Optimization-Based Bound Tightening using a Strengthened QC-Relaxation of the Optimal Power Flow Problem
For power system operators, this provides a more efficient method to tighten variable bounds in AC-OPF, improving solution quality without sacrificing speed.
The paper develops a strengthened QC relaxation of the AC-OPF problem and an OBBT algorithm to compute tight bounds on voltage and phase angle variables, achieving the tightest variable bounds and optimality gaps with negligible runtime impact on benchmark networks.
This article develops a strengthened convex quadratic convex (QC) relaxation of the AC Optimal Power Flow (AC-OPF) problem and presents an optimization-based bound-tightening (OBBT) algorithm to compute tight, feasible bounds on the voltage magnitude variables for each bus and the phase angle difference variables for each branch in the network. Theoretical properties of the strengthened QC relaxation that show its dominance over the other variants of the QC relaxation studied in the literature are also derived. The effectiveness of the strengthened QC relaxation is corroborated via extensive numerical results on benchmark AC-OPF test networks. In particular, the results demonstrate that the proposed relaxation consistently provides the tightest variable bounds and optimality gaps with negligible impacts on runtime performance.