The Alternative-Current Optimal Power Flow (AC-OPF) problem is a major topic in power systems optimization, that essentially focuses on taking into account the transmission network’s characteristics. This is why this problem is of interest for Transmission System Operators (TSO) like « Réseau de transport d’électricité » (Rte) in France. The AC-OPF is a very challenging non-convex problem, written in complex numbers, and solving it to global optimality is still impossible for instances of realistic size. The Semidefinite programming (SDP) relaxation of the AC-OPF is known to give good lower bounds, that may be used to evaluate the optimality gap of a heuristically found solution, or possibly to implement a spatial branch-and-bound algorithm. In this talk, we will describe the state-of-the-art methods to solve the SDP relaxation, which are all based on a SDP completion theorem for matrices with a chordal sparsity pattern. We will also present a method under development, which is quite independent of the methods that we will have presented before. This method consists in solving the SDP dual of the AC-OPF, « natively » expressed in complex variables, with a bundle algorithm.