Probabilistic Nk failureidentification for power systems
Abstract
This work considers a probabilistic generalization of the Nk failureidentification 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 mixedinteger nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cuttingplane algorithm is proposed to solve the convex relaxation and linear approximations of the Nk problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small, medium, and largescale test instances; the test instances include the IEEE 14bus system, the IEEE singlearea and threearea RTS96 systems, the IEEE 118bus system, the WECC 240bus test system, the 1354bus PEGASE system, and the 2383bus Polish winterpeak test system.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 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):
 LAUR1723601
Journal ID: ISSN 00283045
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Networks
 Additional Journal Information:
 Journal Volume: 71; Journal Issue: 3; Journal ID: ISSN 00283045
 Country of Publication:
 United States
 Language:
 English
 Subject:
 24 POWER TRANSMISSION AND DISTRIBUTION; 97 MATHEMATICS AND COMPUTING; Interdiction, convex optimization, Nk, componentfailure probabilities; power network resilience; network interdiction; Nk vulnerability; nonlinear optimization; convex relaxation; cuttingplane algorithm; network flow; DC power flow; AC power flow
Citation Formats
Sundar, Kaarthik, Coffrin, Carleton, Nagarajan, Harsha, and Bent, Russell. Probabilistic Nk failureidentification for power systems. United States: N. p., 2018.
Web. doi:10.1002/net.21806.
Sundar, Kaarthik, Coffrin, Carleton, Nagarajan, Harsha, & Bent, Russell. Probabilistic Nk failureidentification for power systems. United States. doi:10.1002/net.21806.
Sundar, Kaarthik, Coffrin, Carleton, Nagarajan, Harsha, and Bent, Russell. Mon .
"Probabilistic Nk failureidentification for power systems". United States. doi:10.1002/net.21806. https://www.osti.gov/servlets/purl/1463479.
@article{osti_1463479,
title = {Probabilistic Nk failureidentification for power systems},
author = {Sundar, Kaarthik and Coffrin, Carleton and Nagarajan, Harsha and Bent, Russell},
abstractNote = {This work considers a probabilistic generalization of the Nk failureidentification 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 mixedinteger nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cuttingplane algorithm is proposed to solve the convex relaxation and linear approximations of the Nk problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small, medium, and largescale test instances; the test instances include the IEEE 14bus system, the IEEE singlearea and threearea RTS96 systems, the IEEE 118bus system, the WECC 240bus test system, the 1354bus PEGASE system, and the 2383bus Polish winterpeak test system.},
doi = {10.1002/net.21806},
journal = {Networks},
number = 3,
volume = 71,
place = {United States},
year = {2018},
month = {1}
}
Web of Science
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
Radial Distribution Load Flow Using Conic Programming
journal, August 2006
 Jabr, R.A.
 IEEE Transactions on Power Systems, Vol. 21, Issue 3, p. 14581459
WorstCase Interdiction Analysis of LargeScale Electric Power Grids
journal, February 2009
 Salmeron, Javier; Wood, Kevin; Baldick, Ross
 IEEE Transactions on Power Systems, Vol. 24, Issue 1
Momentbased relaxation of the optimal power flow problem
conference, August 2014
 Molzahn, Daniel K.; Hiskens, Ian A.
 2014 Power Systems Computation Conference (PSCC)
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
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
A MixedInteger 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
Reformulation and sampling to solve a stochastic network interdiction problem
journal, October 2008
 Janjarassuk, Udom; Linderoth, Jeff
 Networks, Vol. 52, Issue 3
Convex quadratic relaxations for mixedinteger nonlinear programs in power systems
journal, October 2016
 Hijazi, Hassan; Coffrin, Carleton; Hentenryck, Pascal Van
 Mathematical Programming Computation, Vol. 9, Issue 3
Application of a genetic algorithm to nK power system security assessment
journal, July 2013
 Arroyo, José M.; Fernández, Francisco J.
 International Journal of Electrical Power & Energy Systems, Vol. 49
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
PowerModels. JL: An OpenSource Framework for Exploring Power Flow Formulations
conference, June 2018
 Coffrin, Carleton; Bent, Russell; Sundar, Kaarthik
 2018 Power Systems Computation Conference (PSCC)
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
Multiple Element Contingency Screening
journal, August 2011
 Davis, C. Matthew; Overbye, Thomas J.
 IEEE Transactions on Power Systems, Vol. 26, Issue 3
Shortestpath network interdiction
journal, August 2002
 Israeli, Eitan; Wood, R. Kevin
 Networks, Vol. 40, Issue 2
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
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
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 67, p. 383392
The IEEE Reliability Test System1996. 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
Fast Linear Contingency Analysis
journal, April 1982
 Enns, Mark K.; Quada, John J.; Sackett, Bert
 IEEE Transactions on Power Apparatus and Systems, Vol. PAS101, Issue 4
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
ACFeasibility on Tree Networks is NPHard
journal, January 2016
 Lehmann, Karsten; Grastien, Alban; Van Hentenryck, Pascal
 IEEE Transactions on Power Systems, Vol. 31, Issue 1
Methodology for identifying nearoptimal 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
Stochastic Network Interdiction
journal, April 1998
 Cormican, Kelly J.; Morton, David P.; Wood, R. Kevin
 Operations Research, Vol. 46, Issue 2
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
Quantifying the effect of kline failures in power grids
conference, July 2016
 Soltan, Saleh; Zussman, Gil
 2016 IEEE Power and Energy Society General Meeting (PESGM)
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
The $Nk$ 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
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
Primal and dual bounds for Optimal Transmission Switching
conference, August 2014
 Coffrin, Carleton; Hijazi, Hassan L.; Lehmann, Karsten
 2014 Power Systems Computation Conference (PSCC)
Defending Critical Infrastructure
journal, December 2006
 Brown, Gerald; Carlyle, Matthew; Salmerón, Javier
 Interfaces, Vol. 36, Issue 6
On the implementation of an interiorpoint filter linesearch algorithm for largescale nonlinear programming
journal, April 2005
 Wächter, Andreas; Biegler, Lorenz T.
 Mathematical Programming, Vol. 106, Issue 1
PowerModels. JL: An OpenSource Framework for Exploring Power Flow Formulations
conference, June 2018
 Coffrin, Carleton; Bent, Russell; Sundar, Kaarthik
 2018 Power Systems Computation Conference (PSCC)
Primal and dual bounds for Optimal Transmission Switching
conference, August 2014
 Coffrin, Carleton; Hijazi, Hassan L.; Lehmann, Karsten
 2014 Power Systems Computation Conference (PSCC)
Momentbased relaxation of the optimal power flow problem
conference, August 2014
 Molzahn, Daniel K.; Hiskens, Ian A.
 2014 Power Systems Computation Conference (PSCC)
Quantifying the effect of kline failures in power grids
conference, July 2016
 Soltan, Saleh; Zussman, Gil
 2016 IEEE Power and Energy Society General Meeting (PESGM)