Alternative LP and SOCP Hierarchies for ACOPF Problems

Abstract

The alternating current optimal power flow (ACOPF) problem optimizes the generation and the distribution of electric energy taking into account the active and the reactive power generation limits, demand requirements, bus voltage limits, and network flow limits. The ACOPF problem can be formulated as a nonconvex polynomial program that is generally difficult to solve due to the nonlinear power flow constraints. A recently proposed approach to globally solve the ACOPF problem is through the formulation of a hierarchy of semidefinite programs that are computationally challenging to solve for large-scale problems. In this paper, we explore a solution approach that alleviates this computational burden by using hierarchies of linear and second order cone programs and by exploiting the network structure of the transmission grid. Furthermore, we show that the first level of the second order cone hierarchy is equivalent to solving the conic dual of the approximation that was recently proposed in the literature, which provides the optimal solution of the ACOPF problem for special network topologies.