Safe and Secure Networked Control Systems under Denial-of-Service Attacks
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments
SIAM Journal on Optimization
Sensitivity analysis of the power grid vulnerability to large-scale cascading failures
ACM SIGMETRICS Performance Evaluation Review
Computers and Operations Research
| Hi-index | 0.00 |
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 bilevel mixed integer nonlinear programming 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 16,520 power lines.