Topological vulnerability of power grids to disasters: Bounds, adversarial attacks and reinforcement

Deka, Deepjyoti; Vishwanath, Sriram; Baldick, Ross

doi:10.1371/journal.pone.0204815

Title: Topological vulnerability of power grids to disasters: Bounds, adversarial attacks and reinforcement

Abstract

Natural disasters like hurricanes, floods or earthquakes can damage power grid devices and create cascading blackouts and islands. The nature of failure propagation and extent of damage, among other factors, is dependent on the structural features of the grid, that are distinct from that of random networks. This paper analyzes the structural vulnerability of real power grids to impending disasters and presents intuitive graphical metrics to quantify the extent of topological damage. We develop two improved graph eigen-value based bounds on the grid vulnerability. Further we study adversarial attacks aimed at weakening the grid’s structural robustness and present three combinatorial algorithms to determine the optimal topological attack. Simulations on power grid networks and comparison with existing work show the improvements of the proposed measures and attack schemes.

Authors:

^[1]; Vishwanath, Sriram ^[2]; Baldick, Ross ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Non-Linear Studies
Univ. of Texas, Austin, TX (United States). Dept. of Electrical and Computer Engineering

Publication Date:: Fri Oct 12 00:00:00 EDT 2018

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1627868

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: PLoS ONE

Additional Journal Information:: Journal Volume: 13; Journal Issue: 10; Journal ID: ISSN 1932-6203

Publisher:: Public Library of Science

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; 24 POWER TRANSMISSION AND DISTRIBUTION; Science & Technology - Other Topics

Citation Formats


                    Deka, Deepjyoti, Vishwanath, Sriram, and Baldick, Ross. Topological vulnerability of power grids to disasters: Bounds, adversarial attacks and reinforcement.  United States: N. p., 2018. 
Web.  doi:10.1371/journal.pone.0204815.

Copy to clipboard


                    Deka, Deepjyoti, Vishwanath, Sriram, & Baldick, Ross. Topological vulnerability of power grids to disasters: Bounds, adversarial attacks and reinforcement.  United States.  https://doi.org/10.1371/journal.pone.0204815

Copy to clipboard


                    Deka, Deepjyoti, Vishwanath, Sriram, and Baldick, Ross. Fri .  
"Topological vulnerability of power grids to disasters: Bounds, adversarial attacks and reinforcement".  United States.  https://doi.org/10.1371/journal.pone.0204815.  https://www.osti.gov/servlets/purl/1627868.

Copy to clipboard


                    
@article{osti_1627868,

  title        = {Topological vulnerability of power grids to disasters: Bounds, adversarial attacks and reinforcement},

  author       = {Deka, Deepjyoti and Vishwanath, Sriram and Baldick, Ross},

  abstractNote = {Natural disasters like hurricanes, floods or earthquakes can damage power grid devices and create cascading blackouts and islands. The nature of failure propagation and extent of damage, among other factors, is dependent on the structural features of the grid, that are distinct from that of random networks. This paper analyzes the structural vulnerability of real power grids to impending disasters and presents intuitive graphical metrics to quantify the extent of topological damage. We develop two improved graph eigen-value based bounds on the grid vulnerability. Further we study adversarial attacks aimed at weakening the grid’s structural robustness and present three combinatorial algorithms to determine the optimal topological attack. Simulations on power grid networks and comparison with existing work show the improvements of the proposed measures and attack schemes.},

  doi          = {10.1371/journal.pone.0204815},

  journal      = {PLoS ONE},

  number       = 10,

  volume       = 13,

  place        = {United States},

  year         = {Fri Oct 12 00:00:00 EDT 2018},

  month        = {Fri Oct 12 00:00:00 EDT 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1371/journal.pone.0204815

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

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

Empirically validated availability model of information and communication technologies facilities under hurricane conditions
conference, September 2014

Krishnamurthy, Vaidyanathan; Kwasinski, Alexis
2014 IEEE 36th International Telecommunications Energy Conference (INTELEC)
DOI: 10.1109/INTLEC.2014.6972189

Error and attack tolerance of complex networks
journal, July 2000

Albert, Réka; Jeong, Hawoong; Barabási, Albert-László
Nature, Vol. 406, Issue 6794
DOI: 10.1038/35019019

An initial model fo complex dynamics in electric power system blackouts
conference, January 2001

Dobson, I.; Carreras, B. A.; Lynch, V. E.
Hawaii International Conference on System Sciences. HICSS-34, Proceedings of the 34th Annual Hawaii International Conference on System Sciences
DOI: 10.1109/HICSS.2001.926274

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

Cascade-based attack vulnerability on the US power grid
journal, December 2009

Wang, Jian-Wei; Rong, Li-Li
Safety Science, Vol. 47, Issue 10
DOI: 10.1016/j.ssci.2009.02.002

Generating Statistically Correct Random Topologies for Testing Smart Grid Communication and Control Networks
journal, June 2010

Zhifang Wang, ; Scaglione, Anna; Thomas, Robert J.
IEEE Transactions on Smart Grid, Vol. 1, Issue 1
DOI: 10.1109/TSG.2010.2044814

An Interaction Model for Simulation and Mitigation of Cascading Failures
journal, March 2015

Qi, Junjian; Sun, Kai; Mei, Shengwei
IEEE Transactions on Power Systems, Vol. 30, Issue 2
DOI: 10.1109/TPWRS.2014.2337284

Zero Duality Gap in Optimal Power Flow Problem
journal, February 2012

Lavaei, Javad; Low, Steven H.
IEEE Transactions on Power Systems, Vol. 27, Issue 1
DOI: 10.1109/TPWRS.2011.2160974

Reduced synchronizability of dynamical scale-free networks with onion-like topologies
journal, February 2015

Sun, Shiwen; Li, Ruiqi; Wang, Li
Applied Mathematics and Computation, Vol. 252
DOI: 10.1016/j.amc.2014.12.044

Effective vaccination strategies for realistic social networks
journal, December 2007

Miller, Joel C.; Hyman, James M.
Physica A: Statistical Mechanics and its Applications, Vol. 386, Issue 2
DOI: 10.1016/j.physa.2007.08.054

Towards structural controllability of local-world networks
journal, May 2016

Sun, Shiwen; Ma, Yilin; Wu, Yafang
Physics Letters A, Vol. 380, Issue 22-23
DOI: 10.1016/j.physleta.2016.03.048

Uncertainty Sets for Wind Power Generation
journal, July 2016

Dvorkin, Yury; Lubin, Miles; Backhaus, Scott
IEEE Transactions on Power Systems, Vol. 31, Issue 4
DOI: 10.1109/TPWRS.2015.2476664

Optimal topology design for disturbance minimization in power grids
conference, May 2017

Deka, Deepjyoti; Nagarajan, Harsha; Backhaus, Scott
2017 American Control Conference (ACC)
DOI: 10.23919/ACC.2017.7963363

Robustness of the western United States power grid under edge attack strategies due to cascading failures
journal, July 2011

Wang, Jian-Wei; Rong, Li-Li
Safety Science, Vol. 49, Issue 6
DOI: 10.1016/j.ssci.2010.10.003

Telecommunications Power Plant Damage Assessment for Hurricane Katrina– Site Survey and Follow-Up Results
journal, September 2009

Kwasinski, A.; Weaver, W. W.; Chapman, P. L.
IEEE Systems Journal, Vol. 3, Issue 3
DOI: 10.1109/JSYST.2009.2026783

Robustness of complex networks with the local protection strategy against cascading failures
journal, March 2013

Wang, Jianwei
Safety Science, Vol. 53
DOI: 10.1016/j.ssci.2012.09.011

A Practical Method for the Direct Analysis of Transient Stability
journal, March 1979

Athay, T.; Podmore, R.; Virmani, S.
IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, Issue 2
DOI: 10.1109/TPAS.1979.319407

Generative Growth Model for Power Grids
conference, December 2013

Deka, Deepjyoti; Vishwanath, Sriram
2013 International Conference on Signal-Image Technology & Internet-Based Systems (SITIS)
DOI: 10.1109/SITIS.2013.97

Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures, and Robustness
journal, September 2012

Yagan, Osman; Qian, Dajun; Zhang, Junshan
IEEE Transactions on Parallel and Distributed Systems, Vol. 23, Issue 9
DOI: 10.1109/TPDS.2012.62

Interdependent Networks: Reducing the Coupling Strength Leads to a Change from a First to Second Order Percolation Transition
journal, July 2010

Parshani, Roni; Buldyrev, Sergey V.; Havlin, Shlomo
Physical Review Letters, Vol. 105, Issue 4
DOI: 10.1103/PhysRevLett.105.048701

Power grid vulnerability to geographically correlated failures — Analysis and control implications
conference, April 2014

Bernstein, Andrey; Bienstock, Daniel; Hay, David
IEEE INFOCOM 2014 - IEEE Conference on Computer Communications
DOI: 10.1109/INFOCOM.2014.6848211

Research on Resilience of Power Systems Under Natural Disasters—A Review
journal, March 2016

Wang, Yezhou; Chen, Chen; Wang, Jianhui
IEEE Transactions on Power Systems, Vol. 31, Issue 2
DOI: 10.1109/TPWRS.2015.2429656

Comparing the Topological and Electrical Structure of the North American Electric Power Infrastructure
journal, December 2012

Cotilla-Sanchez, Eduardo; Hines, Paul D. H.; Barrows, Clayton
IEEE Systems Journal, Vol. 6, Issue 4
DOI: 10.1109/JSYST.2012.2183033

Do topological models provide good information about electricity infrastructure vulnerability?
journal, September 2010

Hines, Paul; Cotilla-Sanchez, Eduardo; Blumsack, Seth
Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 20, Issue 3
DOI: 10.1063/1.3489887

Mitigation of malicious attacks on networks
journal, February 2011

Schneider, C. M.; Moreira, A. A.; Andrade, J. S.
Proceedings of the National Academy of Sciences, Vol. 108, Issue 10
DOI: 10.1073/pnas.1009440108

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

Approximate Model of European Interconnected System as a Benchmark System to Study Effects of Cross-Border Trades
journal, May 2005

Zhou, Q.; Bialek, J. W.
IEEE Transactions on Power Systems, Vol. 20, Issue 2
DOI: 10.1109/TPWRS.2005.846178

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments
journal, January 2010

Bienstock, Daniel; Verma, Abhinav
SIAM Journal on Optimization, Vol. 20, Issue 5
DOI: 10.1137/08073562X

Cascading Link Failure in the Power Grid: A Percolation-Based Analysis
conference, June 2011

Xiao, Hongda; Yeh, Edmund M.
2011 ICC - 2011 IEEE International Conference on Communication Workshop (ICC), 2011 IEEE International Conference on Communications Workshops (ICC)
DOI: 10.1109/iccw.2011.5963573

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

Resilience to Degree-Dependent and Cascading Node Failures in Random Geometric Networks
journal, November 2010

Kong, Zhenning; Yeh, Edmund M.
IEEE Transactions on Information Theory, Vol. 56, Issue 11
DOI: 10.1109/TIT.2010.2068910

Uncertainty sets for wind power generation
conference, July 2016

Dvorkin, Yury; Lubin, Miles; Backhaus, Scott
2016 IEEE Power and Energy Society General Meeting (PESGM)
DOI: 10.1109/pesgm.2016.7741079

Catastrophic cascade of failures in interdependent networks
text, January 2009

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

Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
text, January 2010

Parshani, Roni; Buldyrev, Sergey V.; Havlin, Shlomo
arXiv
DOI: 10.48550/arxiv.1004.3989

Power Grid Vulnerability to Geographically Correlated Failures - Analysis and Control Implications
preprint, January 2012

Bernstein, Andrey; Bienstock, Daniel; Hay, David
arXiv
DOI: 10.48550/arxiv.1206.1099

Spontaneous synchrony in power-grid networks
text, January 2013

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

Optimal Topology Design for Disturbance Minimization in Power Grids
preprint, January 2017

Deka, Deepjyoti; Nagarajan, Harsha; Backhaus, Scott
arXiv
DOI: 10.48550/arxiv.1703.00558

Cascade-based attacks on complex networks
text, January 2003

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

An analysis of approximations for maximizing submodular set functions—I
journal, December 1978

Nemhauser, G. L.; Wolsey, L. A.; Fisher, M. L.
Mathematical Programming, Vol. 14, Issue 1
DOI: 10.1007/bf01588971

System-Wide Pollution of Biomedical Data: Consequence of the Search for Hub Genes of Hepatocellular Carcinoma Without Spatiotemporal Consideration
journal, January 2021

Sharma, Ankush; Colonna, Giovanni
Molecular Diagnosis & Therapy, Vol. 25, Issue 1
DOI: 10.1007/s40291-020-00505-3

Effective vaccination strategies for realistic social networks
journal, December 2007

Miller, Joel C.; Hyman, James M.
Physica A: Statistical Mechanics and its Applications, Vol. 386, Issue 2
DOI: 10.1016/j.physa.2007.08.054

Towards structural controllability of local-world networks
journal, May 2016

Sun, Shiwen; Ma, Yilin; Wu, Yafang
Physics Letters A, Vol. 380, Issue 22-23
DOI: 10.1016/j.physleta.2016.03.048

Cascade-based attack vulnerability on the US power grid
journal, December 2009

Wang, Jian-Wei; Rong, Li-Li
Safety Science, Vol. 47, Issue 10
DOI: 10.1016/j.ssci.2009.02.002

Robustness of complex networks with the local protection strategy against cascading failures
journal, March 2013

Wang, Jianwei
Safety Science, Vol. 53
DOI: 10.1016/j.ssci.2012.09.011

Time to replace the Saffir-Simpson hurricane scale?
journal, January 2006

Kantha, Lakshmi
Eos, Transactions American Geophysical Union, Vol. 87, Issue 1
DOI: 10.1029/2006eo010003

Correction to “Approximate Model of European Interconnected System as a Benchmark System to Study Effects of Cross-Border Trades”
journal, August 2005

Zhou, Q.; Bialek, J. W.
IEEE Transactions on Power Systems, Vol. 20, Issue 3
DOI: 10.1109/tpwrs.2005.854741

Interdiction Analysis of Electric Grids Combining Cascading Outage and Medium-Term Impacts
journal, September 2014

Wang, Yezhou; Baldick, Ross
IEEE Transactions on Power Systems, Vol. 29, Issue 5
DOI: 10.1109/tpwrs.2014.2300695

Short-Term Wind Power Ensemble Prediction Based on Gaussian Processes and Neural Networks
journal, January 2014

Lee, Duehee; Baldick, Ross
IEEE Transactions on Smart Grid, Vol. 5, Issue 1
DOI: 10.1109/tsg.2013.2280649

Catastrophic cascade of failures in interdependent networks
text, January 2009

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

Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures and Robustness
text, January 2012

Yagan, Osman; Qian, Dajun; Zhang, Junshan
arXiv
DOI: 10.48550/arxiv.1201.2698

Spontaneous synchrony in power-grid networks
text, January 2013

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

Similar Records in DOE PAGES and OSTI.GOV collections:

Attack on Grid Event Cause Analysis: An Adversarial Machine Learning Approach

Conference Niazazari, Iman ; Livani, Hanif - 2020 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT)

With the ever-increasing reliance on data for data-driven applications in power grids, such as event cause analysis, the authenticity of data streams has become crucially important. The data can be prone to adversarial stealthy attacks aiming to manipulate the data such that residual-based bad data detectors cannot detect them, and the perception of system operators or event classifiers changes about the actual event. This paper investigates the impact of adversarial attacks on convolutional neural network-based event cause analysis frameworks. We have successfully verified the ability of adversaries to maliciously misclassify events through stealthy data manipulations. The vulnerability assessment is studiedmore »« less
https://doi.org/10.1109/isgt45199.2020.9087649

Full Text Available
An Analysis of Post Attack Impacts and Effects of Learning Parameters on Vulnerability Assessment of Power Grid

Conference Paul, Shuva ; Ni, Zhen ; Ding, Fei

Due to the increasing number of heterogeneous devices connected to electric power grid, the attack surface increases the threat actors. Game theory and machine learning are being used to study the power system failures caused by external manipulation. Most of existing works in the literature focus on one-shot process of attacks and fail to show the dynamic evolution of the defense strategy. In this paper, we focus on an adversarial multistage sequential game between the adversaries of the smart electric power transmission and distribution system. We study the impact of exploration rate and convergence of the attack strategies (sequences ofmore »« less
https://doi.org/10.1109/ISGT45199.2020.9087639
Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid

Journal Article Pinar, A ; Meza, J ; Donde, V ; ... - Siam Journal on Optimization

Identifying small groups of lines, whose removal would cause a severe blackout, is critical for the secure operation of the electric power grid. We show how power grid vulnerability analysis can be studied as a mixed integer nonlinear programming (MINLP) problem. Our analysis reveals a special structure in the formulation that can be exploited to avoid nonlinearity and approximate the original problem as a pure combinatorial problem. The key new observation behind our analysis is the correspondence between the Jacobian matrix (a representation of the feasibility boundary of the equations that describe the flow of power in the network) andmore »« less
Full Text Available
Optimization strategies for the vulnerability analysis of the electric power grid.

Journal Article Meza, Juan C ; Pinar, Ali ; Lesieutre, Bernard ; ... - Proposed for publication in Siam Journal on Optimization.

Identifying small groups of lines, whose removal would cause a severe blackout, is critical for the secure operation of the electric power grid. We show how power grid vulnerability analysis can be studied as a mixed integer nonlinear programming (minlp) problem. Our analysis reveals a special structure in the formulation that can be exploited to avoid nonlinearity and approximate the original problem as a pure combinatorial problem. The key new observation behind our analysis is the correspondence between the Jacobian matrix (a representation of the feasibility boundary of the equations that describe the flow of power in the network) andmore »« less
Grid Utility Asset Vulnerability Assessment (GUAVA) Software Tool

Conference Mahapatra, Kaveri ; Barrett, Emily L. ; Chalishazar, Vishvas H. ; ...

Increasing demand and changes in generation portfolios is pushing power grid to operate towards the limit. However, due to lack of analytical tools for understanding various scales of impact on grid, it is becoming more vulnerable to wide scale power outages and blackouts. A vulnerable grid operating at its limit can be easily disrupted by asset failures caused by devastating hurricanes which has been known to damage transmission and distribution lines along its track. In this direction, researchers have focused on determining these assets by conducting Monte Carlo simulations of hurricanes with uncertainties and collected a large set of simulationmore »« less
https://doi.org/10.1109/PESGM48719.2022.9917241

Similar Records

Title: Topological vulnerability of power grids to disasters: Bounds, adversarial attacks and reinforcement

Abstract

Citation Formats

Catastrophic cascade of failures in interdependent networks journal, April 2010

Empirically validated availability model of information and communication technologies facilities under hurricane conditions conference, September 2014

Error and attack tolerance of complex networks journal, July 2000

An initial model fo complex dynamics in electric power system blackouts conference, January 2001

Cascade-based attacks on complex networks journal, December 2002

Cascade-based attack vulnerability on the US power grid journal, December 2009

Generating Statistically Correct Random Topologies for Testing Smart Grid Communication and Control Networks journal, June 2010

An Interaction Model for Simulation and Mitigation of Cascading Failures journal, March 2015

Zero Duality Gap in Optimal Power Flow Problem journal, February 2012

Reduced synchronizability of dynamical scale-free networks with onion-like topologies journal, February 2015

Effective vaccination strategies for realistic social networks journal, December 2007

Towards structural controllability of local-world networks journal, May 2016

Uncertainty Sets for Wind Power Generation journal, July 2016

Optimal topology design for disturbance minimization in power grids conference, May 2017

Robustness of the western United States power grid under edge attack strategies due to cascading failures journal, July 2011

Telecommunications Power Plant Damage Assessment for Hurricane Katrina– Site Survey and Follow-Up Results journal, September 2009

Robustness of complex networks with the local protection strategy against cascading failures journal, March 2013

A Practical Method for the Direct Analysis of Transient Stability journal, March 1979

Generative Growth Model for Power Grids conference, December 2013

Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures, and Robustness journal, September 2012

Interdependent Networks: Reducing the Coupling Strength Leads to a Change from a First to Second Order Percolation Transition journal, July 2010

Power grid vulnerability to geographically correlated failures — Analysis and control implications conference, April 2014

Research on Resilience of Power Systems Under Natural Disasters—A Review journal, March 2016

Comparing the Topological and Electrical Structure of the North American Electric Power Infrastructure journal, December 2012

Do topological models provide good information about electricity infrastructure vulnerability? journal, September 2010

Mitigation of malicious attacks on networks journal, February 2011

Spontaneous synchrony in power-grid networks journal, February 2013

Approximate Model of European Interconnected System as a Benchmark System to Study Effects of Cross-Border Trades journal, May 2005

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments journal, January 2010

Cascading Link Failure in the Power Grid: A Percolation-Based Analysis conference, June 2011

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

Resilience to Degree-Dependent and Cascading Node Failures in Random Geometric Networks journal, November 2010

Uncertainty sets for wind power generation conference, July 2016

Catastrophic cascade of failures in interdependent networks text, January 2009

Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition text, January 2010

Power Grid Vulnerability to Geographically Correlated Failures - Analysis and Control Implications preprint, January 2012

Spontaneous synchrony in power-grid networks text, January 2013

Optimal Topology Design for Disturbance Minimization in Power Grids preprint, January 2017

Cascade-based attacks on complex networks text, January 2003

An analysis of approximations for maximizing submodular set functions—I journal, December 1978

System-Wide Pollution of Biomedical Data: Consequence of the Search for Hub Genes of Hepatocellular Carcinoma Without Spatiotemporal Consideration journal, January 2021

Effective vaccination strategies for realistic social networks journal, December 2007

Towards structural controllability of local-world networks journal, May 2016

Cascade-based attack vulnerability on the US power grid journal, December 2009

Robustness of complex networks with the local protection strategy against cascading failures journal, March 2013

Time to replace the Saffir-Simpson hurricane scale? journal, January 2006

Correction to “Approximate Model of European Interconnected System as a Benchmark System to Study Effects of Cross-Border Trades” journal, August 2005

Interdiction Analysis of Electric Grids Combining Cascading Outage and Medium-Term Impacts journal, September 2014

Short-Term Wind Power Ensemble Prediction Based on Gaussian Processes and Neural Networks journal, January 2014

Catastrophic cascade of failures in interdependent networks text, January 2009

Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures and Robustness text, January 2012

Spontaneous synchrony in power-grid networks text, January 2013

Catastrophic cascade of failures in interdependent networks
journal, April 2010

Empirically validated availability model of information and communication technologies facilities under hurricane conditions
conference, September 2014

Error and attack tolerance of complex networks
journal, July 2000

An initial model fo complex dynamics in electric power system blackouts
conference, January 2001

Cascade-based attacks on complex networks
journal, December 2002

Cascade-based attack vulnerability on the US power grid
journal, December 2009

Generating Statistically Correct Random Topologies for Testing Smart Grid Communication and Control Networks
journal, June 2010

An Interaction Model for Simulation and Mitigation of Cascading Failures
journal, March 2015

Zero Duality Gap in Optimal Power Flow Problem
journal, February 2012

Reduced synchronizability of dynamical scale-free networks with onion-like topologies
journal, February 2015

Effective vaccination strategies for realistic social networks
journal, December 2007

Towards structural controllability of local-world networks
journal, May 2016

Uncertainty Sets for Wind Power Generation
journal, July 2016

Optimal topology design for disturbance minimization in power grids
conference, May 2017

Robustness of the western United States power grid under edge attack strategies due to cascading failures
journal, July 2011

Telecommunications Power Plant Damage Assessment for Hurricane Katrina– Site Survey and Follow-Up Results
journal, September 2009

Robustness of complex networks with the local protection strategy against cascading failures
journal, March 2013

A Practical Method for the Direct Analysis of Transient Stability
journal, March 1979

Generative Growth Model for Power Grids
conference, December 2013

Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures, and Robustness
journal, September 2012

Interdependent Networks: Reducing the Coupling Strength Leads to a Change from a First to Second Order Percolation Transition
journal, July 2010

Power grid vulnerability to geographically correlated failures — Analysis and control implications
conference, April 2014

Research on Resilience of Power Systems Under Natural Disasters—A Review
journal, March 2016

Comparing the Topological and Electrical Structure of the North American Electric Power Infrastructure
journal, December 2012

Do topological models provide good information about electricity infrastructure vulnerability?
journal, September 2010

Mitigation of malicious attacks on networks
journal, February 2011

Spontaneous synchrony in power-grid networks
journal, February 2013

Approximate Model of European Interconnected System as a Benchmark System to Study Effects of Cross-Border Trades
journal, May 2005

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments
journal, January 2010

Cascading Link Failure in the Power Grid: A Percolation-Based Analysis
conference, June 2011

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

Resilience to Degree-Dependent and Cascading Node Failures in Random Geometric Networks
journal, November 2010

Uncertainty sets for wind power generation
conference, July 2016

Catastrophic cascade of failures in interdependent networks
text, January 2009

Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
text, January 2010

Power Grid Vulnerability to Geographically Correlated Failures - Analysis and Control Implications
preprint, January 2012

Spontaneous synchrony in power-grid networks
text, January 2013

Optimal Topology Design for Disturbance Minimization in Power Grids
preprint, January 2017

Cascade-based attacks on complex networks
text, January 2003

An analysis of approximations for maximizing submodular set functions—I
journal, December 1978

System-Wide Pollution of Biomedical Data: Consequence of the Search for Hub Genes of Hepatocellular Carcinoma Without Spatiotemporal Consideration
journal, January 2021

Effective vaccination strategies for realistic social networks
journal, December 2007

Towards structural controllability of local-world networks
journal, May 2016

Cascade-based attack vulnerability on the US power grid
journal, December 2009

Robustness of complex networks with the local protection strategy against cascading failures
journal, March 2013

Time to replace the Saffir-Simpson hurricane scale?
journal, January 2006

Correction to “Approximate Model of European Interconnected System as a Benchmark System to Study Effects of Cross-Border Trades”
journal, August 2005

Interdiction Analysis of Electric Grids Combining Cascading Outage and Medium-Term Impacts
journal, September 2014

Short-Term Wind Power Ensemble Prediction Based on Gaussian Processes and Neural Networks
journal, January 2014

Catastrophic cascade of failures in interdependent networks
text, January 2009

Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures and Robustness
text, January 2012

Spontaneous synchrony in power-grid networks
text, January 2013