Critical Links and Nonlocal Rerouting in Complex Supply Networks

Witthaut, Dirk; Rohden, Martin; Zhang, Xiaozhu; Hallerberg, Sarah; Timme, Marc

doi:10.1103/physrevlett.116.138701

Cited by 84 publications

(82 citation statements)

References 53 publications

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“…Remarkably, we also find a novel, previously unknown asymptotic state in the system that can only be accessed by perturbations at a particular topological class of nodes. The findings complement and extend previous results on the relationship between topological motifs and stability within power grids [31][32][33], and demonstrate the power of sampling based methods for studying the properties of dynamical systems on networks.…”

Section: Introductionsupporting

confidence: 85%

Deciphering the imprint of topology on nonlinear dynamical network stability

et al. 2017

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Coupled oscillator networks show complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures of the transient behaviour of the system, its survivability, as well as its asymptotic behaviour, its basin stability. By combining basin stability and survivability we uncover novel, previously unknown asymptotic states with solitary, desynchronized oscillators which are rotating with a frequency different from their natural one. They occur almost exclusively after perturbations at nodes with specific topological properties. More generally we confirm and significantly refine the results on the distinguished role tree-shaped appendices play for nonlinear stability. We find a topological classification scheme for nodes located in such appendices, that exactly separates them according to their stability properties, thus establishing a strong link between topology and dynamics. Hence, the results can be used for the identification of vulnerable nodes in power grids or other coupled oscillator networks. From this classification we can derive general design principles for resilient power grids. We find that striving for homogeneous network topologies facilitates a better performance in terms of nonlinear dynamical network stability. While the employed second-order Kuramoto-like model is parametrised to be representative for power grids, we expect these insights to transfer to other critical infrastructure systems or complex network dynamics appearing in various other fields.This state corresponds to the desirable synchronous operating mode of the power grid. However, depending on the parameter choices, there might be also undesirable non-synchronous states which correspond to attracting limit cycles within the phase space of the dynamical system. New J. Phys. 19 (2017) 033029 J Nitzbon et al

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Section: Introductionsupporting

confidence: 85%

Deciphering the imprint of topology on nonlinear dynamical network stability

et al. 2017

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“…Although a local perturbation has a limited impact on the connectivity of the network, it may trigger a cascade of failures and protective responses that switch off grid components and may also lead generators to lose synchrony. Much of our current understanding about this process has been derived from quasi-steady-state cascade models [16][17][18][19][20][21], which use iterative procedures to model the successive inactivation of network components caused by power flow redistributions, while omitting the transient dynamics between steady states as well as the dynamics of the generators. Further understanding has resulted from stability studies focused on the synchronization dynamics of power generators in the absence of flow redistributions [22][23][24][25][26].…”

mentioning

confidence: 99%

Cascading Failures as Continuous Phase-Space Transitions

Yang¹,

Motter²

2017

Phys. Rev. Lett.

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In network systems, a local perturbation can amplify as it propagates, potentially leading to a largescale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators, and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in closed form using a global Hamiltonian-like function. From this function we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steadystate cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.Cascading processes underlie a myriad of network phenomena [1], including blackouts in power systems [2,3], secondary extinctions in ecosystems [4,5], and complex contagion in financial networks [6,7]. In all such cases, an otherwise small perturbation may propagate and eventually cause a sizable portion of the system to fail. Various system-independent cascade models have been proposed [8][9][10][11][12][13] and used to draw general conclusions, such as on the impact of interdependencies [14] and countermeasures [15]. There are outstanding questions, however, for which it is necessary to model the cascade dynamics starting from the actual dynamical state of the system.In power-grid networks, the state of the system is determined by the power flow over transmission lines and the frequency of the power generators, which must be respectively below capacity and synchronized under normal steady-state conditions. Although a local perturbation has a limited impact on the connectivity of the network, it may trigger a cascade of failures and protective responses that switch off grid components and may also lead generators to lose synchrony. Much of our current understanding about this process has been derived from quasi-steady-state cascade models [16][17][18][19][20][21], which use iterative procedures to model the successive inactivation of network components caused by power flow redistributions, while omitting the transient dynamics between steady states as well as the dynamics of the generators. Further understanding has resulted from stability studies focused on the synchronization dynamics of power generators in the absence of flow redistributions [22][23][24][25][26].Yet, to date no theoretical approach has been developed to incorporate at the same time these two fundamental aspects of power-grid dynamics-frequency change and flow ...

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“…Here, [ ] B k is the Laplacian of the network after removal of link k and ( ) F k 0 is the pre-outage flow on link k. This equation was studied in the past in different settings [35,22,36,33]. The failure of single links is thus comparably well understood [22,37,38], whereas the simultaneous failure of multiple links was not yet studied to the same extend on a theoretical level.…”

Section: Single and Double Link Failuresmentioning

confidence: 99%

Collective effects of link failures in linear flow networks

2020

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The reliable operation of supply networks is crucial for the proper functioning of many systems, ranging from biological organisms such as the human blood transport system or plant leaves to manmade systems such as power grids or gas pipelines. Whereas the failure of single transportation links has been analysed thoroughly, the understanding of multiple failures is becoming increasingly important to prevent large scale damages. In this publication, we examine the collective nature of the simultaneous failure of several transportation links. In particular, we focus on the difference between single link failures and the collective failure of several links. We demonstrate that collective effects can amplify or attenuate the impacts of multiple link failures-and even lead to a reversal of flows on certain links. A simple classifier is introduced to predict the overall strength of collective effects that we demonstrate to be generally stronger if the failing links are close to each other. Finally, we establish an analogy between link failures in supply networks and dipole fields in discrete electrostatics by showing that multiple failures may be treated as superpositions of multiple electrical dipoles for lattice-like networks. Our results show that the simultaneous failure of multiple links may lead to unexpected effects that cannot be easily described using the theoretical framework for single link failures.

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Critical Links and Nonlocal Rerouting in Complex Supply Networks

Cited by 84 publications

References 53 publications

Deciphering the imprint of topology on nonlinear dynamical network stability

Deciphering the imprint of topology on nonlinear dynamical network stability

Cascading Failures as Continuous Phase-Space Transitions

Collective effects of link failures in linear flow networks

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