The Nk Problem in Power Grids : New Models , Formulations and Numerical Experiments 1

Given a power grid modeled by a network together with equations describing power flows, power generation and consumption, the so-called N − k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. The case where k is small is of practical interest. We present theoretical and numerical results involving a mixed-integer linear model and a continuous nonlinear model related to this problem.

[1]  Probability Subcommittee,et al.  IEEE Reliability Test System , 1979, IEEE Transactions on Power Apparatus and Systems.

[2]  Paul D. Seymour,et al.  Graph minors. III. Planar tree-width , 1984, J. Comb. Theory B.

[3]  李幼升,et al.  Ph , 1989 .

[4]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[5]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[6]  Hande Y. Benson,et al.  INTERIOR-POINT METHODS FOR NONCONVEX NONLINEAR PROGRAMMING: JAMMING AND COMPARATIVE NUMERICAL TESTING , 2000 .

[7]  Ian Dobson,et al.  Evidence for self-organized criticality in electric power system blackouts , 2001, Proceedings of the 34th Annual Hawaii International Conference on System Sciences.

[8]  V. E. Lynch,et al.  Critical points and transitions in an electric power transmission model for cascading failure blackouts. , 2002, Chaos.

[9]  Nicholas I. M. Gould,et al.  Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming , 2002, SIAM J. Optim..

[10]  Ian Dobson,et al.  Blackout mitigation assessment in power transmission systems , 2003, 36th Annual Hawaii International Conference on System Sciences, 2003. Proceedings of the.

[11]  Rogelio E. Alvarez.  Interdicting Electrical Power Grids , 2004 .

[12]  B A Carreras,et al.  Complex dynamics of blackouts in power transmission systems. , 2004, Chaos.

[13]  J. Salmeron,et al.  Analysis of electric grid security under terrorist threat , 2004, IEEE Transactions on Power Systems.

[14]  J. Arroyo,et al.  On the solution of the bilevel programming formulation of the terrorist threat problem , 2005, IEEE Transactions on Power Systems.

[15]  Jacques F. Benders,et al.  Partitioning procedures for solving mixed-variables programming problems , 2005, Comput. Manag. Sci..

[16]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[17]  Stephen P. Boyd.  Convex optimization of graph Laplacian eigenvalues , 2006 .

[18]  Daniel Bienstock,et al.  Using mixed-integer programming to solve power grid blackout problems , 2007, Discret. Optim..

[19]  Vicki M. Bier,et al.  Methodology for identifying near-optimal interdiction strategies for a power transmission system , 2007, Reliab. Eng. Syst. Saf..

[20]  Ali Pinar,et al.  Computing Criticality of Lines in Power Systems , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[21]  J. C. Smith,et al.  Algorithms for discrete and continuous multicommodity flow network interdiction problems , 2007 .

[22]  Jeff T. Linderoth,et al.  Reformulation and sampling to solve a stochastic network interdiction problem , 2008 .

[23]  Ted K. Ralphs,et al.  A Branch-and-cut Algorithm for Integer Bilevel Linear Programs , 2009 .

[24]  Juan C. Meza,et al.  Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid , 2010, SIAM J. Optim..

[25]  Abhinav Verma,et al.  Power grid security analysis: an optimization approach , 2010 .