Global solution of the AC Optimal Power Flow (ACOPF) problem remains an active research topic. In particular, convex conic relaxations of the ACOPF problem have attracted the attention of the researchers since convexity in mathematical programs often implies that they can be solved efficiently. In this category and considering the ACOPF problem formulated as a polynomial program, Lasserre’s hierarchy of moment relaxations theoretically ensures the global solution of the ACOPF problem at some level of the hierarchy. However, the implementation of moment relaxations as semidefinite (SD) programs becomes rapidly intractable even for the first levels of the hierarchy. Seminal works on the application of Laserre’s hierarchy to the solution of the ACOPF problem have shown that the sparsity of the network can be exploited in order to globally solve large-scale power systems. However, further reduction of computational cost is yet to be achieved. In this talk, we will present new tractable convex relaxations of the ACOPF problem where we use additional constraints on the original problem and well-known sparsity-exploiting techniques for SD programming in order to circumvent the necessity of large moment matrices as formulated in moment relaxations.