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Data-Driven Post-Event Analysis with Real-World Oscillation Data from Denmark

Youhong Chen, Debraj Bhattacharjee, Balarko Chaudhuri, Mark O Malley, Nan Qin, Adrian Pilkaer Expethit

TL;DR

The paper addresses locating sources of poorly damped oscillations in grids with high inverter-based resources using PMU data. It leverages Extended Dynamic Mode Decomposition (EDMD), grounded in Koopman operator theory, to extract dominant oscillation contributors from a data-driven perspective without relying on network models. Validation on a real Danish post-event dataset demonstrates that EDMD correctly identifies the main contributor (location 19) consistent with Energinet, outperforming conventional methods such as Dissipating Energy Flow and Q–V phase analyses. The results support EDMD as a powerful tool for post-event analysis and targeted small-signal stabilization (SSO) mitigation in IBR-dominated power systems.

Abstract

This paper demonstrates how Extended Dynamic Mode Decomposition (EDMD), grounded in Koopman operator theory, can effectively identify the main contributor(s) to oscillations in power grids. We use PMU data recorded from a real 0.15 Hz oscillation event in Denmark for post-event analysis. To this end, the EDMD algorithm processed only voltage and current phasors from nineteen PMUs at different voltage levels across the Danish grid. In such a blind-test setting with no supplementary system information, EDMD accurately pinpointed the location of the main contributor to the 0.2 Hz oscillation, consistent with the location of the problematic IBR plant later confirmed by Energinet, where the underlying cause was a control system issue. Conventional approaches, such as the dissipating energy flow (DEF) method used in the ISO-NE OSL tool did not clearly identify this plant. This joint validation with Energinet, reinforcing earlier studies using simulated IBR-dominated systems and real PMU data from ISO-NE, highlights the potential of EDMD-based post-event analysis for identifying major oscillation contributors and enabling targeted SSO mitigation.

Data-Driven Post-Event Analysis with Real-World Oscillation Data from Denmark

TL;DR

The paper addresses locating sources of poorly damped oscillations in grids with high inverter-based resources using PMU data. It leverages Extended Dynamic Mode Decomposition (EDMD), grounded in Koopman operator theory, to extract dominant oscillation contributors from a data-driven perspective without relying on network models. Validation on a real Danish post-event dataset demonstrates that EDMD correctly identifies the main contributor (location 19) consistent with Energinet, outperforming conventional methods such as Dissipating Energy Flow and Q–V phase analyses. The results support EDMD as a powerful tool for post-event analysis and targeted small-signal stabilization (SSO) mitigation in IBR-dominated power systems.

Abstract

This paper demonstrates how Extended Dynamic Mode Decomposition (EDMD), grounded in Koopman operator theory, can effectively identify the main contributor(s) to oscillations in power grids. We use PMU data recorded from a real 0.15 Hz oscillation event in Denmark for post-event analysis. To this end, the EDMD algorithm processed only voltage and current phasors from nineteen PMUs at different voltage levels across the Danish grid. In such a blind-test setting with no supplementary system information, EDMD accurately pinpointed the location of the main contributor to the 0.2 Hz oscillation, consistent with the location of the problematic IBR plant later confirmed by Energinet, where the underlying cause was a control system issue. Conventional approaches, such as the dissipating energy flow (DEF) method used in the ISO-NE OSL tool did not clearly identify this plant. This joint validation with Energinet, reinforcing earlier studies using simulated IBR-dominated systems and real PMU data from ISO-NE, highlights the potential of EDMD-based post-event analysis for identifying major oscillation contributors and enabling targeted SSO mitigation.

Paper Structure

This paper contains 16 sections, 13 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Extended Dynamic Mode Decompression (EDMD)
  4. Data-driven algorithm
  5. Selection of observables
  6. Filtered mode of interest
  7. Calculation of reduced-order $\Tilde{M}_K$
  8. Data-Driven modal analysis
  9. Case study with EDMD-based method
  10. PMU data from oscillation event in Denmark
  11. Observables in EDMD
  12. Top oscillation contributor
  13. Case study with other methods
  14. Dissipating Energy Flow (DEF)
  15. Q-V phase-based method
  16. ...and 1 more sections

Figures (6)

  • Figure 1: Time‐series phasor current magnitude and angle measurements from PMUs across selected locations in the Danish transmission system.(Location 4 is not included due to bad data quality)
  • Figure 2: Time‐series phasor voltage magnitude and angle measurements from PMUs across selected locations in the Danish transmission system.
  • Figure 3: Active and reactive power $P$ and $Q$ calculated from PMU measurements at selected locations in the Danish transmission system.
  • Figure 4: Data-driven participation factors obtained via EDMD for the Danish transmission system. Location 19 is the top contributor to 0.15 Hz oscillation.
  • Figure 5: Top six locations in terms of highest dissipating energy flow in Danish transmission system. Locations 14 and 15 show highest positive energy injection, while location 9 has highest energy absorption.
  • ...and 1 more figures