A tutorial on data‐driven eigenvalue identification: Prony analysis, matrix pencil, and eigensystem realization algorithm

Abstract

Summary To identify power system eigenvalues from measurement data, Prony analysis, matrix pencil (MP), and eigensystem realization algorithm (ERA) are three major methods. This paper reviews the three methods and sheds insight on the principles of the three methods: eigenvalue identification through various Hankel matrix formulations. In addition, multiple channel data handling and noise‐resilience techniques are investigated. In the literature, singular value decomposition (SVD)‐based rank reduction technique has been applied to MP and resulted in a reduced‐order system eigenvalue estimation and an excellent noise resilient feature. In this paper, ERA is refined using the SVD‐based rank reduction to achieve superior performance. Further, a reduced‐order Prony analysis method is proposed. With this technique, Prony analysis can not only give reduced‐order system eigenvalues, but also become noise resilient. Four case studies are conducted to demonstrate the effectiveness of the eigenvalue identification methods, including a tutorial example of an RLC circuit resonance, a power grid oscillation case study for a 16‐machine 68‐bus system, an example of subsynchronous resonance (SSR) of a type‐3 wind grid integration system, and real‐world oscillation events captured by Independent System Operator‐New England (ISO‐NE).

Data-driven Identification of Nonlinear Power System Dynamics Using Output-only Measurements

“…4. Data-driven eigenvalue estimation from synthetic PMU measurements using existing EDMD method and developed ESI method compared with linearized eigenvalues We conducted simulation and numerical studies to compare the ESI method with three prevailing techniques, namely, multi-channel Prony Analysis [9], Matrix Pencil Method [13] and Normal Form Analysis [19], [20]. As shown in Fig.…”

“…This approach provides better accuracy as compared to Prony Method in presence of noisy measurements. However, this approach as well assumes linear nature of system dynamics [13]. A detailed summary and comparative study of Prony Analysis and Matrix Pencil Method is presented in [13].…”

“…However, this approach as well assumes linear nature of system dynamics [13]. A detailed summary and comparative study of Prony Analysis and Matrix Pencil Method is presented in [13]. Another method of Subspace Identification has been developed for output-based identification of linear systems [14].…”

Trend Analysis of Modal Identification based Real-time Power System Oscillations using L1 Trend Filtering

“…Where is the sample size, and parameter 1 allows regulating the size of difference ( − ). The trend filter 1 is a variation of the Hodrick-Prescott filter where the second term of (2) is substituted by its penalized norm, as established by (3). Consequently, the trend filter 1 produces estimations of the linear direction (not specified by the quadratic term of (2)).…”

“…Therefore, the monitoring quality depends on the efficiency and precision of the WAMS applications at a high updating rate of one cycle and low time delay. As part of these applications, there commonly are modal identification algorithms that allow estimating the characteristics of oscillations such as amplitude, frequency, and damping of oscillatory modes present an electric system [3][4][5].…”