# Data-driven Optimal Power Flow: A Physics-Informed Machine Learning Approach

arXiv: https://arxiv.org/abs/2006.00544 · HTML: https://mlsanity.com/paper/2006.00544/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2020.

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

- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [PowerGraph: A power grid benchmark dataset for graph neural networks](https://mlsanity.com/paper/2402.02827/) (2024)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [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)
- [Massively Digitized Power Grid: Opportunities and Challenges of Use-inspired AI](https://mlsanity.com/paper/2205.05180/) (2022)
- [Controlling Smart Inverters using Proxies: A Chance-Constrained DNN-based Approach](https://mlsanity.com/paper/2105.00429/) (2021)
- [A Physics-Informed Machine Learning for Electricity Markets: A NYISO Case Study](https://mlsanity.com/paper/2304.00062/) (2023)
- [Power Flow Analysis Using Deep Neural Networks in Three-Phase Unbalanced Smart Distribution Grids](https://mlsanity.com/paper/2401.07465/) (2024)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Deep Reinforcement Learning for Optimal Power Flow with Renewables Using Graph Information](https://mlsanity.com/paper/2112.11461/) (2021)
- [Sampling Strategies for Static Powergrid Models](https://mlsanity.com/paper/2204.09053/) (2022)
- [Machine Learning for Electricity Market Clearing](https://mlsanity.com/paper/2205.11641/) (2022)
- [Optimal Power Flow in Highly Renewable Power System Based on Attention Neural Networks](https://mlsanity.com/paper/2311.13949/) (2023)
- [Robust Deep Reinforcement Learning for Inverter-based Volt-Var Control in Partially Observable Distribution Networks](https://mlsanity.com/paper/2408.06776/) (2024)
- [Adaptive Informed Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2412.02659/) (2024)
- [Operational risk quantification of power grids using graph neural network surrogates of the DC OPF](https://mlsanity.com/paper/2311.03661/) (2023)
- [Time and Frequency Domain-based Anomaly Detection in Smart Meter Data for Distribution Network Studies](https://mlsanity.com/paper/2504.18231/) (2025)
- [Study Design and Demystification of Physics Informed Neural Networks for Power Flow Simulation](https://mlsanity.com/paper/2509.19233/) (2025)

## Abstract (arXiv)

This paper proposes a data-driven approach for optimal power flow (OPF) based on the stacked extreme learning machine (SELM) framework. SELM has a fast training speed and does not require the time-consuming parameter tuning process compared with the deep learning algorithms. However, the direct application of SELM for OPF is not tractable due to the complicated relationship between the system operating status and the OPF solutions. To this end, a data-driven OPF regression framework is developed that decomposes the OPF model features into three stages. This not only reduces the learning complexity but also helps correct the learning bias. A sample pre-classification strategy based on active constraint identification is also developed to achieve enhanced feature attractions. Numerical results carried out on IEEE and Polish benchmark systems demonstrate that the proposed method outperforms other alternatives. It is also shown that the proposed method can be easily extended to address different test systems by adjusting only a few hyperparameters.