  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.
