Relaxations for Optimal Power Flow problems

We have studied some applications of moment relaxations for the Optimal Power Flow problem. Using these polynomial optimization techniques gives global optimal solutions at a high computational cost. Because of the large number of variables appearing in the Optimal Power Flow problem, direct application of moment relaxations is intractable. In this manner, the solution of large systems requires the reformulation of moment relaxations using mathematical techniques to reduce the computational burden of the problem. We are studying some of these techniques available in the literature, the use of matrix completion theorems for example, and working on the proposal of our own approaches.