Stochastic optimal sizing of distributed energy resources for a cost-effective and resilient Microgrid

Recent developments and advances in distributed energy resources (DERs) make them more affordable, accessible, and prevalent in microgrids. Research on designing and operating a microgrid with various DERs has received increasing attention during the past few years. This paper proposes a two-stage stochastic mixed-integer programming method for jointly determining optimal sizes of various DERs, considering both economic benefits and resilience performance. The proposed method explicitly models the interaction between DER sizing at the planning stage and hourly or sub-hourly microgrid dispatch at the operating stage in both grid-connected and island modes, considering stochastic grid disturbances, load, and renewable generation. A formulation method is then proposed to convert the stochastic sizing problem to an equivalent mix-integer linear programming problem, which can be efficiently solved even with a large number of system operating conditions. Using the proposed stochastic sizing method, a resource planning analysis for a military base in the U.S. is presented. It is found that the proposed method can effectively determine the optimal DER sizes to meet a required resilience goal at the maximum net-benefit. Impacts of several key factors including tariff rates, discount rate, and survivability level on optimal DER sizes are analyzed through case studies.