# DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems

arXiv: https://arxiv.org/abs/2007.01002 · HTML: https://mlsanity.com/paper/2007.01002/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 30 of 47)

- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [DeepOPF-V: Solving AC-OPF Problems Efficiently](https://mlsanity.com/paper/2103.11793/) (2021)
- [Spatial Network Decomposition for Fast and Scalable AC-OPF Learning](https://mlsanity.com/paper/2101.06768/) (2021)
- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [LUMINA: Foundation Models for Topology Transferable ACOPF](https://mlsanity.com/paper/2603.04300/) (2026)
- [Teaching Networks to Solve Optimization Problems](https://mlsanity.com/paper/2202.04104/) (2022)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Learning the Optimal Power Flow: Environment Design Matters](https://mlsanity.com/paper/2403.17831/) (2024)
- [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)
- [QCQP-Net: Reliably Learning Feasible Alternating Current Optimal Power Flow Solutions Under Constraints](https://mlsanity.com/paper/2401.06820/) (2024)
- [Proximal Policy Optimization with Graph Neural Networks for Optimal Power Flow](https://mlsanity.com/paper/2212.12470/) (2022)
- [Discovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling](https://mlsanity.com/paper/2510.24013/) (2025)
- [Bucketized Active Sampling for Learning ACOPF](https://mlsanity.com/paper/2208.07497/) (2022)
- [Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality](https://mlsanity.com/paper/2212.03977/) (2022)
- [Optimal Power Flow Based on Physical-Model-Integrated Neural Network with Worth-Learning Data Generation](https://mlsanity.com/paper/2301.03766/) (2023)
- [DeepOPF-U: A Unified Deep Neural Network to Solve AC Optimal Power Flow in Multiple Networks](https://mlsanity.com/paper/2309.12849/) (2023)
- [Power Flow Analysis Using Deep Neural Networks in Three-Phase Unbalanced Smart Distribution Grids](https://mlsanity.com/paper/2401.07465/) (2024)
- [From Natural Language to Solver-Ready Power System Optimization: An LLM-Assisted, Validation-in-the-Loop Framework](https://mlsanity.com/paper/2508.08147/) (2025)
- [Improving Feasibility via Fast Autoencoder-Based Projections](https://mlsanity.com/paper/2604.03489/) (2026)
- [Self-supervised Equality Embedded Deep Lagrange Dual for Approximate Constrained Optimization](https://mlsanity.com/paper/2306.06674/) (2023)
- [DiffOPF: Diffusion Solver for Optimal Power Flow](https://mlsanity.com/paper/2510.14075/) (2025)
- [LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning](https://mlsanity.com/paper/2605.02133/) (2026)
- [Learning-based AC-OPF Solvers on Realistic Network and Realistic Loads](https://mlsanity.com/paper/2205.09452/) (2022)
- [Physics-Informed Graph Neural Networks for Robust AC-Optimal Power Flow](https://mlsanity.com/paper/2410.04818/) (2024)
- [Adaptive Informed Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2412.02659/) (2024)

## Abstract (arXiv)

High percentage penetrations of renewable energy generations introduce significant uncertainty into power systems. It requires grid operators to solve alternative current optimal power flow (AC-OPF) problems more frequently for economical and reliable operation in both transmission and distribution grids. In this paper, we develop a Deep Neural Network (DNN) approach, called DeepOPF, for solving AC-OPF problems in a fraction of the time used by conventional solvers. A key difficulty for applying machine learning techniques for solving AC-OPF problems lies in ensuring that the obtained solutions respect the equality and inequality physical and operational constraints. Generalized the 2-stage procedure in [1], [2], DeepOPF first trains a DNN model to predict a set of independent operating variables and then directly compute the remaining dependable ones by solving power flow equations. Such an approach not only preserves the power-flow balance equality constraints but also reduces the number of variables to predict by the DNN, cutting down the number of neurons and training data needed. DeepOPF then employs a penalty approach with a zero-order gradient estimation technique in the training process to preserve the remaining inequality constraints. As another contribution, we drive a condition for tuning the size of the DNN according to the desired approximation accuracy, which measures the DNN generalization capability. It provides theoretical justification for using DNN to solve the AC-OPF problem. Simulation results of IEEE 30/118/300-bus and a synthetic 2000-bus test cases show that DeepOPF speeds up the computing time by up to two orders of magnitude as compared to a state-of-the-art solver, at the expense of <0.1% cost difference.