The reliability and resilience of the electrical power grids are essential to industry, economy and society. Microgrids that are able to island from the bulk electrical grid are one technology that may vastly improve electrical power service to customer loads. To achieve these improvements, an islanded microgrid should be able to operate through the loss of one of its generators without shedding electrical load. The loss of one generator will typically result in significant additional loads, including transient overloads, being placed on the remaining generators. There is also the possibility of additional generator tripping during these processes (i.e. cascading failures), which would likely result in the collapse of the microgrid. The novelty of our work consists in incorporating dynamic models of generator controllers into a microgrid optimal dispatch formulation with the ultimate goal to avoid operational failures and ensure the "survivability" of all-inverter microgrids to generator loss and transient overloads. The integration of generator and controller dynamics into the optimal dispatch formulation significantly increases the computational complexity. As we develop algorithms to restore speed of the optimization, our method can be readily implemented into a new operational strategy capable of an unprecedented level of reliability against generator contingencies. In addition, we quantitatively illustrate the effect of the survivability constraints on the microgrid operating costs and how the related trade-off between capital and operating costs should be taken into account at the design stage. The methods developed here also apply to the dispatch of off-grid microgrids.
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