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, existing methods of formulating radiality constraints can cause underutilization of DS flexibilities. Thus, this work proposes a new method for radiality constraints formulation fully enabling 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 tightness and compactness issues. The proposed radiality constraints are specifically applied to post-disaster MG formation, which is involved in many DS resilience-oriented service restoration and/or infrastructure recovery problems. The resulting new MG formation model, which allows more flexible merge and/or separation of sub-grids, etc., establishes superiority over the models in the literature. Case studies are conducted on two test systems.
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