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Data-driven Forced Oscillation Localization using Inferred Impulse Responses

Shaohui Liu, Hao Zhu, Vassilis Kekatos

TL;DR

This paper tackles the problem of locating forced oscillation sources in interconnected power systems by leveraging ambient PMU data to recover system impulse responses without relying on a detailed grid model. The core idea is to formulate FO localization in the Fourier domain as a least-squares problem using impulse responses recovered from ambient data, guaranteeing a theoretical link to linearized dynamics under reasonable assumptions. The authors develop a two-phase algorithm—offline impulse-response recovery from ambient measurements and online FO localization from FO data—that is flexible to measurement types and partial observability. Numerical tests on the IEEE 68-bus system and the NASPI 240-bus dataset demonstrate high localization accuracy across scenarios with single or multiple FO sources and modes, including partial observability and non-generator FO sources. The approach offers a scalable, data-driven alternative to model-dependent methods with practical applicability for real-world grid monitoring and FO mitigation.

Abstract

Poorly damped oscillations pose threats to the stability and reliability of interconnected power systems. In this work, we propose a comprehensive data-driven framework for inferring the sources of forced oscillation (FO) using solely synchrophasor measurements. During normal grid operations, fast-rate ambient data are collected to recover the impulse responses in the small-signal regime, without requiring the system model. When FO events occur, the source is estimated based on the frequency domain analysis by fitting the least-squares (LS) error for the FO data using the impulse responses recovered previously. Although the proposed framework is purely data-driven, the result has been established theoretically via model-based analysis of linearized dynamics under a few realistic assumptions. Numerical validations demonstrate its applicability to realistic power systems including nonlinear, higher-order dynamics with control effects using the IEEE 68-bus system, and the 240-bus system from the IEEE-NASPI FO source location contest. The generalizability of the proposed methodology has been validated using different types of measurements and partial sensor coverage conditions.

Data-driven Forced Oscillation Localization using Inferred Impulse Responses

TL;DR

This paper tackles the problem of locating forced oscillation sources in interconnected power systems by leveraging ambient PMU data to recover system impulse responses without relying on a detailed grid model. The core idea is to formulate FO localization in the Fourier domain as a least-squares problem using impulse responses recovered from ambient data, guaranteeing a theoretical link to linearized dynamics under reasonable assumptions. The authors develop a two-phase algorithm—offline impulse-response recovery from ambient measurements and online FO localization from FO data—that is flexible to measurement types and partial observability. Numerical tests on the IEEE 68-bus system and the NASPI 240-bus dataset demonstrate high localization accuracy across scenarios with single or multiple FO sources and modes, including partial observability and non-generator FO sources. The approach offers a scalable, data-driven alternative to model-dependent methods with practical applicability for real-world grid monitoring and FO mitigation.

Abstract

Poorly damped oscillations pose threats to the stability and reliability of interconnected power systems. In this work, we propose a comprehensive data-driven framework for inferring the sources of forced oscillation (FO) using solely synchrophasor measurements. During normal grid operations, fast-rate ambient data are collected to recover the impulse responses in the small-signal regime, without requiring the system model. When FO events occur, the source is estimated based on the frequency domain analysis by fitting the least-squares (LS) error for the FO data using the impulse responses recovered previously. Although the proposed framework is purely data-driven, the result has been established theoretically via model-based analysis of linearized dynamics under a few realistic assumptions. Numerical validations demonstrate its applicability to realistic power systems including nonlinear, higher-order dynamics with control effects using the IEEE 68-bus system, and the 240-bus system from the IEEE-NASPI FO source location contest. The generalizability of the proposed methodology has been validated using different types of measurements and partial sensor coverage conditions.
Paper Structure (12 sections, 4 theorems, 16 equations, 5 figures, 2 tables, 1 algorithm)

This paper contains 12 sections, 4 theorems, 16 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. FO Localization via Recovered Responses
  4. Localization based on Output Observations
  5. Multiple FO Sources and Modes
  6. FO Localization Algorithm
  7. Numerical Results
  8. Single FO Source with Single FO Mode
  9. Two FO Sources with Multiple Modes
  10. Validation with the IEEE-NASPI FO Contest Dataset
  11. Conclusions
  12. Acknowledgements

Key Result

lemma 1

(State's Impulse Responses) Under (ASassump0)--(ASassump3), the impulse responses of rotor angle or frequency are equivalent to the cross-correlation of the related ambient signals: for $t\geq 0$. Here $C_{\cdot,\cdot}$ denotes the cross-correlation operator and the subscripts indicate its two arguments. Because $T_{u_\ell,\omega_k}(t)$ is the derivative of $T_{u_\ell,\delta_k}(t)$, each one of t

Figures (5)

  • Figure 1: Diagram of the 68-bus system with 16 generators.
  • Figure 2: Spectrum of rotor speed $\omega_{13}$ response from $u_1$: simulated vs. inferred from ambient data.
  • Figure 3: Spectrum of rotor speed $\omega_{13}$ (measured by $f_{37}$) response from $u_{11}$: simulated vs. inferred from ambient data.
  • Figure 4: Diagram of the 240-bus system with 26 monitored generators yuan2020developing. Circled locations are monitored generators with both name and rating matched at the ambient and FO datasets. Locations with stars are FO sources in Case 3 and Case 4.
  • Figure : FO Localization

Theorems & Definitions (4)

  • lemma 1
  • proposition 1
  • lemma 2
  • proposition 2