# Inexact Convex Relaxations for AC Optimal Power Flow: Towards AC Feasibility

arXiv: https://arxiv.org/abs/1902.04815 · HTML: https://mlsanity.com/paper/1902.04815/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2019.

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

- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [Beyond the Neural Fog: Interpretable Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2408.05228/) (2024)
- [Enriching Neural Network Training Dataset to Improve Worst-Case Performance Guarantees](https://mlsanity.com/paper/2303.13228/) (2023)

## Abstract (arXiv)

Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted significant interest as in several instances they provably yield the global optimum to the original non-convex problem. If, however, the relaxation is inexact, the obtained solution is not AC-feasible. The quality of the obtained solution is essential for several practical applications of AC-OPF, but detailed analyses are lacking in existing literature. This paper aims to cover this gap. We provide an in-depth investigation of the solution characteristics when convex relaxations are inexact, we assess the most promising AC feasibility recovery methods for large-scale systems, and we propose two new metrics that lead to a better understanding of the quality of the identified solutions. We perform a comprehensive assessment on 96 different test cases, ranging from 14 to 3120 buses, and we show the following: (i) Despite an optimality gap of less than 1%, several test cases still exhibit substantial distances to both AC feasibility and local optimality and the newly proposed metrics characterize these deviations. (ii) Penalization methods fail to recover an AC-feasible solution in 15 out of 45 cases, and using the proposed metrics, we show that most failed test instances exhibit substantial distances to both AC-feasibility and local optimality. For failed test instances with small distances, we show how our proposed metrics inform a fine-tuning of penalty weights to obtain AC-feasible solutions. (iii) The computational benefits of warm-starting non-convex solvers have significant variation, but a computational speedup exists in over 75% of the cases.