Comparative analysis of existing models for power-grid synchronization

Abstract

The dynamics of power-grid networks is becoming an increasingly active area of research within 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. Here we perform a comprehensive comparative analysis of three leading models recently used to study synchronization dynamics in power-grid networks-a fundamental problem of 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 these models can be derived from first principles within a common framework based on the classical model 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 different models. We demonstrate, in particular, that if the network structure is not homogeneous, generators with identical parameters need to be modeled as non-identical oscillators in general. We also discuss an approach to estimate the required (dynamical) parameters that are unavailable in typical power-grid datasets, their use for computing the constants of each of the three models, and an open-source MATLAB toolbox that we provide for these computations (available at https://sourceforge.net/projects/pg-sync-models).

The Kuramoto model in complex networks

“…Various power-grid models could be derived depending on assumptions adopted for the generators equations (343), and the validity and appropriateness of them depend on specific purposes [371]. Taking into account that the electrodynamical behavior yields a third-order model with voltage dynamics (extended from the classical second-order Kuramoto model (292)), where the third characteristic, voltage, is included besides phase and frequency [361].…”

Building blocks of the basin stability of power grids

“…The governing dynamics for the synchronous interaction between power-grid nodes is often described as the second-order Kuramoto-type model [12,[15][16][17][18][19]21]:…”

“…Filatrella et al [11] derived a synchronization model for powergrid nodes as a form of the Kuramoto model. Other papers investigated the relationship between the network topology and synchronization of power grids [12][13][14][15].…”

Synchrony-optimized networks of Kuramoto oscillators with inertia

“…As already mentioned, power grids can be analyzed and studied in great detail, taking into account hundreds of different power plants, substations, transmission lines, and many other devices. On the other hand, the idea used here is to focus on the complexity of the underlying network of connections, as done, for instance, in [9,10,11,12], and its role on the overall synchronization process. The universality of the dynamical behavior of synchronization in complex networks implies that the simplified description of a real power grid by means of a network of Kuramoto oscillators with inertia is more than a formal analogy, and it should be capable of providing a good qualitative description of the synchronization process in large networks.…”