# Optimal Power Flow Based on Physical-Model-Integrated Neural Network with Worth-Learning Data Generation

arXiv: https://arxiv.org/abs/2301.03766 · HTML: https://mlsanity.com/paper/2301.03766/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 10 Jan 2023.

## Builds on (most cited first, 14 of 14)

- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [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)
- [Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications](https://mlsanity.com/paper/1910.01624/) (2019)
- [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)
- [OPF-Learn: An Open-Source Framework for Creating Representative AC Optimal Power Flow Datasets](https://mlsanity.com/paper/2111.01228/) (2021)
- [A Convex Neural Network Solver for DCOPF with Generalization Guarantees](https://mlsanity.com/paper/2009.09109/) (2020)
- [Is Machine Learning in Power Systems Vulnerable?](https://mlsanity.com/paper/1808.08197/) (2018)
- [Convex Relaxation of Optimal Power Flow, Part II: Exactness](https://mlsanity.com/paper/1405.0814/) (2014)
- [Probabilistic Forecast of Real-Time LMP and Network Congestion](https://mlsanity.com/paper/1503.06171/) (2015)

## Built on by (most cited first, 3 of 3)

- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [OPFData: Large-scale datasets for AC optimal power flow with topological perturbations](https://mlsanity.com/paper/2406.07234/) (2024)
- [Adaptive Informed Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2412.02659/) (2024)

## Abstract (arXiv)

Fast and reliable solvers for optimal power flow (OPF) problems are attracting surging research interest. As surrogates of physical-model-based OPF solvers, neural network (NN) solvers can accelerate the solving process. However, they may be unreliable for ``unseen" inputs when the training dataset is unrepresentative. Enhancing the representativeness of the training dataset for NN solvers is indispensable but is not well studied in the literature. To tackle this challenge, we propose an OPF solver based on a physical-model-integrated NN with worth-learning data generation. The designed NN is a combination of a conventional multi-layer perceptron (MLP) and an OPF-model module, which outputs not only the optimal decision variables of the OPF problem but also the constraints violation degree. Based on this NN, the worth-learning data generation method can identify feasible samples that are not well generalized by the NN. By iteratively applying this method and including the newly identified worth-learning samples in the training set, the representativeness of the training set can be significantly enhanced. Therefore, the solution reliability of the NN solver can be remarkably improved. Experimental results show that the proposed method leads to an over 50% reduction of constraint violations and optimality loss compared to conventional NN solvers.