# A Data-Driven Real-Time Optimal Power Flow Algorithm Using Local Feedback

arXiv: https://arxiv.org/abs/2502.15306 · HTML: https://mlsanity.com/paper/2502.15306/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 21 Feb 2025.

## Builds on (most cited first, 17 of 17)

- [Why Deep Neural Networks for Function Approximation?](https://mlsanity.com/paper/1610.04161/) (2016)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [Learning Optimal Resource Allocations in Wireless Systems](https://mlsanity.com/paper/1807.08088/) (2018)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence](https://mlsanity.com/paper/1405.0766/) (2014)
- [Reinforcement Learning for Optimal Primary Frequency Control: A Lyapunov Approach](https://mlsanity.com/paper/2009.05654/) (2020)
- [Data-Driven Screening of Network Constraints for Unit Commitment](https://mlsanity.com/paper/1907.04694/) (2019)
- [Stability Constrained Reinforcement Learning for Decentralized Real-Time Voltage Control](https://mlsanity.com/paper/2209.07669/) (2022)
- [Controlling Smart Inverters using Proxies: A Chance-Constrained DNN-based Approach](https://mlsanity.com/paper/2105.00429/) (2021)
- [Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems](https://mlsanity.com/paper/1812.00613/) (2018)
- [Optimal Power Flow Pursuit](https://mlsanity.com/paper/1601.07263/) (2016)
- [Explicit Conditions on Existence and Uniqueness of Load-Flow Solutions in Distribution Networks](https://mlsanity.com/paper/1602.08372/) (2016)
- [Accelerated Voltage Regulation in Multi-Phase Distribution Networks Based on Hierarchical Distributed Algorithm](https://mlsanity.com/paper/1903.00072/) (2019)
- [Hierarchical Optimal Power Flow with Improved Gradient Evaluation](https://mlsanity.com/paper/2204.04827/) (2022)
- [Learning Provably Stable Local Volt/Var Controllers for Efficient Network Operation](https://mlsanity.com/paper/2209.12956/) (2022)
- [A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks](https://mlsanity.com/paper/2306.04350/) (2023)
- [Unsupervised Learning for Equitable DER Control](https://mlsanity.com/paper/2403.11068/) (2024)

## Abstract (arXiv)

The increasing penetration of distributed energy resources (DERs) adds variability as well as fast control capabilities to power networks. Dispatching the DERs based on local information to provide real-time optimal network operation is the desideratum. In this paper, we propose a data-driven real-time algorithm that uses only the local measurements to solve time-varying AC optimal power flow (OPF). Specifically, we design a learnable function that takes the local feedback as input in the algorithm. The learnable function, under certain conditions, will result in a unique stationary point of the algorithm, which in turn transfers the OPF problems to be optimized over the parameters of the function. We then develop a stochastic primal-dual update to solve the variant of the OPF problems based on a deep neural network (DNN) parametrization of the learnable function, which is referred to as the training stage. We also design a gradient-free alternative to bypass the cumbersome gradient calculation of the nonlinear power flow model. The OPF solution-tracking error bound is established in the sense of universal approximation of DNN. Numerical results on the IEEE 37-bus test feeder show that the proposed method can track the time-varying OPF solutions with higher accuracy and faster computation compared to benchmark methods.