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A Mixed-Integer LP Procedure for the Analysis of Electric Grid Security Under Disruptive Threat

A Mixed-Integer LP Procedure for the Analysis of Electric Grid Security Under Disruptive Threat,10.1109/TPWRS.2005.851942,IEEE Transactions on Power S

A Mixed-Integer LP Procedure for the Analysis of Electric Grid Security Under Disruptive Threat   (Citations: 25)
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This paper presents a solution procedure for the mixed-integer bilevel programming model of the electric grid security under disruptive threat problem, here concisely denoted by (ST-MIBLP), that was recently reported. Using results from linear programming theory and some basic linearization of products of binary–binary or binary–continuous variables, we recast (ST-MIBLP) into a standard (one-level) mixed-integer linear program (ST-MILP) with no more binary variables than in the original (ST-MIBLP). This transformation provides a framework for globally solving (ST-MIBLP) using available mixed-integer linear programming solvers. Some numerical results obtained by the new method are compared with those recently published, based on IEEE Reliability Test Systems.
Journal: IEEE Transactions on Power Systems - IEEE TRANS POWER SYST , vol. 20, no. 3, pp. 1357-1365, 2005
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    • ...Moreover, Motto et al. [10] transformed the problems [8], [9] into a mixed integer bilevel programming model and presented a solution procedure...
    • ...From [8]–[10], it can be observed that in the new context where terrorists come into play, traditionally robust power systems may be vulnerable...

    Guo Chenet al. Exploring Reliable Strategies for Defending Power Systems Against Targ...

    • ...Additionally, the vulnerability assessment of power systems due to intentional outages has received significant attention by some researchers [20]...

    Ansi Wanget al. Vulnerability Assessment Scheme for Power System Transmission Networks...

    • ...Some examples of this research effort are [3] and [4] which address the problem of identifying critical network components that are potential targets for terrorist agents...
    • ...Static models of vulnerability analysis [4], [5] are used to generate scenarios...
    • ...The level of damage associated with attack plans drives the scenario generation procedure, which is based on the solution of the so-called terrorist threat problem [4]...
    • ...Using the vulnerability analysis proposed in [4], the maximum system load shed in the original network is obtained after destroying at least 28 lines and is equal to 3214 MW, representing 56% of the total demand (5700 MW)...

    José Manuel Arroyoet al. A Risk-Based Approach for Transmission Network Expansion Planning Unde...

    • ...Motto et al. [13] presented an alternative solution procedure for the mixed-integer bilevel programming model of the terrorist threat problem...
    • ...As an example, the worst-case interdiction method of [13] was used for this purpose in the vulnerability-constrained transmission expansion planning approach presented in [17] and [18]...
    • ...In our model, line switching decisions are characterized through lower-level binary variables; therefore, the resulting bilevel program cannot be addressed by means of previously reported techniques relying on the equivalent transformation to a one-level optimization problem [12], [13]...
    • ...The system operator is represented by the optimal power flow in the lower-level problem (4)–(11), which is parameterized in terms of the upper-level decision variables . As is commonly assumed in the technical literature [9]–[13], [15], [16], a dc model of the transmission system is used...
    • ...Constraints (5) constitute the main difference with respect to the bilevel models presented in [9]–[13], [15], and [16]...
    • ...These constraints make the lower-level problem nonconvex due to the presence of lower-level binary variables , and nonlinear due to the products of lower-level decision variables and . Therefore, it is not possible to transform the bilevel problem (1)–(11) into an equivalent one-level optimization problem, as done in [12] and [13], and new tools are thus needed...
    • ...This step involves solving the same problem addressed in [13]...
    • ...Table I presents the maximum system load shed obtained for a number of destroyed lines up to 12. The quality of the solutions found by BDLS is assessed through the comparison with the optimal solutions achieved by the approach of Motto et al. [13], denoted by MO. The methodology MO does not consider line switching and thus provides an upper bound on the optimal system load shed...

    Andrés Delgadilloet al. Analysis of Electric Grid Interdiction With Line Switching

    • ...Since each of these lower-level problems is continuous and convex, it can be represented by its constraints, the constraints of its dual problem and the strong duality condition [24]...

    Lina P. Garceset al. A Bilevel Approach to Transmission Expansion Planning Within a Market ...

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