Resilience Enhancement of Microgrids with Distributionally Robust Optimal Sizing and Location of Distributed Energy Resources Under Supply-Demand Uncertainty and Random Contingencies

Microgrids equipped with local distributed energy resources (DERs) and islanding capabilities have been shown to enhance the resilience in modern power systems by mitigating disturbances. However, the size and location of distributed energy resources are critical factors in determining their economic and technical viability. In this study, we model random contingencies alongside commonly studied generation and demand uncertainties to guide investment decisions, improving system defenses against unexpected outage events whilst maintaining economic and technical optimality. We develop distributionally robust optimization models for the two-stage stochastic programming optimal design and operations problem under simultaneous continuous supply-demand uncertainty, and discrete random contingencies. The solution methods rely on known tractable reformulations of distributionally robust optimization (DRO) problems that allow us to solve the problem using off-the-shelf commercial solvers.

Keywords: Microgrid, Resilience, Sizing and location, Stochastic optimization, Distributionally robust optimization, Two-stage stochastic programming, Uncertainty, Line failures, Distributed energy resources, N-k security.