  This paper deals with optimal transmission switching (OTS) problems involving
discrete binary decisions about network topology and non-convex power flow
constraints. We adopt a semidefinite programming formulation for the OPF
problem which, however, remains nonconvex due to the presence of discrete
variables and bilinear products between the decision variables. To tackle the
latter, we introduce a novel physically-inspired, virtual-voltage approximation
that leads to provable lower and upper bounds on the solution of the original
problem. To deal with the exponential complexity caused by the discrete
variables, we introduce a graph partition-based algorithm which breaks the
problem into several parallel mixed-integer subproblems of smaller size.
Simulations demonstrate the high degree of accuracy and affordable
computational requirements of our approach.
