# Power Flow Analysis Using Deep Neural Networks in Three-Phase Unbalanced Smart Distribution Grids

arXiv: https://arxiv.org/abs/2401.07465 · HTML: https://mlsanity.com/paper/2401.07465/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 15 Jan 2024.

## Builds on (most cited first, 15 of 15)

- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Machine Learning for AC Optimal Power Flow](https://mlsanity.com/paper/1910.08842/) (2019)
- [Power Flow Balancing with Decentralized Graph Neural Networks](https://mlsanity.com/paper/2111.02169/) (2021)
- [Data-driven Optimal Power Flow: A Physics-Informed Machine Learning Approach](https://mlsanity.com/paper/2006.00544/) (2020)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Solving AC Power Flow with Graph Neural Networks under Realistic Constraints](https://mlsanity.com/paper/2204.07000/) (2022)
- [Physics-Informed Machine Learning for Data Anomaly Detection, Classification, Localization, and Mitigation: A Review, Challenges, and Path Forward](https://mlsanity.com/paper/2309.10788/) (2023)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Physics-Informed Convolutional Autoencoder for Cyber Anomaly Detection in Power Distribution Grids](https://mlsanity.com/paper/2312.04758/) (2023)
- [On the existence and linear approximation of the power flow solution in power distribution networks](https://mlsanity.com/paper/1403.5031/) (2014)
- [Investigating the Impact of Electric Vehicles on the Voltage Profile of Distribution Networks](https://mlsanity.com/paper/2012.12806/) (2020)
- [Impacts of Variable-Impedance-Based Power Flow Control on Renewable Energy Integration](https://mlsanity.com/paper/2204.12642/) (2022)
- [A Robust Data-driven Process Modeling Applied to Time-series Stochastic Power Flow](https://mlsanity.com/paper/2301.02651/) (2023)

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

- [An Unsupervised Adversarial Autoencoder for Cyber Attack Detection in Power Distribution Grids](https://mlsanity.com/paper/2404.02923/) (2024)
- [Multivariate Physics-Informed Convolutional Autoencoder for Anomaly Detection in Power Distribution Systems with High Penetration of DERs](https://mlsanity.com/paper/2406.02927/) (2024)
- [Power Flow Approximations for Multiphase Distribution Networks using Gaussian Processes](https://mlsanity.com/paper/2504.21260/) (2025)

## Abstract (arXiv)

Most power systems' approaches are currently tending towards stochastic and probabilistic methods due to the high variability of renewable sources and the stochastic nature of loads. Conventional power flow (PF) approaches such as forward-backward sweep (FBS) and Newton-Raphson require a high number of iterations to solve non-linear PF equations making them computationally very intensive. PF is the most important study performed by utility, required in all stages of the power system, especially in operations and planning. This paper discusses the applications of deep learning (DL) to predict PF solutions for three-phase unbalanced power distribution grids. Three deep neural networks (DNNs); Radial Basis Function Network (RBFnet), Multi-Layer Perceptron (MLP), and Convolutional Neural Network (CNN), are proposed in this paper to predict PF solutions. The PF problem is formulated as a multi-output regression model where two or more output values are predicted based on the inputs. The training and testing data are generated through the OpenDSS-MATLAB COM interface. These methods are completely data-driven where the training relies on reducing the mismatch at each node without the need for the knowledge of the system. The novelty of the proposed methodology is that the models can accurately predict the PF solutions for the unbalanced distribution grids with mutual coupling and are robust to different R/X ratios, topology changes as well as generation and load variability introduced by the integration of distributed energy resources (DERs) and electric vehicles (EVs). To test the efficacy of the DNN models, they are applied to IEEE 4-node and 123-node test cases, and the American Electric Power (AEP) feeder model. The PF results for RBFnet, MLP, and CNN models are discussed in this paper demonstrating that all three DNN models provide highly accurate results in predicting PF solutions.