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Title: Applied Koopman operator theory for power systems technology
Authors: Susuki, Yoshihiko
Mezic, Igor
Raak, Fredrik
Hikihara, Takashi  kyouindb  KAKEN_id
Author's alias: 薄, 良彦
引原, 隆士
Keywords: power system
nonlinear dynamical system
Koopman operator
Koopman mode
Issue Date: 1-Oct-2016
Publisher: Institute of Electronics, Information and Communications Engineers (IEICE)
Journal title: Nonlinear Theory and Its Applications, IEICE
Volume: 7
Issue: 4
Start page: 430
End page: 459
Abstract: Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman operator itself is linear but infinite-dimensional (evolves on a function space). This linear operator captures the full information of the dynamics described by the original nonlinear system. In particular, spectral properties of the Koopman operator play a crucial role in analyzing the original system. In the first part of this paper, we review the so-called Koopman operator theory for nonlinear dynamical systems, with emphasis on modal decomposition and computation that are direct to wide applications. Then, in the second part, we present a series of applications of the Koopman operator theory to power systems technology. The applications are established as data-centric methods, namely, how to use massive quantities of data obtained numerically and experimentally, through spectral analysis of the Koopman operator: coherency identification of swings in coupled synchronous generators, precursor diagnostic of instabilities in the coupled swing dynamics, and stability assessment of power systems without any use of mathematical models. Future problems of this research direction are identified in the last concluding part of this paper.
Rights: © 2016 IEICE
DOI(Published Version): 10.1587/nolta.7.430
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