We propose a semidefinite relaxation based spatial branch and bound algorithm for the solution of Optimal Power Flow (OPF) problem to global optimality. 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 and also removes some of the restrictive assumptions of earlier SDP approaches. We present test cases where solutions fail to satisfy the SDP rank condition and have a non-zero duality gap. The proposed branch and bound algorithm is able to solve these cases to global optimality. |