Abstract Data-based assessment of dynamic performances has attracted a lot of interest in the modern power system with high-accurate measurement technologies such as Synchrophasor. In this paper, we report the research effort to do this for voltage dynamics in a rudimentary model of power systems. We propose to combine 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 spectral properties of the Koopman operator through voltage measurement of a single bus. The spectral properties clarify local information on the voltage dynamics such as frequency/damping in transient responses and global one such as the flow structure of the underlying mathematical model.