Global Optimal Power Flow over Large-Scale Power Transmission Network
For power system operators, this method provides a computationally feasible way to obtain near-globally optimal solutions for large-scale OPF problems, where existing convex relaxations fail to yield feasible points.
The paper addresses the global optimal power flow (OPF) problem over large-scale power transmission networks, which is a challenging nonlinear optimization problem. The proposed iterative procedure, using semidefinite programming, achieves suboptimal values within 0.01% of the global optimum for networks with thousands of buses.
Optimal power flow (OPF) over power transmission networks poses challenging large-scale nonlinear optimization problems, which involve a large number of quadratic equality and indefinite quadratic inequality constraints. These computationally intractable constraints are often expressed by linear constraints plus matrix additional rank-one constraints on the outer products of the voltage vectors. The existing convex relaxation technique, which drops the difficult rank-one constraints for tractable computation, cannot yield even a feasible point. We address these computationally difficult problems by an iterative procedure, which generates a sequence of improved points that converge to a rank-one solution. Each iteration calls a semi-definite program. Intensive simulations for the OPF problems over networks with a few thousands of buses are provided to demonstrate the efficiency of our approach. The suboptimal values of the OPF problems found by our computational procedure turn out to be the global optimal value with computational tolerance less than 0.01%.