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

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).