Global Optimal Power Flow over Large-Scale Power Transmission Network

TL;DR

This paper introduces an iterative semi-definite programming method for solving large-scale optimal power flow problems, achieving solutions that are globally optimal with high accuracy.

Contribution

It proposes a novel iterative approach that converges to a rank-one solution for large-scale OPF problems, overcoming limitations of existing convex relaxation methods.

Findings

Efficiently solves OPF problems over networks with thousands of buses.

Achieves solutions within 0.01% of the global optimum.

Demonstrates scalability and effectiveness through extensive simulations.

Abstract

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%.