This paper presents a new methodology to detect low-frequency
oscillations in power grids by use of time-synchronized data
from phasor measurement unit (PMU). Principal component analysis
(PCA) is first applied to the massive PMU data to extract the
low-dimensional features, i.e., the principal components (PCs). Then
based on persistent homology, a \emph{cyclicity response function}
is proposed to detect low-frequency oscillations through the use of
PCs. Whenever the cyclicity response exceeds a numerically robust
threshold, a low-frequency oscillation can be detected instantly.
Such swift detection can then be followed by modal analysis tools for more detailed information of oscillation. Numerical examples
using real data illustrate the effectiveness of
the proposed methodology in quick detection of oscillations during operations.