The Koopman Operator in Systems and Control pp 507-522 | Cite as

# Data-Driven Voltage Analysis of an Electric Power Grid via Delay Embedding and Extended Dynamic Mode Decomposition

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## Abstract

Data-driven analysis of dynamic performance has attracted a lot of interest in the modern power grid with highly accurate measurement technologies such as Synchrophasor. In this chapter, we report the research effort to do this for voltage dynamics in a rudimentary model of power grids. We use the combination of the so-called delay embedding with the extended dynamic mode decomposition, which is a technique for approximating the Koopman operator directly from time-series data. This combination enables us to approximate the spectral properties of the Koopman operator through voltage–amplitude measurement of a single bus. The spectral properties clarify not only the local information on the voltage dynamics such as frequency/damping in transient responses but also global one such as the flow structure of the underlying mathematical model.

## Notes

### Acknowledgements

The authors greatly appreciate Professor Takashi Hikihara (Kyoto University) for valuable discussion on this work and Professor Igor Mezić (University of California, Santa Barbara) for his careful reading of the draft of this chapter with valuable comments, which are cited in the remark of the appendix. During part of the work on this chapter, the authors were at Laboratory of Advanced Electrical Systems Theory, Department of Electrical Engineering, Kyoto University, Kyoto, Japan. The work is supported in part by JST-CREST program #JP-MJCR15K3 and JSPS-KAKEN #15H03964.

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