In recent years, piece-wise convex relaxations of power flow equations have attracted substantial academic interest. These approaches build such relaxations by partitioning the variables' domain. However, the ensued formulations grow very rapidly in size with the number of partitions, thus becoming computationally intractable to achieve strong dual bounds for realistic-size instances. In this work, we propose piece-wise polyhedral relaxations of power flow equations utilizing the latest advancements in mixed-integer programming (MIP) modeling techniques. A computational campaign conducted on 24 PGLib benchmark instances of the OPF problem shows that the choice of MIP formulation on piece-wise polyhedral relaxation of power flow equations significantly impacts the computational time.