ESR15-Edgar Fuentes

First year's research has lead us to a refinement of  our goals. Regarding the scalability of moment relaxations for the optimization of large power networks, we have found some interesting decompositions for the moment matrix leading to new relaxations reducing the computational effort while keeping the tightness of moment relaxations. Following up with this work, we now proceed to consider the sparsity of the network in order to reduce the number of variables in the programs. We are also interested in the addition of discrete variables to power network optimization problems. We have already implemented some nonlinear, nonconvex, approaches noticing that the solutions are suboptimal. Now, we proceed to apply what we learn about convex optimization to develop new approaches that allow us to find better solutions in least computational time possible. Tackling real-world problems is always a good motivation. This is the case for me as I have the opportunity to participate within the

Since February 3rd, Hadrien Godard has joined Artelys after finishing his PhD thesis on global solution of the Optimal Power Flow problem. Hadrien's experience with this problem has helped to enhance our solution proposals. We have had some insightful discussions and I am sure that we will reach very good results with this collaboration.

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.

I have arrived to Paris and I am very happy to have met the team at Artelys. The environment is really positive and everyone is willing to help. At this point, I will be learning from the state of the art of polynomial optimization techniques for solving power systems optimization problems on transmission and distribution networks. Without any doubts, we will reach our goals because of the support of all POEMA network members and, in particular, the researching team at Artelys.