Spontaneous synchrony in power-grid networks

Abstract

An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. Here we derive a condition under which the desired synchronous state of a power grid is stable, and use this condition to identify tunable parameters of the generators that are determinants of spontaneous synchronization. Our analysis gives rise to an approach to specify parameter assignments that can enhance synchronization of any given network, which we demonstrate for a selection of both test systems and real power grids. Because our results concern spontaneous synchronization, they are relevant both for reducing dependence on conventional control devices, thus offering an additional layer of protection given that most power outages involve equipment or operational errors, and for contributing to the development of "smart grids" that can recover from failures in real time.

Cluster synchronization and isolated desynchronization in complex networks with symmetries

“…18 for more explanation. Generalizations of equation (1) have been studied in refs 5,9,10,19. The types of natural and man-made systems, which can be modelled by equations of the same form as equation (1), are large 20,21 .…”

“…S ynchronization in complex networks is essential to the proper functioning of a wide variety of natural and engineered systems, ranging from electric power grids to neural networks 1 . Global synchronization, in which all nodes evolve in unison, is a well-studied effect, the conditions for which are often related to the network structure through the master stability function 2 .…”

Synchronization in complex networks of phase oscillators: A survey

“…Notice that, with the exception of the inertial terms M iθi and the possibly non-unit coefficients D i , the power network dynamics (8)-(10) are a perfect electrical analog of the coupled oscillator model (1) with ω i ∈ {−P l,i , P m,i , P d,i }. Thus, it is not surprising that scientists from different disciplines recently advocated coupled oscillator approaches to analyze synchronization in power networks (Tanaka et al, 1997;Subbarao et al, 2001;Hill and Chen, 2006;Filatrella et al, 2008;Buzna et al, 2009;Fioriti et al, 2009;Simpson-Porco et al, 2013;Dörfler and Bullo, 2012b;Rohden et al, 2012;Dörfler et al, 2013;Mangesius et al, 2012;Motter et al, 2013;Ainsworth and Grijalva, 2013). The theoretical tools presented in this article establish how frequency synchronization in power networks depend on the nodal parameters (P l,i , P m,i , P d,i ) as well as the interconnecting electrical network with weights a ij .…”

“…The analysis of synchronization problems in general periodic and heterogeneous state space oscillator networks remains a challenging and important problem. Additionally, synchronization phenomena can also occur among chaotic and aperiodic oscillators (Pecora and Carroll, 1990), whose analysis is thus far mainly restricted to numerical linearization via the Master Stability Function approach (Pecora and Carroll, 1998;Boccaletti et al, 2006;Arenas et al, 2008;Motter et al, 2013). It is yet unclear which analysis methods carry over from phase oscillator networks to state space or chaotic oscillator networks.…”

“…Various conditions have been proposed to quantify this trade-off for sparse graphs, both in theoretical studies as well as in power network applications. The coupling is typically quantified by the algebraic connectivity λ 2 (L) (Wu and Kumagai, 1980;Pecora and Carroll, 1998;Nishikawa et al, 2003;Jadbabaie et al, 2004;Restrepo et al, 2005;Boccaletti et al, 2006;Arenas et al, 2008;Dörfler and Bullo, 2012b;Motter et al, 2013), the weighted nodal degree deg i = n j=1 a ij (Wu and Kumagai, 1982;Korniss et al, 2006;Gómez-Gardeñes et al, 2007;Buzna et al, 2009;Bullo, 2012b, 2013a;Skardal et al, 2013), or various metrics related to the notion of effective resistance (Wu and Kumagai, 1982;Korniss et al, 2006;Dörfler and Bullo, 2013a). The frequency dissimilarity is quantified either by absolute norms ω p or by incremental norms 11 B T ω p , for p ∈ N. Here, we specifically consider the three incremental norms:…”