# An Efficient Learning-Based Solver for Two-Stage DC Optimal Power Flow with Feasibility Guarantees

arXiv: https://arxiv.org/abs/2304.01409 · HTML: https://mlsanity.com/paper/2304.01409/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Model-Free Renewable Scenario Generation Using Generative Adversarial Networks](https://mlsanity.com/paper/1707.09676/) (2017)
- [DeepOPF: Deep Neural Network for DC Optimal Power Flow](https://mlsanity.com/paper/1905.04479/) (2019)
- [Learning for DC-OPF: Classifying active sets using neural nets](https://mlsanity.com/paper/1902.05607/) (2019)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Learning to Solve Optimization Problems with Hard Linear Constraints](https://mlsanity.com/paper/2208.10611/) (2022)
- [On Correctness of Automatic Differentiation for Non-Differentiable Functions](https://mlsanity.com/paper/2006.06903/) (2020)
- [Computationally Efficient Safe Reinforcement Learning for Power Systems](https://mlsanity.com/paper/2110.10333/) (2021)
- [A Convex Neural Network Solver for DCOPF with Generalization Guarantees](https://mlsanity.com/paper/2009.09109/) (2020)
- [Scenario Forecasting of Residential Load Profiles](https://mlsanity.com/paper/1906.07373/) (2019)
- [Learning to Optimize Power Distribution Grids using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2007.03728/) (2020)
- [Safe and Efficient Model Predictive Control Using Neural Networks: An Interior Point Approach](https://mlsanity.com/paper/2203.12196/) (2022)
- [Adversarially Robust Learning for Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/2111.06961/) (2021)
- [Corrective Control to Handle Forecast Uncertainty: A Chance Constrained Optimal Power Flow](https://mlsanity.com/paper/1609.02194/) (2016)
- [Stochastic DC Optimal Power Flow With Reserve Saturation](https://mlsanity.com/paper/1910.04667/) (2019)

## Built on by (most cited first, 1 of 1)

- [Fast and Reliable N-k Contingency Screening with Input-Convex Neural Networks](https://mlsanity.com/paper/2410.00796/) (2024)

## Abstract (arXiv)

In this paper, we consider the scenario-based two-stage stochastic DC optimal power flow (OPF) problem for optimal and reliable dispatch when the load is facing uncertainty. Although this problem is a linear program, it remains computationally challenging to solve due to the large number of scenarios needed to accurately represent the uncertainties. To mitigate the computational issues, many techniques have been proposed to approximate the second-stage decisions so they can be dealt more efficiently. The challenge of finding good policies to approximate the second-stage decisions is that these solutions need to be feasible, which has been difficult to achieve with existing policies. To address these challenges, this paper proposes a learning method to solve the two-stage problem in a more efficient and optimal way. A technique called the gauge map is incorporated into the learning architecture design to guarantee the learned solutions' feasibility to the network constraints. Namely, we can design policies that are feed forward functions and only output feasible solutions. Simulation results on standard IEEE systems show that, compared to iterative solvers and the widely used affine policy, our proposed method not only learns solutions of good quality but also accelerates the computation by orders of magnitude.