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

arXiv: https://arxiv.org/abs/1405.0766 · HTML: https://mlsanity.com/paper/1405.0766/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2014.

## Built on by (most cited first, 17 of 17)

- [Leveraging power grid topology in machine learning assisted optimal power flow](https://mlsanity.com/paper/2110.00306/) (2021)
- [Learning to run a power network with trust](https://mlsanity.com/paper/2110.12908/) (2021)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [GENCO - A Unified Neural Solver Embedded in a Development Framework for Steady-State Grid Analysis](https://mlsanity.com/paper/2608.09921/) (2026)
- [Risk-Aware Learning for Scalable Voltage Optimization in Distribution Grids](https://mlsanity.com/paper/2110.01490/) (2021)
- [CommonPower: A Framework for Safe Data-Driven Smart Grid Control](https://mlsanity.com/paper/2406.03231/) (2024)
- [Scalable Learning for Optimal Load Shedding Under Power Grid Emergency Operations](https://mlsanity.com/paper/2111.11980/) (2021)
- [Minimizing Worst-Case Violations of Neural Networks](https://mlsanity.com/paper/2212.10930/) (2022)
- [Machine Learning for Scalable and Optimal Load Shedding Under Power System Contingency](https://mlsanity.com/paper/2405.05521/) (2024)
- [Optimal Power Flow in Highly Renewable Power System Based on Attention Neural Networks](https://mlsanity.com/paper/2311.13949/) (2023)
- [Beyond the Neural Fog: Interpretable Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2408.05228/) (2024)
- [Enriching Neural Network Training Dataset to Improve Worst-Case Performance Guarantees](https://mlsanity.com/paper/2303.13228/) (2023)
- [An Active Learning-based Approach for Hosting Capacity Analysis in Distribution Systems](https://mlsanity.com/paper/2305.07818/) (2023)
- [A Data-Driven Real-Time Optimal Power Flow Algorithm Using Local Feedback](https://mlsanity.com/paper/2502.15306/) (2025)
- [Tree-Preconditioned Differentiable Optimization and Axioms as Layers](https://mlsanity.com/paper/2601.06036/) (2025)
- [Learning efficient representations of complex constraints for scalable optimization](https://mlsanity.com/paper/2603.08283/) (2026)
- [GridSFM: A Foundation Model for Solving AC Optimal Power Flow](https://mlsanity.com/paper/2609.30173/) (2026)

## 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.