# Exact Convex Relaxation of Optimal Power Flow in Radial Networks

arXiv: https://arxiv.org/abs/1311.7170 · HTML: https://mlsanity.com/paper/1311.7170/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2013.

## Built on by (most cited first, 3 of 3)

- [PowerGym: A Reinforcement Learning Environment for Volt-Var Control in Power Distribution Systems](https://mlsanity.com/paper/2109.03970/) (2021)
- [A Graph Policy Network Approach for Volt-Var Control in Power Distribution Systems](https://mlsanity.com/paper/2109.12073/) (2021)
- [OpenGridGym: An Open-Source AI-Friendly Toolkit for Distribution Market Simulation](https://mlsanity.com/paper/2203.04410/) (2022)

## Abstract (arXiv)

The optimal power flow (OPF) problem determines power generation/demand that minimize a certain objective such as generation cost or power loss. It is nonconvex. We prove that, for radial networks, after shrinking its feasible set slightly, the global optimum of OPF can be recovered via a second-order cone programming (SOCP) relaxation under a condition that can be checked a priori. The condition holds for the IEEE 13-, 34-, 37-, 123-bus networks and two real-world networks, and has a physical interpretation.