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Physics-informed Graphical Neural Network for Power System State Estimation

Quang-Ha Ngo, Bang L. H. Nguyen, Tuyen V. Vu, Jianhua Zhang, Tuan Ngo

TL;DR

This paper tackles the challenge of accurately estimating power system states under sparse measurements by integrating physics with graph learning. It introduces a physics-informed graph neural network (PINN) that fuses a model-based Kalman-filter dynamic estimator with a graph neural network, leveraging the branch current formulation to inject physics into learning. The method is evaluated on IEEE 5-bus, 123-bus, and 8500-bus systems, showing substantial reductions in mean squared error (MSE) compared with traditional ML approaches, and demonstrates robustness to load perturbations. The results highlight the practical potential of PINN for scalable, physics-consistent dynamic state estimation in modern smart grids, with future work aimed at scaling and security under attacks.

Abstract

State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power system dynamics, primarily because of limitations in encoding the grid topology and sparse measurements. This paper proposes a physics-informed graphical learning state estimation method to address these limitations by leveraging both domain physical knowledge and a graph neural network (GNN). We employ a GNN architecture that can handle the graph-structured data of power systems more effectively than traditional data-driven methods. The physics-based knowledge is constructed from the branch current formulation, making the approach adaptable to both transmission and distribution systems. The validation results of three IEEE test systems show that the proposed method can achieve lower mean square error more than 20% than the conventional methods.

Physics-informed Graphical Neural Network for Power System State Estimation

TL;DR

This paper tackles the challenge of accurately estimating power system states under sparse measurements by integrating physics with graph learning. It introduces a physics-informed graph neural network (PINN) that fuses a model-based Kalman-filter dynamic estimator with a graph neural network, leveraging the branch current formulation to inject physics into learning. The method is evaluated on IEEE 5-bus, 123-bus, and 8500-bus systems, showing substantial reductions in mean squared error (MSE) compared with traditional ML approaches, and demonstrates robustness to load perturbations. The results highlight the practical potential of PINN for scalable, physics-consistent dynamic state estimation in modern smart grids, with future work aimed at scaling and security under attacks.

Abstract

State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power system dynamics, primarily because of limitations in encoding the grid topology and sparse measurements. This paper proposes a physics-informed graphical learning state estimation method to address these limitations by leveraging both domain physical knowledge and a graph neural network (GNN). We employ a GNN architecture that can handle the graph-structured data of power systems more effectively than traditional data-driven methods. The physics-based knowledge is constructed from the branch current formulation, making the approach adaptable to both transmission and distribution systems. The validation results of three IEEE test systems show that the proposed method can achieve lower mean square error more than 20% than the conventional methods.
Paper Structure (17 sections, 10 equations, 15 figures, 3 tables, 2 algorithms)

This paper contains 17 sections, 10 equations, 15 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Model-Based Estimation of Dynamic Power Systems
  4. Graph Neural Network Structure
  5. Physics-Informed Learning on Graphs
  6. PINN-based State Estimation Implementation
  7. Investigated Power Systems
  8. Data Acquisition Procedure
  9. Response to Load Changes
  10. Configuration of Training Model
  11. RESULTS AND ANALYSIS
  12. Model-based Method Accuracy
  13. IEEE 5 Buses
  14. IEEE 123 Buses
  15. IEEE 8500 Buses
  16. ...and 2 more sections

Figures (15)

  • Figure 1: The power line in a distribution system
  • Figure 2: A message-passing process in each GNN layer
  • Figure 3: The overall flowchart of the PINN framework
  • Figure 4: The training process diagram
  • Figure 5: Training time of PINN under different batch sizes
  • ...and 10 more figures