  The Alternating Current Optimal Transmission Switching (ACOTS) problem
incorporates line switching decisions into the fundamental AC optimal power
flow (ACOPF) problem. The advantages of the ACOTS problem are well-known in
terms of reducing the operational cost and improving system reliability. ACOTS
optimization models contain discrete variables and nonlinear, non-convex
structures, which make it difficult to solve. We derive strengthened quadratic
convex (QC) relaxations for ACOTS by combining several methodologies recently
developed in the ACOPF literature. First, we relax the ACOTS model with the
on/off QC relaxation, which has been empirically observed to be both tight and
computationally efficient in approximating the ACOPF problem. Further, we
tighten this relaxation by using strong linearization with extreme-point
representation, and by adding several types of new valid inequalities. In
particular, we derive a novel kind of "on/off cycle-based polynomial
constraints", by taking advantage of the network structure. Those constraints
are linearized using convex-hull representations and implemented in an
efficient "branch-and-cut" framework. We also tighten the relaxation using the
optimization-based bound tightening algorithm. Our extensive numerical
experiments on medium-scale PGLib instances show that, compared with the
state-of-the-art formulations, our strengthening techniques are able to improve
the quality of ACOTS relaxations on many of the PGLib instances, with some
being substantial improvements.
