# Statistical Learning For DC Optimal Power Flow

arXiv: https://arxiv.org/abs/1801.07809 · HTML: https://mlsanity.com/paper/1801.07809/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2018.

## Built on by (most cited first, 12 of 12)

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- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [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)
- [A Physics-Informed Machine Learning for Electricity Markets: A NYISO Case Study](https://mlsanity.com/paper/2304.00062/) (2023)
- [DeepOPF-AL: Augmented Learning for Solving AC-OPF Problems with Multiple Load-Solution Mappings](https://mlsanity.com/paper/2206.03365/) (2022)
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- [Towards Understanding the Unreasonable Effectiveness of Learning AC-OPF Solutions](https://mlsanity.com/paper/2111.11168/) (2021)
- [Machine Learning for Improved Gas Network Models in Coordinated Energy Systems](https://mlsanity.com/paper/2209.12731/) (2022)
- [Learning to Solve Constrained Bilevel Control Co-Design Problems](https://mlsanity.com/paper/2507.09050/) (2025)
- [A Neural Network Framework for Discovering Closed-form Solutions to Quadratic Programs with Linear Constraints](https://mlsanity.com/paper/2510.23737/) (2025)
- [AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs](https://mlsanity.com/paper/2609.30088/) (2026)

## Abstract (arXiv)

The optimal power flow problem plays an important role in the market clearing and operation of electric power systems. However, with increasing uncertainty from renewable energy operation, the optimal operating point of the system changes more significantly in real-time. In this paper, we aim at developing control policies that are able to track the optimal set-point with high probability. The approach is based on the observation that the OPF solution corresponding to a certain uncertainty realization is a basic feasible solution, which provides an affine control policy. The optimality of this basis policy is restricted to uncertainty realizations that share the same set of active constraints. We propose an ensemble control policy that combines several basis policies to improve performance. Although the number of possible bases is exponential in the size of the system, we show that only a few of them are relevant to system operation. We adopt a statistical learning approach to learn these important bases, and provide theoretical results that validate our observations. For most systems, we observe that efficient ensemble policies constructed using as few as ten bases, are able to obtain optimal solutions with high probability.