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Neural Networks for AC Optimal Power Flow: Improving Worst-Case Guarantees during Training

Bastien Giraud, Rahul Nellikath, Johanna Vorwerk, Maad Alowaifeer, Spyros Chatzivasileiadis

TL;DR

This work tackles the safety challenge of using neural surrogates for AC-OPF by introducing a verification-informed training framework that directly minimizes worst-case constraint violations. It leverages scalable bound-propagation through $oldsymbol{ ext{α}}$-$oldsymbol{ ext{β}}$-CROWN and McCormick relaxations to incorporate formal constraints into training, yielding NNs with provable safety characteristics. After training, post-hoc verification demonstrates substantial reductions in worst-case violations and, on large-scale proxies up to $793$ buses, enables feasibility restoration and warm-start strategies to produce physically realizable operating points with real-time-like performance. The approach offers a practical path to data-driven, safe, and fast AC-OPF deployment, bridging ML acceleration with rigorous constraint satisfaction for real-time control.

Abstract

The AC Optimal Power Flow (AC-OPF) problem is central to power system operation but challenging to solve efficiently due to its nonconvex and nonlinear nature. Neural networks (NNs) offer fast surrogates, yet their black-box behavior raises concerns about constraint violations that can compromise safety. We propose a verification-informed NN framework that incorporates worst-case constraint violations directly into training, producing models that are both accurate and provably safer. Through post-hoc verification, we achieve substantial reductions in worst-case violations and, for the first time, verify all operational constraints of large-scale AC-OPF proxies. Practical feasibility is further enhanced via restoration and warm-start strategies for infeasible operating points. Experiments on systems ranging from 57 to 793 buses demonstrate scalability, speed, and reliability, bridging the gap between ML acceleration and safe, real-time deployment of AC-OPF solutions - and paving the way toward data-driven optimal control.

Neural Networks for AC Optimal Power Flow: Improving Worst-Case Guarantees during Training

TL;DR

This work tackles the safety challenge of using neural surrogates for AC-OPF by introducing a verification-informed training framework that directly minimizes worst-case constraint violations. It leverages scalable bound-propagation through --CROWN and McCormick relaxations to incorporate formal constraints into training, yielding NNs with provable safety characteristics. After training, post-hoc verification demonstrates substantial reductions in worst-case violations and, on large-scale proxies up to buses, enables feasibility restoration and warm-start strategies to produce physically realizable operating points with real-time-like performance. The approach offers a practical path to data-driven, safe, and fast AC-OPF deployment, bridging ML acceleration with rigorous constraint satisfaction for real-time control.

Abstract

The AC Optimal Power Flow (AC-OPF) problem is central to power system operation but challenging to solve efficiently due to its nonconvex and nonlinear nature. Neural networks (NNs) offer fast surrogates, yet their black-box behavior raises concerns about constraint violations that can compromise safety. We propose a verification-informed NN framework that incorporates worst-case constraint violations directly into training, producing models that are both accurate and provably safer. Through post-hoc verification, we achieve substantial reductions in worst-case violations and, for the first time, verify all operational constraints of large-scale AC-OPF proxies. Practical feasibility is further enhanced via restoration and warm-start strategies for infeasible operating points. Experiments on systems ranging from 57 to 793 buses demonstrate scalability, speed, and reliability, bridging the gap between ML acceleration and safe, real-time deployment of AC-OPF solutions - and paving the way toward data-driven optimal control.
Paper Structure (22 sections, 27 equations, 3 figures, 3 tables)

This paper contains 22 sections, 27 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Learning AC Optimal Power Flow
  3. Optimal Power Flow Problem
  4. Neural Networks for Optimal Power Flow
  5. Power Neural Network
  6. Voltage Neural Network
  7. Neural Network Verification
  8. Worst-Case Guarantees for Neural Networks
  9. Minimizing Worst-Case Violations During Training
  10. $\alpha$-max $\beta$-min
  11. McCormick Relaxations
  12. Obtaining a Physically Realizable State
  13. Feasibility Restoration
  14. Warm Start
  15. Case Studies
  16. ...and 7 more sections

Figures (3)

  • Figure 1: Over- and under-approximating a unit phasor’s magnitude using the $\alpha$–max and $\beta$–min formulas \ref{['eq:overapprox']} and \ref{['eq:underapprox']}.
  • Figure 2: Guarantee $\nu$ against $\delta$-factor for the Power NN models across the 57-, 118-, 300- and 793-bus systems.
  • Figure 3: Guarantee $\nu$ against $\delta$-factor for the Voltage NN models across the 57-, 118-, 300- and 793-bus systems.