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Power Flow Approximations for Multiphase Distribution Networks using Gaussian Processes

Daniel Glover, Parikshit Pareek, Deepjyoti Deka, Anamika Dubey

TL;DR

This work addresses the challenge of efficiently approximating multiphase distribution power flow under high DER penetration and uncertain loads. It adopts Gaussian Process Regression to learn a probabilistic mapping from net injections to nodal voltages, offering data efficiency and uncertainty quantification, and benchmarks against a deep neural network and LinDistFlow on realistic feeders. Results show that the GP surrogate achieves high accuracy with far fewer training samples and scales to large networks, outperforming DNNs in data-limited regimes while remaining competitive under larger datasets. The approach promises practical benefits for fast, transparent state estimation and OPF in grid-edge operations, with future work aimed at scalability, kernel design, and topology-change handling.

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.

Power Flow Approximations for Multiphase Distribution Networks using Gaussian Processes

TL;DR

This work addresses the challenge of efficiently approximating multiphase distribution power flow under high DER penetration and uncertain loads. It adopts Gaussian Process Regression to learn a probabilistic mapping from net injections to nodal voltages, offering data efficiency and uncertainty quantification, and benchmarks against a deep neural network and LinDistFlow on realistic feeders. Results show that the GP surrogate achieves high accuracy with far fewer training samples and scales to large networks, outperforming DNNs in data-limited regimes while remaining competitive under larger datasets. The approach promises practical benefits for fast, transparent state estimation and OPF in grid-edge operations, with future work aimed at scalability, kernel design, and topology-change handling.

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.
Paper Structure (11 sections, 5 equations, 7 figures, 5 tables)

This paper contains 11 sections, 5 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Gaussian Process Regression & Power Flow
  3. Three-Phase Distribution System Model
  4. Gaussian Process Regression
  5. Methodology & Learning Models
  6. Gaussian Process Power Flow Approximation Model
  7. Benchmark PF Models: DNN and LinDistFlow
  8. Simulation Case Study
  9. Distribution Simulation Environment
  10. Model Evaluation & Discussion
  11. Conclusion

Figures (7)

  • Figure 1: Deep Neural Network Architecture
  • Figure 2: IEEE 123-Bus Test System with DERs
  • Figure 3: Case 1: Phase A Voltage Magnitude Prediction Hour 33
  • Figure 4: Case 2 Training: GP Mean Absolute Error Three Phases
  • Figure 5: Case 3: Phase A Voltage Magnitude Prediction Hour 107
  • ...and 2 more figures