Optimal transmission line switching for large-scale power systems using the Alternating Direction Method of Multipliers

It is known that in some cases, switching some transmission lines of an electric power system off may improve the optimal economic dispatch cost. This modification of the economic dispatch problem is known as optimal transmission line switching. Unfortunately, the modified problem involves binary decision variables which make the problem difficult to solve for large-scale power systems. This paper presents a method that scales well for large power systems, based on a decomposition approach known as the Alternating Direction Method of Multipliers (ADMM). The problem is broken into a convex component and a series of binary rounding operations, coupled via a penalty function. The output of the ADMM algorithm is post-processed in order to obtain a near-optimal solution to the original problem at relatively low computational cost. We measure the ADMM solution against a convex relaxation of the original problem, thereby certifying its quality without needing to solve the original combinatorial problem. The method is illustrated using the Polish 2383-bus test system.