Probabilistic N-k failure-identification for power systems

Sundar, Kaarthik; Coffrin, Carleton; Nagarajan, Harsha; Bent, Russell

doi:10.1002/net.21806

Title: Probabilistic N-k failure-identification for power systems

Abstract

This work considers a probabilistic generalization of the N-k failure-identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of k components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the k components. The resulting problem is formulated as a bilevel mixed-integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting-plane algorithm is proposed to solve the convex relaxation and linear approximations of the N-k problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small-, medium-, and large-scale test instances; the test instances include the IEEE 14-bus system, the IEEE single-area and three-area RTS96 systems, the IEEE 118-bus system, the WECC 240-bus test system, the 1354-bus PEGASE system, and the 2383-bus Polish winter-peak test system.

Authors:

^[1];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: 2018-01-22

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

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1463479

Report Number(s):: LA-UR-17-23601
Journal ID: ISSN 0028-3045

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Networks

Additional Journal Information:: Journal Volume: 71; Journal Issue: 3; Journal ID: ISSN 0028-3045

Country of Publication:: United States

Language:: English

Subject:: 24 POWER TRANSMISSION AND DISTRIBUTION; 97 MATHEMATICS AND COMPUTING; Interdiction, convex optimization, N-k, component-failure probabilities; power network resilience; network interdiction; N-k vulnerability; nonlinear optimization; convex relaxation; cutting-plane algorithm; network flow; DC power flow; AC power flow

Citation Formats


                    Sundar, Kaarthik, Coffrin, Carleton, Nagarajan, Harsha, and Bent, Russell. Probabilistic N-k failure-identification for power systems.  United States: N. p., 2018. 
Web.  doi:10.1002/net.21806.

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                    Sundar, Kaarthik, Coffrin, Carleton, Nagarajan, Harsha, & Bent, Russell. Probabilistic N-k failure-identification for power systems.  United States.  https://doi.org/10.1002/net.21806

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                    Sundar, Kaarthik, Coffrin, Carleton, Nagarajan, Harsha, and Bent, Russell. Mon .  
"Probabilistic N-k failure-identification for power systems".  United States.  https://doi.org/10.1002/net.21806.  https://www.osti.gov/servlets/purl/1463479.

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@article{osti_1463479,

  title        = {Probabilistic N-k failure-identification for power systems},

  author       = {Sundar, Kaarthik and Coffrin, Carleton and Nagarajan, Harsha and Bent, Russell},

  abstractNote = {This work considers a probabilistic generalization of the N-k failure-identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of k components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the k components. The resulting problem is formulated as a bilevel mixed-integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting-plane algorithm is proposed to solve the convex relaxation and linear approximations of the N-k problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small-, medium-, and large-scale test instances; the test instances include the IEEE 14-bus system, the IEEE single-area and three-area RTS96 systems, the IEEE 118-bus system, the WECC 240-bus test system, the 1354-bus PEGASE system, and the 2383-bus Polish winter-peak test system.},

  doi          = {10.1002/net.21806},

  journal      = {Networks},

  number       = 3,

  volume       = 71,

  place        = {United States},

  year         = {2018},

  month        = {1}

}

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Works referenced in this record:

Bilevel programming applied to power system vulnerability analysis under multiple contingencies
journal, January 2010

Arroyo, J. M.
IET Generation, Transmission & Distribution, Vol. 4, Issue 2
DOI: 10.1049/iet-gtd.2009.0098

Radial Distribution Load Flow Using Conic Programming
journal, August 2006

Jabr, R.A.
IEEE Transactions on Power Systems, Vol. 21, Issue 3, p. 1458-1459
DOI: 10.1109/TPWRS.2006.879234

Worst-Case Interdiction Analysis of Large-Scale Electric Power Grids
journal, February 2009

Salmeron, Javier; Wood, Kevin; Baldick, Ross
IEEE Transactions on Power Systems, Vol. 24, Issue 1
DOI: 10.1109/TPWRS.2008.2004825

Moment-based relaxation of the optimal power flow problem
conference, August 2014

Molzahn, Daniel K.; Hiskens, Ian A.
2014 Power Systems Computation Conference (PSCC)
DOI: 10.1109/pscc.2014.7038397

The QC Relaxation: A Theoretical and Computational Study on Optimal Power Flow
journal, July 2016

Coffrin, Carleton; Hijazi, Hassan L.; Van Hentenryck, Pascal
IEEE Transactions on Power Systems, Vol. 31, Issue 4
DOI: 10.1109/TPWRS.2015.2463111

Analysis of Electric Grid Security Under Terrorist Threat
journal, May 2004

Salmeron, J.; Wood, K.; Baldick, R.
IEEE Transactions on Power Systems, Vol. 19, Issue 2
DOI: 10.1109/TPWRS.2004.825888

A Mixed-Integer LP Procedure for the Analysis of Electric Grid Security Under Disruptive Threat
journal, August 2005

Motto, A. L.; Arroyo, J. M.; Galiana, F. D.
IEEE Transactions on Power Systems, Vol. 20, Issue 3
DOI: 10.1109/TPWRS.2005.851942

Reformulation and sampling to solve a stochastic network interdiction problem
journal, October 2008

Janjarassuk, Udom; Linderoth, Jeff
Networks, Vol. 52, Issue 3
DOI: 10.1002/net.20237

Convex quadratic relaxations for mixed-integer nonlinear programs in power systems
journal, October 2016

Hijazi, Hassan; Coffrin, Carleton; Hentenryck, Pascal Van
Mathematical Programming Computation, Vol. 9, Issue 3
DOI: 10.1007/s12532-016-0112-z

Application of a genetic algorithm to n-K power system security assessment
journal, July 2013

Arroyo, José M.; Fernández, Francisco J.
International Journal of Electrical Power & Energy Systems, Vol. 49
DOI: 10.1016/j.ijepes.2012.12.011

Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid
journal, January 2010

Pinar, Ali; Meza, Juan; Donde, Vaibhav
SIAM Journal on Optimization, Vol. 20, Issue 4
DOI: 10.1137/070708275

PowerModels. JL: An Open-Source Framework for Exploring Power Flow Formulations
conference, June 2018

Coffrin, Carleton; Bent, Russell; Sundar, Kaarthik
2018 Power Systems Computation Conference (PSCC)
DOI: 10.23919/pscc.2018.8442948

Analysis of Electric Grid Interdiction With Line Switching
journal, May 2010

Delgadillo, Andrés; Arroyo, José Manuel; Alguacil, Natalia
IEEE Transactions on Power Systems, Vol. 25, Issue 2
DOI: 10.1109/TPWRS.2009.2032232

Multiple Element Contingency Screening
journal, August 2011

Davis, C. Matthew; Overbye, Thomas J.
IEEE Transactions on Power Systems, Vol. 26, Issue 3
DOI: 10.1109/TPWRS.2010.2087366

Shortest-path network interdiction
journal, August 2002

Israeli, Eitan; Wood, R. Kevin
Networks, Vol. 40, Issue 2
DOI: 10.1002/net.10039

Bound Tightening for the Alternating Current Optimal Power Flow Problem
journal, September 2016

Chen, Chen; Atamturk, Alper; Oren, Shmuel S.
IEEE Transactions on Power Systems, Vol. 31, Issue 5
DOI: 10.1109/TPWRS.2015.2497160

Analyzing Vulnerability of Power Systems with Continuous Optimization Formulations
journal, July 2016

Kim, Taedong; Wright, Stephen J.; Bienstock, Daniel
IEEE Transactions on Network Science and Engineering, Vol. 3, Issue 3
DOI: 10.1109/TNSE.2016.2587484

Semidefinite programming for optimal power flow problems
journal, July 2008

Bai, Xiaoqing; Wei, Hua; Fujisawa, Katsuki
International Journal of Electrical Power & Energy Systems, Vol. 30, Issue 6-7, p. 383-392
DOI: 10.1016/j.ijepes.2007.12.003

The IEEE Reliability Test System-1996. A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee
journal, January 1999

Grigg, C.; Wong, P.; Albrecht, P.
IEEE Transactions on Power Systems, Vol. 14, Issue 3
DOI: 10.1109/59.780914

Fast Linear Contingency Analysis
journal, April 1982

Enns, Mark K.; Quada, John J.; Sackett, Bert
IEEE Transactions on Power Apparatus and Systems, Vol. PAS-101, Issue 4
DOI: 10.1109/TPAS.1982.317142

Severe Multiple Contingency Screening in Electric Power Systems
journal, May 2008

Donde, V.; Lopez, V.; Lesieutre, B.
IEEE Transactions on Power Systems, Vol. 23, Issue 2
DOI: 10.1109/TPWRS.2008.919243

AC-Feasibility on Tree Networks is NP-Hard
journal, January 2016

Lehmann, Karsten; Grastien, Alban; Van Hentenryck, Pascal
IEEE Transactions on Power Systems, Vol. 31, Issue 1
DOI: 10.1109/TPWRS.2015.2407363

Methodology for identifying near-optimal interdiction strategies for a power transmission system
journal, September 2007

Bier, Vicki M.; Gratz, Eli R.; Haphuriwat, Naraphorn J.
Reliability Engineering & System Safety, Vol. 92, Issue 9
DOI: 10.1016/j.ress.2006.08.007

Stochastic Network Interdiction
journal, April 1998

Cormican, Kelly J.; Morton, David P.; Wood, R. Kevin
Operations Research, Vol. 46, Issue 2
DOI: 10.1287/opre.46.2.184

A unified network performance measure with importance identification and the ranking of network components
journal, May 2007

Qiang, Qiang; Nagurney, Anna
Optimization Letters, Vol. 2, Issue 1
DOI: 10.1007/s11590-007-0049-2

Quantifying the effect of k-line failures in power grids
conference, July 2016

Soltan, Saleh; Zussman, Gil
2016 IEEE Power and Energy Society General Meeting (PESGM)
DOI: 10.1109/pesgm.2016.7741362

On the Solution of the Bilevel Programming Formulation of the Terrorist Threat Problem
journal, May 2005

Arroyo, J. M.; Galiana, F. D.
IEEE Transactions on Power Systems, Vol. 20, Issue 2
DOI: 10.1109/TPWRS.2005.846198

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

A “Random Chemistry” Algorithm for Identifying Collections of Multiple Contingencies That Initiate Cascading Failure
journal, August 2012

Eppstein, Margaret J.; Hines, Paul D. H.
IEEE Transactions on Power Systems, Vol. 27, Issue 3
DOI: 10.1109/TPWRS.2012.2183624

Primal and dual bounds for Optimal Transmission Switching
conference, August 2014

Coffrin, Carleton; Hijazi, Hassan L.; Lehmann, Karsten
2014 Power Systems Computation Conference (PSCC)
DOI: 10.1109/pscc.2014.7038446

Defending Critical Infrastructure
journal, December 2006

Brown, Gerald; Carlyle, Matthew; Salmerón, Javier
Interfaces, Vol. 36, Issue 6
DOI: 10.1287/inte.1060.0252

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
journal, April 2005

Wächter, Andreas; Biegler, Lorenz T.
Mathematical Programming, Vol. 106, Issue 1
DOI: 10.1007/s10107-004-0559-y

PowerModels. JL: An Open-Source Framework for Exploring Power Flow Formulations
conference, June 2018

Coffrin, Carleton; Bent, Russell; Sundar, Kaarthik
2018 Power Systems Computation Conference (PSCC)
DOI: 10.23919/PSCC.2018.8442948

Primal and dual bounds for Optimal Transmission Switching
conference, August 2014

Coffrin, Carleton; Hijazi, Hassan L.; Lehmann, Karsten
2014 Power Systems Computation Conference (PSCC)
DOI: 10.1109/PSCC.2014.7038446

Moment-based relaxation of the optimal power flow problem
conference, August 2014

Molzahn, Daniel K.; Hiskens, Ian A.
2014 Power Systems Computation Conference (PSCC)
DOI: 10.1109/PSCC.2014.7038397

Quantifying the effect of k-line failures in power grids
conference, July 2016

Soltan, Saleh; Zussman, Gil
2016 IEEE Power and Energy Society General Meeting (PESGM)
DOI: 10.1109/PESGM.2016.7741362

Fast Linear Contingency Analysis
journal, April 1982

Enns, Mark K.; Quada, John J.; Sackett, Bert
IEEE Power Engineering Review, Vol. PER-2, Issue 4
DOI: 10.1109/mper.1982.5519401

Analysis of electric grid interdiction with line switching
conference, July 2010

Delgadillo, A.; Arroyo, J.; Alguacil, N.
Energy Society General Meeting, IEEE PES General Meeting
DOI: 10.1109/pes.2010.5588117

The QC relaxation: A theoretical and computational study on optimal power flow
conference, July 2017

Coffrin, Carleton; Hijazi, Hassan; Van Hentenryck, Pascal
2017 IEEE Power & Energy Society General Meeting (PESGM)
DOI: 10.1109/pesgm.2017.8274004

AC-Feasibility on Tree Networks is NP-Hard
preprint, January 2014

Lehmann, Karsten; Grastien, Alban; Van Hentenryck, Pascal
arXiv
DOI: 10.48550/arxiv.1410.8253

PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulations
preprint, January 2017

Coffrin, Carleton; Bent, Russell; Sundar, Kaarthik
arXiv
DOI: 10.48550/arxiv.1711.01728

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Title: Probabilistic N-k failure-identification for power systems

Abstract

Citation Formats

Bilevel programming applied to power system vulnerability analysis under multiple contingencies journal, January 2010

Radial Distribution Load Flow Using Conic Programming journal, August 2006

Worst-Case Interdiction Analysis of Large-Scale Electric Power Grids journal, February 2009

Moment-based relaxation of the optimal power flow problem conference, August 2014

The QC Relaxation: A Theoretical and Computational Study on Optimal Power Flow journal, July 2016

Analysis of Electric Grid Security Under Terrorist Threat journal, May 2004

A Mixed-Integer LP Procedure for the Analysis of Electric Grid Security Under Disruptive Threat journal, August 2005

Reformulation and sampling to solve a stochastic network interdiction problem journal, October 2008

Convex quadratic relaxations for mixed-integer nonlinear programs in power systems journal, October 2016

Application of a genetic algorithm to n-K power system security assessment journal, July 2013

Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid journal, January 2010

PowerModels. JL: An Open-Source Framework for Exploring Power Flow Formulations conference, June 2018

Analysis of Electric Grid Interdiction With Line Switching journal, May 2010

Multiple Element Contingency Screening journal, August 2011

Shortest-path network interdiction journal, August 2002

Bound Tightening for the Alternating Current Optimal Power Flow Problem journal, September 2016

Analyzing Vulnerability of Power Systems with Continuous Optimization Formulations journal, July 2016

Semidefinite programming for optimal power flow problems journal, July 2008

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Methodology for identifying near-optimal interdiction strategies for a power transmission system journal, September 2007

Stochastic Network Interdiction journal, April 1998

A unified network performance measure with importance identification and the ranking of network components journal, May 2007

Quantifying the effect of k-line failures in power grids conference, July 2016

On the Solution of the Bilevel Programming Formulation of the Terrorist Threat Problem journal, May 2005

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

A “Random Chemistry” Algorithm for Identifying Collections of Multiple Contingencies That Initiate Cascading Failure journal, August 2012

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On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming journal, April 2005

PowerModels. JL: An Open-Source Framework for Exploring Power Flow Formulations conference, June 2018

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Moment-based relaxation of the optimal power flow problem conference, August 2014

Quantifying the effect of k-line failures in power grids conference, July 2016

Fast Linear Contingency Analysis journal, April 1982

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The QC relaxation: A theoretical and computational study on optimal power flow conference, July 2017

AC-Feasibility on Tree Networks is NP-Hard preprint, January 2014

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Bilevel programming applied to power system vulnerability analysis under multiple contingencies
journal, January 2010

Radial Distribution Load Flow Using Conic Programming
journal, August 2006

Worst-Case Interdiction Analysis of Large-Scale Electric Power Grids
journal, February 2009

Moment-based relaxation of the optimal power flow problem
conference, August 2014

The QC Relaxation: A Theoretical and Computational Study on Optimal Power Flow
journal, July 2016

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journal, May 2004

A Mixed-Integer LP Procedure for the Analysis of Electric Grid Security Under Disruptive Threat
journal, August 2005

Reformulation and sampling to solve a stochastic network interdiction problem
journal, October 2008

Convex quadratic relaxations for mixed-integer nonlinear programs in power systems
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Application of a genetic algorithm to n-K power system security assessment
journal, July 2013

Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid
journal, January 2010

PowerModels. JL: An Open-Source Framework for Exploring Power Flow Formulations
conference, June 2018

Analysis of Electric Grid Interdiction With Line Switching
journal, May 2010

Multiple Element Contingency Screening
journal, August 2011

Shortest-path network interdiction
journal, August 2002

Bound Tightening for the Alternating Current Optimal Power Flow Problem
journal, September 2016

Analyzing Vulnerability of Power Systems with Continuous Optimization Formulations
journal, July 2016

Semidefinite programming for optimal power flow problems
journal, July 2008

The IEEE Reliability Test System-1996. A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee
journal, January 1999

Fast Linear Contingency Analysis
journal, April 1982

Severe Multiple Contingency Screening in Electric Power Systems
journal, May 2008

AC-Feasibility on Tree Networks is NP-Hard
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Methodology for identifying near-optimal interdiction strategies for a power transmission system
journal, September 2007

Stochastic Network Interdiction
journal, April 1998

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journal, May 2007

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On the Solution of the Bilevel Programming Formulation of the Terrorist Threat Problem
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The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments
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A “Random Chemistry” Algorithm for Identifying Collections of Multiple Contingencies That Initiate Cascading Failure
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