Investments in distribution grid resiliency: A stochastic programming model for dynamic microgrid design

Investment in technologies that allow for dynamic formation of microgrids, such as distributed energy resources to provide power and switches to adapt network topology, can improve the reliability of distribution networks. However, deciding what resources and devices to install and their locations is challenging. We propose a two-stage stochastic programming model to choose distribution-level investments in switches, batteries, generators, solar arrays, and network upgrades to allow for microgrid formation and serving more load when outages occur. Our model maximizes the average (across failure scenarios) power served in the feeder when an outage occurs, which distinguishes it from existing models that include fixed feasibility thresholds. We propose and compare several variants of our model with respect to whether customer load is dispatchable, the number of time periods in a failure scenario, and the relaxation obtained by ignoring binary restriction on the recourse variables. We conduct a study of the computational challenge of the model variants and the quality of solutions they provide. Our model uses a simple network flow approximation of power flow in the recourse model that evaluates the amount of load that is served. We investigate the impact of this approximation by introducing a two-phase method in which candidate solutions generated via the network flow model are evaluated in a more accurate power flow model for selection. We find that the network flow model is sufficient to guide the investment model to solutions that are high-quality in the more accurate model, especially under more flexible dispatch policies. We also observe that allowing customer loads to be dispatchable during an outage leads to an investment model that is easier to solve and has less error in the network flow approximation.