Multiple matrix rank constrained optimization for optimal power flow over large scale transmission networks

The optimal power flow (OPF) problem for power transmission networks is an NP-hard optimization problem with numerous quadratic equality and indefinite quadratic inequality constraints on bus voltages. The existing nonlinear solvers often fail in yielding a feasible solution. In this paper, we follow our previously developed nonsmooth optimization approach to address this difficult large-scale OPF problem, which is an iterative process to generate a sequence of improved solutions that converge to an optimal solution. Each iteration calls an SDP of a moderate dimension. Intensive simulations for OPF over networks with a large number of buses are provided to demonstrate the efficiency of our approach.