Global Optimization of Optimal Power Flow Using a Branch & Bound Algorithm

We propose two algorithms for the solution of the Optimal Power Flow (OPF) problem to global optimality. The algorithms are based on the spatial branch and bound framework with lower bounds on the optimal objective function value calculated by solving either the Lagrangian dual or the semidefinite programming (SDP) relaxation. We show that this approach can solve to global optimality the general form of the OPF problem including: generation power bounds, apparent and real power line limits, voltage limits and thermal loss limits. The approach makes no assumption on the topology or resistive connectivity of the network. This work also removes some of the restrictive assumptions of the SDP approaches [1], [2], [3], [4], [5]. We present the performance of the algorithms on a number of standard IEEE systems, which are known to have a zero duality gap. We also make parameter perturbations to the test cases that result in solutions that fail to satisfy the SDP rank condition and have a non-zero duality gap. The proposed branch and bound algorithms are able to solve these cases to global optimality.