a b s t r a c tThis paper addresses the allocation of defensive or hardening resources in an electric power grid to mitigate the vulnerability against multiple contingencies. This planning problem is characterized by a defender-attacker-defender model which is formulated as a trilevel programming problem. In the upper level, the system planner identifies the components to be defended or hardened in order to reduce the damage associated with plausible outages. In the middle level, the disruptive agent determines the set of out-of-service components so that the damage in the system is maximized. Finally, in the lower level, the system operator minimizes the damage caused by the outages selected by the disruptive agent by means of an optimal operation of the power system. We propose a novel two-stage solution approach that attains optimality with moderate computational effort. The original trilevel program is first transformed into an equivalent bilevel program, which is subsequently solved by an efficient implicit enumeration algorithm. Numerical results show the effectiveness of the proposed methodology.

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Abstract-This paper addresses the vulnerability analysis of the electric grid under terrorist threat. This problem is formulated as a mixed-integer nonlinear bilevel program. In the upper-level optimization, the terrorist agent maximizes the damage caused in the power system, which is measured in terms of the level of system load shed. On the other hand, in the lower-level optimization, the system operator minimizes the damage by means of an optimal operation of the power system. The distinctive modeling feature introduced in this paper is that, among the different corrective actions available, the system operator has the capability to modify the network topology.Due to its nonconvexity and nonlinearity, the resulting bilevel programming problem cannot be equivalently transformed into a standard one-level optimization problem. Therefore, this paper proposes a new approach based on Benders decomposition within a restart framework. Some numerical results obtained by the proposed algorithm are provided and compared with those published, based on the IEEE Reliability Test System.