Comparative analysis of existing models for power-grid synchronization

The dynamics of power-grid networks is becoming an increasingly active area of researchwithin the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on simplifying assumptions that can be either difficult to assess or not fully justified for realistic applications. Herewe perform a comprehensive comparative analysis of three leadingmodels recently used to study synchronization dynamics in power-grid networks—a fundamental problemof practical significance given that frequency synchronization of all power generators in the same interconnection is a necessary condition for a power grid to operate.We show that each of thesemodels can be derived fromfirst principles within a common framework based on the classicalmodel of a generator, thereby clarifying all assumptions involved. This framework allows us to view power grids as complex networks of coupled second-order phase oscillators with both forcing and damping terms. Using simple illustrative examples, test systems, and real power-grid datasets, we study the inherent frequencies of the oscillators as well as their coupling structure, comparing across the differentmodels.We demonstrate, in particular, that if the network structure is not homogeneous, generators with identical parameters need to bemodeled as non-identical oscillators in general.We also discuss an approach to estimate the required (dynamical) systemparameters that are unavailable in typical power-grid datasets, their use for computing the constants of each of the threemodels, and an open-sourceMATLAB toolbox that we provide for these computations.