mlsanityData to 7 Oct 2026

Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence

arXiv 1405.0766 ↗First posted 5 May 2014math.OC cs.SY eess.SYcited by 17

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Abstract (arXiv)

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relations among them. Part II presents sufficient conditions under which the convex relaxations are exact.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 May 2014.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 1; 2023: 4; 2024: 3; 2025: 2; 2026: 3.

17 papers.

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  1. 2021Leveraging power grid topology in machine learning assisted optimal power flowcited by 21
  2. 2021Learning to run a power network with trustcited by 17
  3. 2023Dual Conic Proxies for AC Optimal Power Flowcited by 11
  4. 2021Risk-Aware Learning for Scalable Voltage Optimization in Distribution Gridscited by 5
  5. 2026GENCO - A Unified Neural Solver Embedded in a Development Framework for Steady-State Grid Analysiscited by 4
  6. 2021Scalable Learning for Optimal Load Shedding Under Power Grid Emergency Operationscited by 3
  7. 2022Minimizing Worst-Case Violations of Neural Networkscited by 3
  8. 2024CommonPower: A Framework for Safe Data-Driven Smart Grid Controlcited by 3
  9. 2024Machine Learning for Scalable and Optimal Load Shedding Under Power System Contingencycited by 2
  10. 2023Optimal Power Flow in Highly Renewable Power System Based on Attention Neural Networkscited by 1
  11. 2024Beyond the Neural Fog: Interpretable Learning for AC Optimal Power Flowcited by 1
  12. 2023Enriching Neural Network Training Dataset to Improve Worst-Case Performance Guaranteescited by 0
5 more
  1. 2023An Active Learning-based Approach for Hosting Capacity Analysis in Distribution Systemscited by 0
  2. 2025A Data-Driven Real-Time Optimal Power Flow Algorithm Using Local Feedbackcited by 0
  3. 2025Tree-Preconditioned Differentiable Optimization and Axioms as Layerscited by 0
  4. 2026Learning efficient representations of complex constraints for scalable optimizationcited by 0
  5. 2026GridSFM: A Foundation Model for Solving AC Optimal Power Flowcited by 0