# Optimization-Based Bound Tightening using a Strengthened QC-Relaxation of the Optimal Power Flow Problem

arXiv: https://arxiv.org/abs/1809.04565 · HTML: https://mlsanity.com/paper/1809.04565/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2018.

## Built on by (most cited first, 3 of 3)

- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [LEVIS: Large Exact Verifiable Input Spaces for Neural Networks](https://mlsanity.com/paper/2408.08824/) (2024)

## Abstract (arXiv)

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.