Cascading Failures as Continuous Phase-Space Transitions

Yang Yang and Adilson E. Motter
Phys. Rev. Lett. 119, 248302 – Published 14 December 2017
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Abstract

In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale 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 a 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-steady-state 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.

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  • Received 7 September 2016

DOI:https://doi.org/10.1103/PhysRevLett.119.248302

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsStatistical Physics & ThermodynamicsNetworks

Authors & Affiliations

Yang Yang1 and Adilson E. Motter1,2,*

  • 1Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
  • 2Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA

  • *motter@northwestern.edu

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Issue

Vol. 119, Iss. 24 — 15 December 2017

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