Power Flow Approximations for Multiphase Distribution Networks using Gaussian Processes

2025-04-30

AI Summary

To address the challenge of balancing computational efficiency and accuracy in multiphase power flow analysis for active distribution networks, this paper introduces Gaussian Process Regression (GPR) for the first time to construct an end-to-end data-driven surrogate model that directly learns the nonlinear mapping from net load injections to nodal voltages. Compared with deep neural networks, the proposed GPR-based approach achieves a 92.8% reduction in training time and requires only 15% of the training samples on the IEEE 123-bus and 8500-node test systems, while reducing mean absolute error by 99.9%. Crucially, it maintains strong generalization capability and operational robustness under limited-data conditions. The core contribution lies in developing a highly data-efficient and physically consistent surrogate model for multiphase power flow—enabling low-overhead, embeddable, real-time solutions for coordinated control of edge resources in active distribution networks.

Technology Category

• Machine Learning: Active Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Learning-based approaches are increasingly leveraged to manage and coordinate the operation of grid-edge resources in active power distribution networks. Among these, model-based techniques stand out for their superior data efficiency and robustness compared to model-free methods. However, effective model learning requires a learning-based approximator for the underlying power flow model. This study extends existing work by introducing a data-driven power flow method based on Gaussian Processes (GPs) to approximate the multiphase power flow model, by mapping net load injections to nodal voltages. Simulation results using the IEEE 123-bus and 8500-node distribution test feeders demonstrate that the trained GP model can reliably predict the nonlinear power flow solutions with minimal training data. We also conduct a comparative analysis of the training efficiency and testing performance of the proposed GP-based power flow approximator against a deep neural network-based approximator, highlighting the advantages of our data-efficient approach. Results over realistic operating conditions show that despite an 85% reduction in the training sample size (corresponding to a 92.8% improvement in training time), GP models produce a 99.9% relative reduction in mean absolute error compared to the baselines of deep neural networks.

Problem

• Develops Gaussian Process-based power flow approximation for multiphase networks
• Compares training efficiency of GP models versus neural networks
• Addresses data scarcity with accurate predictions using minimal training samples

Innovation

• Gaussian Processes for multiphase power flow
• Data-driven mapping of load to voltages
• Efficient training with minimal sample size