# Convex Restriction of Power Flow Feasibility Sets

arXiv: https://arxiv.org/abs/1803.00818 · HTML: https://mlsanity.com/paper/1803.00818/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2018.

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

- [Graph Reinforcement Learning for Power Grids: A Comprehensive Survey](https://mlsanity.com/paper/2407.04522/) (2024)
- [CommonPower: A Framework for Safe Data-Driven Smart Grid Control](https://mlsanity.com/paper/2406.03231/) (2024)
- [Certified Safety Radii in Forecast-Error Space for Wasserstein Distributionally Robust Small Signal Stability-Constrained AC Optimal Power Flow via Lifted Spectrahedral Containment](https://mlsanity.com/paper/2608.30201/) (2026)

## Abstract (arXiv)

The convex restriction of the power flow feasible sets identifies the convex subset of power injections where the solution for power flow is guaranteed to exist and satisfy the operational constraints. In contrast to convex relaxations, the convex restriction provides a sufficient condition for power flow feasibility and is particularly useful for problems involving uncertainty in the power generation and demand. In this paper, we present a general framework of constructing convex restriction of an algebraic set defined by equality and inequality constraints and apply the framework to power flow feasibility problem. The procedure results in convex quadratic constraints that provide a sufficiently large region for practical operation of the grid.