Bound Tightening for the Alternating Current Optimal Power Flow Problem

We consider the Alternating Current Optimal Power Flow (ACOPF) problem, formulated as a nonconvex Quadratically-Constrained Quadratic Program (QCQP) with complex variables. ACOPF may be solved to global optimality with a semidefinite programming (SDP) relaxation in cases where 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. One way to find a global optimum is to partition the problem using a spatial branch-and-bound method. Tightening upper and lower variable bounds can improve solution times in spatial branching by potentially reducing the number of partitions needed. We propose special-purpose closed-form bound tightening methods to tighten limits on nodal powers, line flows, phase angle differences, and voltage magnitudes. Computational experiments are conducted using a spatial branch-and-cut solver. We construct variants of IEEE test cases with high duality gaps to demonstrate the effectiveness of the bound tightening procedures.