Radiality Constraints for Resilient Reconfiguration of Distribution Systems: Formulation and Application to Microgrid Formation

Network reconfiguration is an effective strategy for different purposes of distribution systems (DSs), e.g., resilience enhancement. In particular, DS automation, distributed generation integration and microgrid (MG) technology development, etc., are empowering much more flexible reconfiguration and operation of the system, e.g., DSs or MGs with flexible boundaries. However, the formulation of DS reconfiguration-related optimization problems to include those new flexibilities is non-trivial, especially for the issue of topology, which has to be radial. That is, the existing methods of formulating the radiality constraints can cause under-utilization of DS flexibilities. Thus, in this work, we propose a new method for radiality constraints formulation that fully enables the topological and some other related flexibilities of DSs, so that the reconfiguration-related optimization problems can have extended feasibility and enhanced optimality. Graph-theoretic supports are provided to certify its theoretical validity. As integer variables are involved, we also analyze the issues of tightness and compactness. The proposed radiality constraints are specifically applied to post-disturbance MG formation, which is involved in many resilience-oriented DS service restoration and infrastructure recovery problems. The resulting new MG formation model, which allows more flexible merge and/or separation of the sub-grids, etc., establishes superiority over the models in the literature. Demonstrative case studies are conducted on two test systems.