The dynamics of electric power systems are widely studied through the phase synchronization
of oscillators, typically with the use of the Kuramoto equation. While there are numerous
well-known order parameters to characterize these dynamics, shortcoming of these metrics
are also recognized. To capture all transitions from phase disordered states over
phase locking to fully synchronized systems, new metrics were proposed and demonstrated
on homogeneous models. In this paper, we aim to address a gap in the literature, namely,
to examine how the gradual improvement of power grid models affects the goodness of
certain metrics. To study how the details of models are perceived by the different
metrics, 12 variations of a power grid model were created, introducing varying levels
of heterogeneity through the coupling strength, the nodal powers, and the moment of
inertia. The grid models were compared using a second-order Kuramoto equation and
adaptive Runge–Kutta solver, measuring the values of the phase, the frequency, and
the universal order parameters. Finally, frequency results of the models were compared
to grid measurements. We found that the universal order parameter was able to capture
more details of the grid models, especially in cases of decreasing moment of inertia.
Even the most heterogeneous models showed notable synchronization, encouraging the
use of such models. Finally, we show local frequency results related to the multi-peaks
of static models, which implies that spatial heterogeneity can also induce such multi-peak
behavior.
