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Graph topology estimation of power grids using pairwise mutual information of time series data

Daniel T. Speckhard

TL;DR

This work addresses topology estimation for power grids from time-series voltage data by casting buses as random variables and reconstructing a radial graph via pairwise mutual information (MI) within the Chow-Liu maximum spanning tree framework. It evaluates multiple MI approximations—Gaussian, discrete, and JVHW entropy estimation—using incremental voltage changes $|\Delta V|$ to improve dependence detection, across MATPOWER IEEE networks and GridLAB-D datasets with varied data length, sampling rate, and precision. Key findings show near-perfect SDR on IEEE and SG1 datasets, with leaf-SDR often slightly lower on larger SG2 grids, and that data quality (precision, downsampling, step size) substantially influences performance; redundant data should be collapsed to boost accuracy. The work provides practical guidelines for data collection and MI-based topology inference and releases open-source code for replication and extension. Overall, the approach offers a computationally tractable, information-theoretic pathway to validate or recover grid topology in dynamic, data-constrained settings, enabling improved monitoring and control in modern power systems.

Abstract

The topology of a power grid is estimated using an information theoretic approach. By modeling the grid as a graph and using voltage magnitude data of individual nodes in the grid, the mutual information between pairs of nodes is computed using different approximation methods. Using the well-known Chow-Liu algorithm, a maximum spanning tree based on mutual information is computed to estimate the power grid topology. This manuscript explores the application of this method to different datasets and explores the domain of applicability. The data quality, precision, time windows, frequency and the method for calculating the mutual information are varied to see the effect on the successful reconstruction of the graph and it's leaf nodes. Success is shown for IEEE networks generated with MATPOWER and data generated using GridLAB-D. The algorithm is then cross-validated on IEEE networks.

Graph topology estimation of power grids using pairwise mutual information of time series data

TL;DR

This work addresses topology estimation for power grids from time-series voltage data by casting buses as random variables and reconstructing a radial graph via pairwise mutual information (MI) within the Chow-Liu maximum spanning tree framework. It evaluates multiple MI approximations—Gaussian, discrete, and JVHW entropy estimation—using incremental voltage changes to improve dependence detection, across MATPOWER IEEE networks and GridLAB-D datasets with varied data length, sampling rate, and precision. Key findings show near-perfect SDR on IEEE and SG1 datasets, with leaf-SDR often slightly lower on larger SG2 grids, and that data quality (precision, downsampling, step size) substantially influences performance; redundant data should be collapsed to boost accuracy. The work provides practical guidelines for data collection and MI-based topology inference and releases open-source code for replication and extension. Overall, the approach offers a computationally tractable, information-theoretic pathway to validate or recover grid topology in dynamic, data-constrained settings, enabling improved monitoring and control in modern power systems.

Abstract

The topology of a power grid is estimated using an information theoretic approach. By modeling the grid as a graph and using voltage magnitude data of individual nodes in the grid, the mutual information between pairs of nodes is computed using different approximation methods. Using the well-known Chow-Liu algorithm, a maximum spanning tree based on mutual information is computed to estimate the power grid topology. This manuscript explores the application of this method to different datasets and explores the domain of applicability. The data quality, precision, time windows, frequency and the method for calculating the mutual information are varied to see the effect on the successful reconstruction of the graph and it's leaf nodes. Success is shown for IEEE networks generated with MATPOWER and data generated using GridLAB-D. The algorithm is then cross-validated on IEEE networks.
Paper Structure (21 sections, 1 theorem, 15 equations, 38 figures, 4 tables, 1 algorithm)

This paper contains 21 sections, 1 theorem, 15 equations, 38 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Theoretical estimation approach
  4. Gaussian approximation
  5. Discrete mutual information
  6. JVHW Entropy Estimation
  7. Datasets
  8. Collapsing Redundant Data
  9. Performance Metrics
  10. Results
  11. Algorithm Performance with Change in Voltage Magnitude
  12. Gaussian Approximation of Data
  13. Reducing Data Requirements for Estimation
  14. Data Length Analysis
  15. Data Precision
  16. ...and 6 more sections

Key Result

Theorem 1

In a radial distribution power grid, mutual information-based maximum spanning tree algorithm finds the optimal approximation of $P(V_{S})$ and its associated topology connection, if current injections are approximated as independent.

Figures (38)

  • Figure 1: The program flow of the Chow-Liu Algorithm applied to electrical grid topology estimation. When only voltage magnitude data is available, only the top half of the parallel split in the workflow is executed.
  • Figure 2: The heatmap of mutual information is shown for data generated with GridLAB-D. The white circles represent true branches in the grid and the green crosses represent estimated branches based on the Chow-Liu approximation.
  • Figure 3: Histogram and Gaussian model based on mean and standard deviation of voltage magnitude data at Node 18 from the SG1 dataset generated in GridLAB-D.
  • Figure 4: The SG1 graph, based on a dataset generated in GridLAB-D, changes shape when redundant nodes are removed. The non-redundant nodes are marked red.
  • Figure 5: The improved workflow removes redundant data before calculating mutual information. This added step greatly improves the performance of topology estimation.
  • ...and 33 more figures

Theorems & Definitions (1)

  • Theorem 1