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In this paper, we consider the optimal power flow (OPF) problem whichconsists in determining the power production at each bus of an electric networkby minimizing the production cost. Our contribution is an exact solutionalgorithm for the OPF problem. It consits in a spatial branch-and-boundalgorithm based on a compact quadratically constrained convex relaxation. Thiscompact relaxation is computed by solving the rank relaxation once at thebeginning of the algorithm. The key point of this approach is that the lowerbound at the root node of the branch-and-bound tree is equal to the rankrelaxation value, but is obtained by solving a quadratic convex problem whichis much faster than solving a SDP. To construct this compact relaxation, we addonly O(n) variables that model the squares of the initial variables, where $n$is the number of buses in the power system. The relations between the initialand auxiliary variables are therefore non-convex. By relaxing them in ourrelaxation, we have only O(n) equalities to force by the branch-and-boundalgorithm to prove global optimality. Our first experiments show that our newalgorithm Compact OPF (COPF) performs better than the methods of the literaturewe compare it with

A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem