Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid

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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) and ... continued below

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Pinar, A.; Meza, J.; Donde, V. & Lesieutre, B. November 13, 2007.

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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) and the Laplacian matrix in spectral graph theory (a representation of the graph of the power grid). The reduced combinatorial problem is known as the network inhibition problem, for which we present a mixed integer linear programming formulation. Our experiments on benchmark power grids show that the reduced combinatorial model provides an accurate approximation, to enable vulnerability analyses of real-sized problems with more than 10,000 power lines.

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  • Journal Name: Siam Journal on Optimization

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  • Report No.: LBNL-63473
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 952575
  • Archival Resource Key: ark:/67531/metadc930504

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  • November 13, 2007

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Jan. 4, 2017, 6:46 p.m.

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Pinar, A.; Meza, J.; Donde, V. & Lesieutre, B. Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid, article, November 13, 2007; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc930504/: accessed November 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.