Cascading Failures as Continuous Phase-Space Transitions

Yang, Yang; Motter, Adilson E.

doi:10.1103/PhysRevLett.119.248302

Title: Cascading Failures as Continuous Phase-Space Transitions

Abstract

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

Authors:

Yang, Yang ^[1]; Motter, Adilson E. ^[2]

Northwestern Univ., Evanston, IL (United States). Dept. of Physics and Astronomy
Northwestern Univ., Evanston, IL (United States). Dept. of Physics and Astronomy, Northwestern Inst. on Complex Systems

Publication Date:: Thu Dec 14 00:00:00 EST 2017

Research Org.:: Northwestern Univ., Evanston, IL (United States)

Sponsoring Org.:: USDOE Advanced Research Projects Agency - Energy (ARPA-E)

OSTI Identifier:: 1414576

Alternate Identifier(s):: OSTI ID: 1413368

Grant/Contract Number:: AR0000702

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 119; Journal Issue: 24; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Yang, Yang, and Motter, Adilson E. Cascading Failures as Continuous Phase-Space Transitions.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevLett.119.248302.

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                    Yang, Yang, & Motter, Adilson E. Cascading Failures as Continuous Phase-Space Transitions.  United States.  https://doi.org/10.1103/PhysRevLett.119.248302

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                    Yang, Yang, and Motter, Adilson E. Thu .  
"Cascading Failures as Continuous Phase-Space Transitions".  United States.  https://doi.org/10.1103/PhysRevLett.119.248302.  https://www.osti.gov/servlets/purl/1414576.

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@article{osti_1414576,

  title        = {Cascading Failures as Continuous Phase-Space Transitions},

  author       = {Yang, Yang and Motter, Adilson E.},

  abstractNote = {In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. 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.},

  doi          = {10.1103/PhysRevLett.119.248302},

  journal      = {Physical Review Letters},

  number       = 24,

  volume       = 119,

  place        = {United States},

  year         = {Thu Dec 14 00:00:00 EST 2017},

  month        = {Thu Dec 14 00:00:00 EST 2017}

}

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Works referenced in this record:

Catastrophic cascade of failures in interdependent networks
journal, April 2010

Buldyrev, Sergey V.; Parshani, Roni; Paul, Gerald
Nature, Vol. 464, Issue 7291
DOI: 10.1038/nature08932

Coherent Swing Instability of Power Grids
journal, February 2011

Susuki, Yoshihiko; Mezić, Igor; Hikihara, Takashi
Journal of Nonlinear Science, Vol. 21, Issue 3
DOI: 10.1007/s00332-010-9087-5

The unfolding and control of network cascades
journal, January 2017

Motter, Adilson E.; Yang, Yang
Physics Today, Vol. 70, Issue 1
DOI: 10.1063/PT.3.3426

Cascade Control and Defense in Complex Networks
journal, August 2004

Motter, Adilson E.
Physical Review Letters, Vol. 93, Issue 9
DOI: 10.1103/PhysRevLett.93.098701

Cascade-based attacks on complex networks
journal, December 2002

Motter, Adilson E.; Lai, Ying-Cheng
Physical Review E, Vol. 66, Issue 6
DOI: 10.1103/PhysRevE.66.065102

Cascading extinctions and community collapse in model food webs
journal, June 2009

Dunne, Jennifer A.; Williams, Richard J.
Philosophical Transactions of the Royal Society B: Biological Sciences, Vol. 364, Issue 1524
DOI: 10.1098/rstb.2008.0219

Synchronization in complex oscillator networks and smart grids
journal, January 2013

Dorfler, F.; Chertkov, M.; Bullo, F.
Proceedings of the National Academy of Sciences, Vol. 110, Issue 6
DOI: 10.1073/pnas.1212134110

Critical Links and Nonlocal Rerouting in Complex Supply Networks
journal, March 2016

Witthaut, Dirk; Rohden, Martin; Zhang, Xiaozhu
Physical Review Letters, Vol. 116, Issue 13
DOI: 10.1103/PhysRevLett.116.138701

How dead ends undermine power grid stability
journal, June 2014

Menck, Peter J.; Heitzig, Jobst; Kurths, Jürgen
Nature Communications, Vol. 5, Issue 1
DOI: 10.1038/ncomms4969

A Structure Preserving Model for Power System Stability Analysis
journal, January 1981

Bergen, A. R.; Hill, D. J.
IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, Issue 1
DOI: 10.1109/TPAS.1981.316883

Self-Organized Synchronization in Decentralized Power Grids
journal, August 2012

Rohden, Martin; Sorge, Andreas; Timme, Marc
Physical Review Letters, Vol. 109, Issue 6
DOI: 10.1103/PhysRevLett.109.064101

Sandpile on Scale-Free Networks
journal, October 2003

Goh, K. -I.; Lee, D. -S.; Kahng, B.
Physical Review Letters, Vol. 91, Issue 14
DOI: 10.1103/PhysRevLett.91.148701

Financial Networks and Contagion
journal, October 2014

Elliott, Matthew; Golub, Benjamin; Jackson, Matthew O.
American Economic Review, Vol. 104, Issue 10
DOI: 10.1257/aer.104.10.3115

Transient Dynamics Increasing Network Vulnerability to Cascading Failures
journal, May 2008

Simonsen, Ingve; Buzna, Lubos; Peters, Karsten
Physical Review Letters, Vol. 100, Issue 21
DOI: 10.1103/PhysRevLett.100.218701

Coupled catastrophes: sudden shifts cascade and hop among interdependent systems
journal, November 2015

Brummitt, Charles D.; Barnett, George; D'Souza, Raissa M.
Journal of The Royal Society Interface, Vol. 12, Issue 112
DOI: 10.1098/rsif.2015.0712

Realistic control of network dynamics
journal, June 2013

Cornelius, Sean P.; Kath, William L.; Motter, Adilson E.
Nature Communications, Vol. 4, Issue 1
DOI: 10.1038/ncomms2939

Contagion in financial networks
journal, March 2010

Gai, Prasanna; Kapadia, Sujit
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 466, Issue 2120
DOI: 10.1098/rspa.2009.0410

Spontaneous synchrony in power-grid networks
journal, February 2013

Motter, Adilson E.; Myers, Seth A.; Anghel, Marian
Nature Physics, Vol. 9, Issue 3
DOI: 10.1038/nphys2535

Model for cascading failures in complex networks
journal, April 2004

Crucitti, Paolo; Latora, Vito; Marchiori, Massimo
Physical Review E, Vol. 69, Issue 4
DOI: 10.1103/PhysRevE.69.045104

An Open Source Power System Analysis Toolbox
journal, August 2005

Milano, F.
IEEE Transactions on Power Systems, Vol. 20, Issue 3
DOI: 10.1109/TPWRS.2005.851911

MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education
journal, February 2011

Zimmerman, Ray Daniel; Murillo-Sanchez, Carlos Edmundo; Thomas, Robert John
IEEE Transactions on Power Systems, Vol. 26, Issue 1
DOI: 10.1109/TPWRS.2010.2051168

Rescuing ecosystems from extinction cascades through compensatory perturbations
journal, January 2011

Sahasrabudhe, Sagar; Motter, Adilson E.
Nature Communications, Vol. 2, Issue 1
DOI: 10.1038/ncomms1163

A simple model of global cascades on random networks
journal, April 2002

Watts, D. J.
Proceedings of the National Academy of Sciences, Vol. 99, Issue 9
DOI: 10.1073/pnas.082090499

Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization
journal, June 2007

Dobson, Ian; Carreras, Benjamin A.; Lynch, Vickie E.
Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 17, Issue 2, Article No. 026103
DOI: 10.1063/1.2737822

Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows
journal, September 2017

Moussawi, A.; Derzsy, N.; Lin, X.
Scientific Reports, Vol. 7, Issue 1
DOI: 10.1038/s41598-017-11765-1

Suppressing cascades of load in interdependent networks
journal, February 2012

Brummitt, C. D.; D'Souza, R. M.; Leicht, E. A.
Proceedings of the National Academy of Sciences, Vol. 109, Issue 12
DOI: 10.1073/pnas.1110586109

Comparative analysis of existing models for power-grid synchronization
journal, January 2015

Nishikawa, Takashi; Motter, Adilson E.
New Journal of Physics, Vol. 17, Issue 1
DOI: 10.1088/1367-2630/17/1/015012

Financial Networks and Contagion
journal, January 2012

Elliott, Matthew; Golub, Benjamin; Jackson, Matthew O.
SSRN Electronic Journal
DOI: 10.2139/ssrn.2175056

An open source power system analysis toolbox
conference, January 2006

Milano, F.
2006 IEEE Power Engineering Society General Meeting
DOI: 10.1109/pes.2006.1708946

Contagion in Financial Networks
journal, January 2007

Gai, Prasanna; Kapadia, Sujit
SSRN Electronic Journal
DOI: 10.2139/ssrn.967255

Contagion in Financial Networks
journal, September 2016

Glasserman, Paul; Young, H. Peyton
Journal of Economic Literature, Vol. 54, Issue 3
DOI: 10.1257/jel.20151228

Catastrophic cascade of failures in interdependent networks
text, January 2009

Buldyrev, Sergey V.; Parshani, Roni; Paul, Gerald
arXiv
DOI: 10.48550/arxiv.0907.1182

Suppressing cascades of load in interdependent networks
text, January 2011

Brummitt, Charles D.; D'Souza, Raissa M.; Leicht, E. A.
arXiv
DOI: 10.48550/arxiv.1106.4499

Synchronization in Complex Oscillator Networks and Smart Grids
text, January 2012

Dörfler, Florian; Chertkov, Michael; Bullo, Francesco
arXiv
DOI: 10.48550/arxiv.1208.0045

Spontaneous synchrony in power-grid networks
text, January 2013

Motter, Adilson E.; Myers, Seth A.; Anghel, Marian
arXiv
DOI: 10.48550/arxiv.1302.1914

Realistic Control of Network Dynamics
text, January 2013

Cornelius, Sean P.; Kath, William L.; Motter, Adilson E.
arXiv
DOI: 10.48550/arxiv.1307.0015

The Unfolding and Control of Network Cascades
text, January 2017

Motter, Adilson E.; Yang, Yang
arXiv
DOI: 10.48550/arxiv.1701.00578

Cascade-based attacks on complex networks
text, January 2003

Motter, Adilson E.; Lai, Ying-Cheng
arXiv
DOI: 10.48550/arxiv.cond-mat/0301086

Sandpile on Scale-Free Networks
text, January 2003

Goh, K. -I.; Lee, D. -S.; Kahng, B.
arXiv
DOI: 10.48550/arxiv.cond-mat/0305425

A model for cascading failures in complex networks
text, January 2003

Crucitti, Paolo; Latora, Vito; Marchiori, Massimo
arXiv
DOI: 10.48550/arxiv.cond-mat/0309141

Cascade control and defense in complex networks
text, January 2004

Motter, Adilson E.
arXiv
DOI: 10.48550/arxiv.cond-mat/0401074

Works referencing / citing this record:

Vulnerability analysis of interdependent network via integer programming approaches
journal, November 2019

Hou, Shanshan; Garrido, Andres; Fan, Neng
Optimization Letters, Vol. 14, Issue 7
DOI: 10.1007/s11590-019-01504-y

Dynamically induced cascading failures in power grids
journal, May 2018

Schäfer, Benjamin; Witthaut, Dirk; Timme, Marc
Nature Communications, Vol. 9, Issue 1
DOI: 10.1038/s41467-018-04287-5

Effects of dynamical and structural modifications on synchronization
journal, August 2019

Chen, Lijia; Ji, Peng; Waxman, David
Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 29, Issue 8
DOI: 10.1063/1.5110727

Dynamical modeling of cascading failures in the Turkish power grid
journal, September 2019

Schäfer, Benjamin; Yalcin, G. Cigdem
Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 29, Issue 9
DOI: 10.1063/1.5110974

General methodology for inferring failure-spreading dynamics in networks
journal, August 2018

Guan, Xiangyang; Chen, Cynthia
Proceedings of the National Academy of Sciences, Vol. 115, Issue 35
DOI: 10.1073/pnas.1722313115

Dynamic behavior analysis of an internet flow interaction model under cascading failures
journal, August 2019

Wu, Xiaoyu; Gu, Rentao; Ji, Yuefeng
Physical Review E, Vol. 100, Issue 2
DOI: 10.1103/physreve.100.022309

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Title: Cascading Failures as Continuous Phase-Space Transitions

Abstract

Citation Formats

Catastrophic cascade of failures in interdependent networks journal, April 2010

Coherent Swing Instability of Power Grids journal, February 2011

The unfolding and control of network cascades journal, January 2017

Cascade Control and Defense in Complex Networks journal, August 2004

Cascade-based attacks on complex networks journal, December 2002

Cascading extinctions and community collapse in model food webs journal, June 2009

Synchronization in complex oscillator networks and smart grids journal, January 2013

Critical Links and Nonlocal Rerouting in Complex Supply Networks journal, March 2016

How dead ends undermine power grid stability journal, June 2014

A Structure Preserving Model for Power System Stability Analysis journal, January 1981

Self-Organized Synchronization in Decentralized Power Grids journal, August 2012

Sandpile on Scale-Free Networks journal, October 2003

Financial Networks and Contagion journal, October 2014

Transient Dynamics Increasing Network Vulnerability to Cascading Failures journal, May 2008

Coupled catastrophes: sudden shifts cascade and hop among interdependent systems journal, November 2015

Realistic control of network dynamics journal, June 2013

Contagion in financial networks journal, March 2010

Spontaneous synchrony in power-grid networks journal, February 2013

Model for cascading failures in complex networks journal, April 2004

An Open Source Power System Analysis Toolbox journal, August 2005

MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education journal, February 2011

Rescuing ecosystems from extinction cascades through compensatory perturbations journal, January 2011

A simple model of global cascades on random networks journal, April 2002

Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization journal, June 2007

Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows journal, September 2017

Suppressing cascades of load in interdependent networks journal, February 2012

Comparative analysis of existing models for power-grid synchronization journal, January 2015

Financial Networks and Contagion journal, January 2012

An open source power system analysis toolbox conference, January 2006

Contagion in Financial Networks journal, January 2007

Contagion in Financial Networks journal, September 2016

Catastrophic cascade of failures in interdependent networks text, January 2009

Suppressing cascades of load in interdependent networks text, January 2011

Synchronization in Complex Oscillator Networks and Smart Grids text, January 2012

Spontaneous synchrony in power-grid networks text, January 2013

Realistic Control of Network Dynamics text, January 2013

The Unfolding and Control of Network Cascades text, January 2017

Cascade-based attacks on complex networks text, January 2003

Sandpile on Scale-Free Networks text, January 2003

A model for cascading failures in complex networks text, January 2003

Cascade control and defense in complex networks text, January 2004

Vulnerability analysis of interdependent network via integer programming approaches journal, November 2019

Dynamically induced cascading failures in power grids journal, May 2018

Effects of dynamical and structural modifications on synchronization journal, August 2019

Dynamical modeling of cascading failures in the Turkish power grid journal, September 2019

General methodology for inferring failure-spreading dynamics in networks journal, August 2018

Dynamic behavior analysis of an internet flow interaction model under cascading failures journal, August 2019

Catastrophic cascade of failures in interdependent networks
journal, April 2010

Coherent Swing Instability of Power Grids
journal, February 2011

The unfolding and control of network cascades
journal, January 2017

Cascade Control and Defense in Complex Networks
journal, August 2004

Cascade-based attacks on complex networks
journal, December 2002

Cascading extinctions and community collapse in model food webs
journal, June 2009

Synchronization in complex oscillator networks and smart grids
journal, January 2013

Critical Links and Nonlocal Rerouting in Complex Supply Networks
journal, March 2016

How dead ends undermine power grid stability
journal, June 2014

A Structure Preserving Model for Power System Stability Analysis
journal, January 1981

Self-Organized Synchronization in Decentralized Power Grids
journal, August 2012

Sandpile on Scale-Free Networks
journal, October 2003

Financial Networks and Contagion
journal, October 2014

Transient Dynamics Increasing Network Vulnerability to Cascading Failures
journal, May 2008

Coupled catastrophes: sudden shifts cascade and hop among interdependent systems
journal, November 2015

Realistic control of network dynamics
journal, June 2013

Contagion in financial networks
journal, March 2010

Spontaneous synchrony in power-grid networks
journal, February 2013

Model for cascading failures in complex networks
journal, April 2004

An Open Source Power System Analysis Toolbox
journal, August 2005

MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education
journal, February 2011

Rescuing ecosystems from extinction cascades through compensatory perturbations
journal, January 2011

A simple model of global cascades on random networks
journal, April 2002

Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization
journal, June 2007

Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows
journal, September 2017

Suppressing cascades of load in interdependent networks
journal, February 2012

Comparative analysis of existing models for power-grid synchronization
journal, January 2015

Financial Networks and Contagion
journal, January 2012

An open source power system analysis toolbox
conference, January 2006

Contagion in Financial Networks
journal, January 2007

Contagion in Financial Networks
journal, September 2016

Catastrophic cascade of failures in interdependent networks
text, January 2009

Suppressing cascades of load in interdependent networks
text, January 2011

Synchronization in Complex Oscillator Networks and Smart Grids
text, January 2012

Spontaneous synchrony in power-grid networks
text, January 2013

Realistic Control of Network Dynamics
text, January 2013

The Unfolding and Control of Network Cascades
text, January 2017

Cascade-based attacks on complex networks
text, January 2003

Sandpile on Scale-Free Networks
text, January 2003

A model for cascading failures in complex networks
text, January 2003

Cascade control and defense in complex networks
text, January 2004

Vulnerability analysis of interdependent network via integer programming approaches
journal, November 2019

Dynamically induced cascading failures in power grids
journal, May 2018

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journal, August 2019

Dynamical modeling of cascading failures in the Turkish power grid
journal, September 2019

General methodology for inferring failure-spreading dynamics in networks
journal, August 2018

Dynamic behavior analysis of an internet flow interaction model under cascading failures
journal, August 2019