Power, Control, and Data Processing Systems

Deep Operator Learning-Based Prediction of Primal and Dual Variables in AC Optimal Power Flow

Document Type : Original Research

Authors

Reza Mohammad Yousefi 1
Ahmad Salehi Dobakhshari 2

1 Electrical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran

2 Faculty of Engineering, University of Guilan, Rasht, Iran

https://doi.org/10.30511/pcdp.2026.2096254.1104
Abstract
This paper proposes a deep operator learning framework for fast and accurate prediction of both primal and dual variables in alternating-current optimal power flow (AC-OPF). Unlike conventional neural-network surrogates that learn a fixed input--output mapping and often ignore dual information, the proposed method is designed to approximate the underlying operator that maps varying system operating conditions to optimal OPF solutions. The framework is built on a primal--dual DeepONet architecture, where branch and trunk networks jointly encode system conditions and query locations to predict generator dispatch, voltage states, and associated Lagrange multipliers.

To better capture optimization structure, a differentiable dual completion layer is incorporated to improve dual feasibility and complementary slackness, and a KKT-informed loss function is used to guide training toward physically consistent and optimization-aware solutions. The proposed model is evaluated on standard IEEE benchmark systems, where it achieves high prediction accuracy for both primal and dual variables, millisecond-level inference time, and significantly reduced KKT residuals compared with conventional learning-based OPF approximations. These results highlight the promise of deep operator learning as an efficient surrogate for real-time AC-OPF analysis and power-system operation.

Keywords

Deep Operator Learning
DeepONet
AC Optimal Power Flow
Primal--Dual Learning
Lagrange Multipliers
KKT Conditions
Power System Optimization
Subjects
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Power, Control, and Data Processing Systems
Volume 4, Issue 1
Winter 2027
Pages 62-79

  • Receive Date 31 July 2026
  • Revise Date 29 August 2026
  • Accept Date 14 September 2026
  • First Publish Date 14 September 2026
  • Publish Date 01 March 2027

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