  Modern power systems are at risk of largely reducing the inertia of
generation assets and prone to experience extreme dynamics. The consequence is
that, during electromechanical transients triggered by large contingencies,
transmission of electrical power may take place in a broad spectrum well beyond
the single fundamental component. Traditional modeling approaches rely on the
phasor representation derived from the Fourier Transform (FT) of the signal
under analysis. During large transients, though, FT-based analysis may fail to
accurately identify the fundamental component parameters, in terms of
amplitude, frequency and phase. In this paper, we propose an alternative
approach relying on the Hilbert Transform (HT), that, in view of the
possibility to identify the whole spectrum, enables the tracking of signal
dynamics. We compare FT- and HT-based approaches during representative
operating conditions, i.e., amplitude modulations, frequency ramps and step
changes, in synthetic and real-world datasets. We further validate the
approaches using a contingency analysis on the IEEE 39-bus.
