Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid

Journal Article · Tue Nov 13 04:00:00 EST 2007 · Siam Journal on Optimization

OSTI ID:952575

Pinar, A; Meza, J; Donde, V; Lesieutre, B

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.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: Computational Research Division; Environmental Energy Technologies Division
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 952575
• Report Number(s): LBNL-63473
• Journal Information: Siam Journal on Optimization, Journal Name: Siam Journal on Optimization; ISSN 1052-6234
• Country of Publication: United States
• Language: English

Related Subjects

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION
99 GENERAL AND MISCELLANEOUS
BENCHMARKS
ELECTRIC POWER
Electric Power Grid
GRAPH THEORY
LAPLACIAN
LINEAR PROGRAMMING
NONLINEAR PROGRAMMING
OPTIMIZATION
REMOVAL
VULNERABILITY