  The benefits of transmission line switching are well-known in terms of
reducing operational cost and improving system reliability of power systems.
However, finding the optimal power network configuration is a challenging task
due to the combinatorial nature of the underlying optimization problem. In this
work, we identify a certain "node-based" set that appears as substructure of
the optimal transmission switching problem and then conduct a polyhedral study
of this set. We construct an extended formulation of the integer hull of this
set and present the inequality description of the integer hull in the original
space in some cases. These inequalities in the original space can be used as
cutting-planes for the transmission line switching problem. Finally, we present
the results of our computational experiments using these cutting-planes on
difficult test cases from the literature.
