Three-Stage Robust Model for Resilient DERs Planning in Distribution Networks

To simultaneously improve the economic efficiency and resilience of distribution networks, this paper proposes a three-stage robust planning model for siting and sizing distributed wind turbines, battery storages, and dispatchable generators (e.g., diesel generators) in distribution systems. In the first stage, these distributed energy resources (DERs) are properly planned in distribution systems. In the second stage (normal conditions), the wind uncertainty is addressed with a robust method, and operation costs in the worst-case wind scenario are minimized by wisely scheduling the allocated DERs. In the third stage (emergency conditions), the stochastic nature of wind energy and line outage is simultaneously considered and characterized by polyhedral uncertainty sets and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N-K$</tex> criteria, respectively. Moreover, a novel microgrid formation model considering master-slave DERs is proposed to improve the resilience of distribution systems during emergency conditions. Consequently, this planning model is formulated as a min-(max-min)-(max-min) optimization problem, which cannot be directly solved by commercial solvers. Hence, a novel tri-level decomposition method is proposed to solve this three-stage nonlinear model by decomposing it into several mixed-integer linear problems. Last, simulation results on distribution systems demonstrate the effectiveness of the planning model.