, it appears that microgrids play important roles, especially for distribution systems [3][4][5]. As a critical function of resilience, after an extreme natural events, microgrids in islanded mode or grid-connected mode, are expected to restore the system as quickly as possible. Especially, it is important to restore critical loads (CLs). However, it is a challenging task for microgrids to maintain system frequency and bus voltages with limited operating resources and small system inertia, especially, after a major outage. The frequency deviations should be kept within operating limits in order to avoid permanent damage to the diesel and steam generators. Some CLs are sensitive to the power quality. The voltage deviations at the CLs should be reduced in order to guarantee a reliable supply at CLs.Sufficient operating resources are essential for the resilience of microgrids. Researchers have proposed various methods to enhance to controllability with limited operating resources from all components of systems. As proposed in [6], power converter based wind energy generation systems can be operated to increase the system inertia by implementing frequency droop control. An identical control strategy has been applied on several different kinds of renewable generation systems and energy storage systems to increase the system inertias as proposed in [7][8][9]. However, it is still a challenging task for microgrids to reliably supply the CLs in microgrids with fluctuating renewable energy after extreme natural events. Recently, loads have also been proposed as a type of operating resource by implementing load-response [10]. As described in [11], load-response can contribute to the frequency control. With the development...