Bound Tightening for Alternating Current Optimal Power Flow Instances with Duality Gap

Chen Chen, Alper Atamturk and Shmuel S. Oren., “Bound Tightening for Alternating Current Optimal Power Flow Instances with Duality Gap”. EEE Transactions on Power Systems 31, 3729-3736, 2015. https://ieeexplore.ieee.org/document/7328765

Abstract: We consider the Alternating Current Optimal Power Flow (ACOPF) problem, formulated as a nonconvex Quadratically-Constarined Quadratic Program (QCQP) with complex variables. ACOPF may be solved to global optimality with a semidefinite programming (SDP) relaxation for cases for which its QCQP formulation attains zero duality gap. However, when there is positive duality gap, no optimal solution to the SDP relaxation is feasible for ACOPF. To solve cases with duality gap we implement a spatial branch-and-bound (SBB) algorithm that uses a sparse strengthened SDP relaxation. SBB methods rely on partitioning the feasible space; consequently, tightening upper and lower variable bounds can improve solution times. We propose closed-form bound tightening methods to tighten limits on nodal powers, line flows, phase angle differences, and voltage magnitude limits. We also construct variants of IEEE test cases with high duality gaps to demonstrate the effectiveness of the bound tightening procedures.