Promises of conic relaxations in optimal transmission switching of power systems

Abstract

This paper studies the problem of optimal transmission switching (OTS) for power systems. The goal is to identify a topology of the power grid that minimizes the cost of the system operation while satisfying the physical and operational constraints. Most of the existing methods are based on converting the OTS problem into a mixed-integer linear program (MILP), and then iteratively solving a series of convex problems. The performance of these methods depends heavily on the strength of the MILP formulation. In this paper, we first show that finding the strongest variable upper bounds to be used in the MILP formulation of the OTS problem based on the big-M method is NP-hard. Then, we propose a convex conic relaxation of the big-M MILP formulation based on a semidefinite program (SDP). Strong valid inequalities using the reformulation-linearization technique (RLT) are proposed to strengthen the SDP relaxation by multiplying different linear constraints and then convexifying them in a lifted space. We extensively evaluate the performance of the proposed method on IEEE benchmarks systems.