Studying power-grid synchronization with incremental refinement of model heterogeneity

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.