Learning to accelerate tightening of convex relaxations of the AC optimal power flow problem

Fatih Cengil (), Harsha Nagarajan (), Russell Bent (), Sandra Eksioglu () and Burak Eksioglu ()
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Fatih Cengil: University of Arkansas, Department of Industrial Engineering
Harsha Nagarajan: Los Alamos National Laboratory, Applied Mathematics and Plasma Physics (T-5)
Russell Bent: Los Alamos National Laboratory, Applied Mathematics and Plasma Physics (T-5)
Sandra Eksioglu: University of Arkansas, Department of Industrial Engineering
Burak Eksioglu: University of Arkansas, Department of Industrial Engineering

Computational Optimization and Applications, 2025, vol. 92, issue 3, No 2, 786 pages

Abstract: Abstract We propose a novel machine learning (ML)-based approach to significantly reduce the run times of the optimality-based bound tightening (OBBT) algorithm for strengthening the convex relaxations of the non-convex Alternating Current Optimal Power Flow (AC-OPF) problem. While OBBT can yield near-global solutions via tight convex relaxations, its runtime remains a critical bottleneck on large-scale power grids. Our key contribution is a dynamic policy that selects smaller subsets of voltage magnitude and phase-angle difference variables for sequential bound tightening at every iteration of the OBBT algorithm. This ensures that the bound-tightening process remains adaptive, thereby circumventing the stalling in the optimality gap often observed with static, predetermined subsets (like in our previous work (Cengil in Electric Power Syst Res 212: 108275, 2022)). By leveraging historical load profiles to re-evaluate and rank variables dynamically, our proposed framework preserves the benefits of OBBT while significantly reducing computation time. Through a parallel implementation of the proposed OBBT algorithm, we observe an average speed-up of 9.3 $$\times $$ , with maximum improvement up to 20 $$\times $$ – relative to the conventional exhaustive OBBT – on a held-out set of benchmark instances that range in size up to 3,375 buses. To the best of our knowledge, this is the first ML-based OBBT approach to demonstrate such large-scale performance gains on realistic AC-OPF problems, offering a promising pathway toward more efficient global solutions in power system operations.

Keywords: Optimal power flow; global optimization; convex relaxation; machine learning; neural network; bound tightening (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-025-00715-7

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