  The Reactive Optimal Power Flow (ROPF) problem consists in computing an
optimal power generation dispatch for an alternating current transmission
network that respects power flow equations and operational constraints. Some
means of action on the voltage are modelled in the ROPF problem such as the
possible activation of shunts, which implies discrete variables. The ROPF
problem belongs to the class of nonconvex MINLPs (Mixed-Integer Nonlinear
Problems), which are NP-hard problems. In this paper, we solve three new
variants of the ROPF problem by using a semidefinite optimization-based
Branch-and-Bound algorithm. We present results on MATPOWER instances and we
show that this method can solve to global optimality most instances. On the
instances not solved to optimality, our algorithm is able to find solutions
with a value better than the ones obtained by a rounding algorithm. We also
demonstrate that applying an appropriate clique merging algorithm can
significantly speed up the resolution of semidefinite relaxations of ROPF large
instances.
