# Mathematical Programming formulations for the Alternating Current Optimal Power Flow problem

arXiv: https://arxiv.org/abs/2007.05334 · HTML: https://mlsanity.com/paper/2007.05334/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Graph Reinforcement Learning for Power Grids: A Comprehensive Survey](https://mlsanity.com/paper/2407.04522/) (2024)
- [Beyond the Neural Fog: Interpretable Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2408.05228/) (2024)
- [Physics-Informed Graph Neural Networks for Robust AC-Optimal Power Flow](https://mlsanity.com/paper/2410.04818/) (2024)
- [Sparse Polynomial Optimization: Theory and Practice](https://mlsanity.com/paper/2208.11158/) (2022)

## Abstract (arXiv)

Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the cost of generating power. Current can either be direct or alternating: while the former yields approximate linear programming formulations, the latter yields formulations of a much more interesting sort: namely, nonconvex nonlinear programs in complex numbers. In this technical survey, we derive formulation variants and relaxations of the alternating current optimal power flow problem.