# DeepOPF-V: Solving AC-OPF Problems Efficiently

arXiv: https://arxiv.org/abs/2103.11793 · HTML: https://mlsanity.com/paper/2103.11793/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 22 Mar 2021.

## Builds on (most cited first, 9 of 9)

- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [DeepOPF: Deep Neural Network for DC Optimal Power Flow](https://mlsanity.com/paper/1905.04479/) (2019)
- [Smart-PGSim: Using Neural Network to Accelerate AC-OPF Power Grid Simulation](https://mlsanity.com/paper/2008.11827/) (2020)
- [Learning to Solve Network Flow Problems via Neural Decoding](https://mlsanity.com/paper/2002.04091/) (2020)
- [Hybrid Learning Aided Inactive Constraints Filtering Algorithm to Enhance AC OPF Solution Time](https://mlsanity.com/paper/2006.01336/) (2020)
- [Emulating AC OPF solvers for Obtaining Sub-second Feasible, Near-Optimal Solutions](https://mlsanity.com/paper/2012.10031/) (2020)
- [Sparsity-Exploiting Moment-Based Relaxations of the Optimal Power Flow Problem](https://mlsanity.com/paper/1404.5071/) (2014)

## Built on by (most cited first, 18 of 18)

- [OPF-Learn: An Open-Source Framework for Creating Representative AC Optimal Power Flow Datasets](https://mlsanity.com/paper/2111.01228/) (2021)
- [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)
- [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)
- [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)
- [LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning](https://mlsanity.com/paper/2605.02133/) (2026)
- [DeepOPF-AL: Augmented Learning for Solving AC-OPF Problems with Multiple Load-Solution Mappings](https://mlsanity.com/paper/2206.03365/) (2022)
- [HoP: Homeomorphic Polar Learning for Hard Constrained Optimization](https://mlsanity.com/paper/2502.00304/) (2025)
- [Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow](https://mlsanity.com/paper/2502.06978/) (2025)
- [Revisiting Deep AC-OPF](https://mlsanity.com/paper/2509.00655/) (2025)
- [DClEVerNet: Deep Combinatorial Learning for Efficient EV Charging Scheduling in Large-scale Networked Facilities](https://mlsanity.com/paper/2305.11195/) (2023)
- [Dynamic Domain Adaptation-Driven Physics-Informed Graph Representation Learning for AC-OPF](https://mlsanity.com/paper/2506.00478/) (2025)
- [Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies](https://mlsanity.com/paper/2606.03125/) (2026)
- [Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration](https://mlsanity.com/paper/2608.25095/) (2026)
- [Scaling Laws for Physics-Aware ACOPF Surrogate Learning](https://mlsanity.com/paper/2609.16282/) (2026)
- [Learning Samples Importance: Parameterizing Dual Variables in Everywhere Learning](https://mlsanity.com/paper/2609.36310/) (2026)

## Abstract (arXiv)

AC optimal power flow (AC-OPF) problems need to be solved more frequently in the future to maintain stable and economic power system operation. To tackle this challenge, a deep neural network-based voltage-constrained approach (DeepOPF-V) is proposed to solve AC-OPF problems with high computational efficiency. Its unique design predicts voltages of all buses and then uses them to reconstruct the remaining variables without solving non-linear AC power flow equations. A fast post-processing process is developed to enforce the box constraints. The effectiveness of DeepOPF-V is validated by simulations on IEEE 118/300-bus systems and a 2000-bus test system. Compared with existing studies, DeepOPF-V achieves decent computation speedup up to four orders of magnitude and comparable performance in optimality gap and preserving the feasibility of the solution.