Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow

• URL: http://arxiv.org/abs/2502.06978v1
• Date: Mon, 10 Feb 2025 19:18:18 GMT
• Title: Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow
• Authors: Guancheng Qiu, Mathieu Tanneau, Pascal Van Hentenryck,
• Abstract summary: This paper proposes a dual conic proxy architecture for the semidefinite (SDP) relaxation ACOPF problems. The proposed method combines a differentiable dual neural network strategy that leverages structure of the dual SDP problem. Results show that the proposed SDPbased proxies can outperform weaker conic relaxations.
• Score: 16.02181642119643
• License:
• Abstract: The nonlinear, non-convex AC Optimal Power Flow (AC-OPF) problem is fundamental for power systems operations. The intrinsic complexity of AC-OPF has fueled a growing interest in the development of optimization proxies for the problem, i.e., machine learning models that predict high-quality, close-to-optimal solutions. More recently, dual conic proxy architectures have been proposed, which combine machine learning and convex relaxations of AC-OPF, to provide valid certificates of optimality using learning-based methods. Building on this methodology, this paper proposes, for the first time, a dual conic proxy architecture for the semidefinite (SDP) relaxation of AC-OPF problems. Although the SDP relaxation is stronger than the second-order cone relaxation considered in previous work, its practical use has been hindered by its computational cost. The proposed method combines a neural network with a differentiable dual completion strategy that leverages the structure of the dual SDP problem. This approach guarantees dual feasibility, and therefore valid dual bounds, while providing orders of magnitude of speedups compared to interior-point algorithms. The paper also leverages self-supervised learning, which alleviates the need for time-consuming data generation and allows to train the proposed models efficiently. Numerical experiments are presented on several power grid benchmarks with up to 500 buses. The results demonstrate that the proposed SDP-based proxies can outperform weaker conic relaxations, while providing several orders of magnitude speedups compared to a state-of-the-art interior-point SDP solver.

Related papers

• Joint Transmit and Pinching Beamforming for PASS: Optimization-Based or Learning-Based? [89.05848771674773]
  A novel antenna system ()-enabled downlink multi-user multiple-input single-output (MISO) framework is proposed. It consists of multiple waveguides, which equip numerous low-cost antennas, named (PAs) The positions of PAs can be reconfigured to both spanning large-scale path and space.
  arXiv  Detail & Related papers  (2025-02-12T18:54:10Z)
• Dual Interior Point Optimization Learning [16.02181642119643]
  This paper studies how to learn dual feasible solutions that complement primal approaches and provide quality guarantees. The proposed dual completion outperforms methods for learning optimization proxies which do not exploit the structure of the dual problem.
  arXiv  Detail & Related papers  (2024-02-04T20:06:20Z)
• Dual Conic Proxies for AC Optimal Power Flow [16.02181642119643]
  No existing learning-based approach can provide valid dual bounds for AC-OPF. This paper addresses this gap by training optimization proxies for a convex relaxation of AC-OPF. The paper combines this new architecture with a self-supervised learning scheme, which alleviates the need for costly training data generation.
  arXiv  Detail & Related papers  (2023-10-04T17:06:30Z)
• Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality [3.412750324146571]
  AC optimal power flow is a fundamental optimization problem in power system analysis. Deep learning based approaches have gained intensive attention to conduct the time-consuming training process offline. This paper proposes an end-to-end unsupervised learning based framework for AC-OPF.
  arXiv  Detail & Related papers  (2022-12-07T22:26:45Z)
• Predictive GAN-powered Multi-Objective Optimization for Hybrid Federated Split Learning [56.125720497163684]
  We propose a hybrid federated split learning framework in wireless networks. We design a parallel computing scheme for model splitting without label sharing, and theoretically analyze the influence of the delayed gradient caused by the scheme on the convergence speed.
  arXiv  Detail & Related papers  (2022-09-02T10:29:56Z)
• Data-Driven Chance Constrained AC-OPF using Hybrid Sparse Gaussian Processes [57.70237375696411]
  The paper proposes a fast data-driven setup that uses the sparse and hybrid Gaussian processes (GP) framework to model the power flow equations with input uncertainty. We advocate the efficiency of the proposed approach by a numerical study over multiple IEEE test cases showing up to two times faster and more accurate solutions.
  arXiv  Detail & Related papers  (2022-08-30T09:27:59Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• High-Fidelity Machine Learning Approximations of Large-Scale Optimal Power Flow [49.2540510330407]
  AC-OPF is a key building block in many power system applications. Motivated by increased penetration of renewable sources, this paper explores deep learning to deliver efficient approximations to the AC-OPF.
  arXiv  Detail & Related papers  (2020-06-29T20:22:16Z)
• Joint Parameter-and-Bandwidth Allocation for Improving the Efficiency of Partitioned Edge Learning [73.82875010696849]
  Machine learning algorithms are deployed at the network edge for training artificial intelligence (AI) models. This paper focuses on the novel joint design of parameter (computation load) allocation and bandwidth allocation.
  arXiv  Detail & Related papers  (2020-03-10T05:52:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.