# DeepOPF+: A Deep Neural Network Approach for DC Optimal Power Flow for Ensuring Feasibility

arXiv: https://arxiv.org/abs/2009.03147 · HTML: https://mlsanity.com/paper/2009.03147/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2020.

## Built on by (most cited first, 11 of 11)

- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (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)
- [Grid-SiPhyR: An end-to-end learning to optimize framework for combinatorial problems in power systems](https://mlsanity.com/paper/2206.06789/) (2022)
- [Optimal Power Flow in Highly Renewable Power System Based on Attention Neural Networks](https://mlsanity.com/paper/2311.13949/) (2023)
- [ECLipsE-Gen-Local: Efficient Compositional Local Lipschitz Estimates for Deep Neural Networks](https://mlsanity.com/paper/2510.05261/) (2025)
- [MxGPS: Multiplex Graph Transformers for a Power Grid Foundation Model](https://mlsanity.com/paper/2607.13763/) (2026)
- [DClEVerNet: Deep Combinatorial Learning for Efficient EV Charging Scheduling in Large-scale Networked Facilities](https://mlsanity.com/paper/2305.11195/) (2023)
- [Operational risk quantification of power grids using graph neural network surrogates of the DC OPF](https://mlsanity.com/paper/2311.03661/) (2023)
- [Toward Rapid, Optimal, and Feasible Power Dispatch through Generalized Neural Mapping](https://mlsanity.com/paper/2311.04838/) (2023)
- [Impact of Data Poisoning Attacks on Feasibility and Optimality of Neural Power System Optimizers](https://mlsanity.com/paper/2502.05727/) (2025)
- [GridSFM: A Foundation Model for Solving AC Optimal Power Flow](https://mlsanity.com/paper/2609.30173/) (2026)

## Abstract (arXiv)

Deep Neural Networks (DNNs) approaches for the Optimal Power Flow (OPF) problem received considerable attention recently. A key challenge of these approaches lies in ensuring the feasibility of the predicted solutions to physical system constraints. Due to the inherent approximation errors, the solutions predicted by DNNs may violate the operating constraints, e.g., the transmission line capacities, limiting their applicability in practice. To address this challenge, we develop DeepOPF+ as a DNN approach based on the so-called "preventive" framework. Specifically, we calibrate the generation and transmission line limits used in the DNN training, thereby anticipating approximation errors and ensuring that the resulting predicted solutions remain feasible. We theoretically characterize the calibration magnitude necessary for ensuring universal feasibility. Our DeepOPF+ approach improves over existing DNN-based schemes in that it ensures feasibility and achieves a consistent speed up performance in both light-load and heavy-load regimes. Detailed simulation results on a range of test instances show that the proposed DeepOPF+ generates 100% feasible solutions with minor optimality loss. Meanwhile, it achieves a computational speedup of two orders of magnitude compared to state-of-the-art solvers.