# Solutions of DC OPF are Never AC Feasible

arXiv: https://arxiv.org/abs/1912.00319 · HTML: https://mlsanity.com/paper/1912.00319/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2019.

## Built on by (most cited first, 16 of 16)

- [CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations](https://mlsanity.com/paper/2403.17660/) (2024)
- [OPFData: Large-scale datasets for AC optimal power flow with topological perturbations](https://mlsanity.com/paper/2406.07234/) (2024)
- [Leveraging power grid topology in machine learning assisted optimal power flow](https://mlsanity.com/paper/2110.00306/) (2021)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems](https://mlsanity.com/paper/2112.08091/) (2021)
- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [Predictability and Fairness in Load Aggregation and Operations of Virtual Power Plants](https://mlsanity.com/paper/2110.03001/) (2021)
- [Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality](https://mlsanity.com/paper/2212.03977/) (2022)
- [Optimal Power Grid Operations with Foundation Models](https://mlsanity.com/paper/2409.02148/) (2024)
- [Quantum Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2311.06293/) (2023)
- [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)
- [Unit Commitment Predictor With a Performance Guarantee: A Support Vector Machine Classifier](https://mlsanity.com/paper/2310.08601/) (2023)
- [Data-Driven Stochastic AC-OPF using Gaussian Processes](https://mlsanity.com/paper/2402.11365/) (2024)
- [Dynamic Domain Adaptation-Driven Physics-Informed Graph Representation Learning for AC-OPF](https://mlsanity.com/paper/2506.00478/) (2025)

## Abstract (arXiv)

In this paper, we analyze the relationship between generation dispatch solutions produced by the DC optimal power flow (DC OPF) problem by the AC optimal power flow (AC OPF) problem. While there has been much previous work in analyzing the approximation error of the DC assumption, the AC feasibility has not been fully explored, although difficulty achieving AC feasibility is known in practice. Here, we consider the set of feasible points in a standard DC OPF problem and the set of feasible points in a standard AC OPF problem. Under some very light assumptions, we show that the intersection of these sets is the empty set; i.e., that no solution to the DC OPF problem will satisfy the AC power flow constraints. Then, it is demonstrated that even with generation adjustments in DC OPF to account for losses, DC OPF solutions are still not AC feasible.