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Distribution Grid Line Outage Identification with Unknown Pattern and Performance Guarantee

Chenhan Xiao, Yizheng Liao, Yang Weng

TL;DR

This work proposes a practical yet robust detection approach that utilizes only readily available voltage magnitudes, eliminating the need for costly phase angles or power flow data and proves that the optimal parameters can be learned with convergence guarantees via leveraging the statistical and physical properties of voltage data.

Abstract

Line outage identification in distribution grids is essential for sustainable grid operation. In this work, we propose a practical yet robust detection approach that utilizes only readily available voltage magnitudes, eliminating the need for costly phase angles or power flow data. Given the sensor data, many existing detection methods based on change-point detection require prior knowledge of outage patterns, which are unknown for real-world outage scenarios. To remove this impractical requirement, we propose a data-driven method to learn the parameters of the post-outage distribution through gradient descent. However, directly using gradient descent presents feasibility issues. To address this, we modify our approach by adding a Bregman divergence constraint to control the trajectory of the parameter updates, which eliminates the feasibility problems. As timely operation is the key nowadays, we prove that the optimal parameters can be learned with convergence guarantees via leveraging the statistical and physical properties of voltage data. We evaluate our approach using many representative distribution grids and real load profiles with 17 outage configurations. The results show that we can detect and localize the outage in a timely manner with only voltage magnitudes and without assuming a prior knowledge of outage patterns.

Distribution Grid Line Outage Identification with Unknown Pattern and Performance Guarantee

TL;DR

This work proposes a practical yet robust detection approach that utilizes only readily available voltage magnitudes, eliminating the need for costly phase angles or power flow data and proves that the optimal parameters can be learned with convergence guarantees via leveraging the statistical and physical properties of voltage data.

Abstract

Line outage identification in distribution grids is essential for sustainable grid operation. In this work, we propose a practical yet robust detection approach that utilizes only readily available voltage magnitudes, eliminating the need for costly phase angles or power flow data. Given the sensor data, many existing detection methods based on change-point detection require prior knowledge of outage patterns, which are unknown for real-world outage scenarios. To remove this impractical requirement, we propose a data-driven method to learn the parameters of the post-outage distribution through gradient descent. However, directly using gradient descent presents feasibility issues. To address this, we modify our approach by adding a Bregman divergence constraint to control the trajectory of the parameter updates, which eliminates the feasibility problems. As timely operation is the key nowadays, we prove that the optimal parameters can be learned with convergence guarantees via leveraging the statistical and physical properties of voltage data. We evaluate our approach using many representative distribution grids and real load profiles with 17 outage configurations. The results show that we can detect and localize the outage in a timely manner with only voltage magnitudes and without assuming a prior knowledge of outage patterns.
Paper Structure (21 sections, 9 theorems, 23 equations, 11 figures, 6 tables, 1 algorithm)

This paper contains 21 sections, 9 theorems, 23 equations, 11 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Outage Identification via Voltage Magnitude
  4. Gaussian Distribution of Voltage Increment
  5. Outage Identification via Distribution Change
  6. Outage Identification with Unknown Pattern
  7. Unknown Parameters Estimation via Projected Gradient Descent with Bregman Divergence Constraint
  8. Timely Outage Identification with Performance Guarantee
  9. Restricted Convexity for Convergence Guarantee
  10. Acceleration for Timely Operation
  11. Validate on Extensive Outage Scenarios with Real-World Data
  12. Parameters Estimation with Accuracy and Convergence
  13. Outage Detection with Small Delay and Rare False Alarm
  14. Analysis of Execution Time for Timely Operation
  15. Outage Branch Localization with Accuracy
  16. ...and 6 more sections

Key Result

Lemma 1

In a connected distribution grid $(\mathcal{G},\mathcal{E})$, the admittance matrix $\boldsymbol{Y}_\mathcal{G}\in\mathcal{C}^{M \times M}$ is invertible after eliminating the slack-bus corresponding column and row.

Figures (11)

  • Figure 1: An overview of the distribution grid line outage detection problem: we collect voltage magnitudes from smart meters installed at households and use the posterior probability ratio computed in \ref{['eq:posterior']} to detect the change in the underlying distribution of voltage increments.
  • Figure 2: The empirical histogram of $|\Delta I|$.
  • Figure 3: The Projected Gradient Descent update of $\boldsymbol{\Sigma}_1$.
  • Figure 4: Visualization of learning parameters in $g\sim\mathcal{N}(0,\frac{1}{2}),f\sim\mathcal{N}(1,\frac{1}{5})$.
  • Figure 5: Distance between best update and ground truth against iterations.
  • ...and 6 more figures

Theorems & Definitions (13)

  • Lemma 1
  • Theorem 1
  • proof
  • Theorem 2
  • Theorem 3
  • Lemma 2
  • Theorem 4
  • Definition 1
  • Theorem 5
  • Lemma 3
  • ...and 3 more