  Optimal Power Flow (OPF) can be modeled as a non-convex Quadratically
Constrained Quadratic Program (QCQP). Our purpose is to solve OPF to global
optimality. To this end, we specialize the Mixed-Integer Quadratic Convex
Reformulation method (MIQCR) to (OPF). This is a method in two steps. First, a
Semi-Definite Programming (SDP) relaxation of (OPF) is solved. Then the optimal
dual variables of this relaxation are used to reformulate OPF into an
equivalent new quadratic program, where all the non-convexity is moved to one
additional constraint. In the second step, this reformulation is solved within
a branch-and-bound algorithm, where at each node a quadratic and convex
relaxation of the reformulated problem, obtained by relaxing the non-convex
added constraint, is solved. The key point of our approach is that the lower
bound at the root node of the branch-and-bound tree is equal to the SDP
relaxation value. We test this method on several OPF cases, from two-bus
networks to more-than-a-thousand-buses networks from the MAT-POWER repository.
Our first results are very encouraging.
