Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid

Pınar, Ali; Meza, Juan C.; Donde, Vaibhav; Lesieutre, Bernard C.

doi:10.1137/070708275

Cited by 124 publications

(111 citation statements)

References 22 publications

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“…A different line of research on vulnerability problems focuses on attacks with certain structural properties, see [7], [21]. An example of this approach is used in [21], where as an approximation to the N − k problem with AC power flows, a linear mixed-integer program to solve the following combinatorial problem: remove a minimum number of arcs, such that in the resulting network there is a partition of the nodes into two sets, N 1 and N 2 , such that…”

Section: Previous Work On Vulnerability Problemsmentioning

confidence: 99%

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments

Bienstock¹,

Verma²

2010

SIAM J. Optim.

149

133

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Given a power grid modeled by a network together with equations describing the power flows, power generation and consumption, and the laws of physics, the so-called N − k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. The case where k is small is of practical interest. We present theoretical and computational results involving a mixed-integer model and a continuous nonlinear model related to this question.

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Section: Previous Work On Vulnerability Problemsmentioning

confidence: 99%

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments

Bienstock¹,

Verma²

2010

SIAM J. Optim.

149

133

View full text Add to dashboard Cite

show abstract

“…Of specific relevance to our work is the literature on security-constrained optimal power flow in situations where large numbers of system components fail. This literature is mostly based on worstcase network interdiction analysis and includes solution methods based on bi-level and mixed-integer programming (see [24,25,1,8,33,32]) and graph algorithms (see [22,3,8,15,16]). …”

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confidence: 99%

Contingency-constrained unit commitment with post-contingency corrective recourse

et al. 2014

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We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-ε reliability criterion. This reliability criterion is a generalization of the wellknown N-k criterion, and dictates that at least (1 − ε j ) fraction of the total system demand must be met following the failures of k or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art.

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“…Consequently, in the power systems area, except of few very recent works [10]- [12] mostly linear approximations of nonlinear BP optimization problems have been reported [2], [5], [13]- [17]. The survey paper [9] mentions several generic approaches for BP such as: implicit enumeration (e.g., branch-and-bound), complementary pivoting algorithms, penalty function methods, steepest descent methods, and mathematical programming with equilibrium constraints (MPEC), among others.…”

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confidence: 99%

Computation of Worst Operation Scenarios Under Uncertainty for Static Security Management

Capitanescu

Wehenkel

2013

IEEE Trans. Power Syst.

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Abstract-This paper deals with day-ahead static security assessment with respect to a postulated set of contingencies while taking into account uncertainties about the next day system conditions. We propose a heuristic approach to compute the worst-case under operation uncertainty for a contingency with respect to overloads. We formulate this problem as a non-convex nonlinear bilevel program that we solve approximately by a heuristic approach which relies on the solution of successive optimal power flow (OPF) and security-constrained optimal power flow (SCOPF) problems of a special type. The method aims at revealing those combinations of uncertainties and contingencies for which the best combination of preventive and corrective actions would not suffice to ensure security. Extensive numerical results on a small, a medium, and a very large system prove the interest of the approach.Index Terms-Bilevel programming, operation under uncertainty, optimal power flow, security-constrained optimal power flow, worst-case analysis. NOMENCLATUREIn the paper vectors are written using bold characters. A. SetsSet of power flow equations in pre-contingency state. Set of power flow equations after contingency .Set of operating limits in pre-contingency state.Set of operating limits after contingency .Set of postulated contingencies.Set of violated constraints.Set of problematic constraints.Union of all sets of problematic constraints.Set of problematic patterns.

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Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid

Cited by 124 publications

References 22 publications

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments

Contingency-constrained unit commitment with post-contingency corrective recourse

Computation of Worst Operation Scenarios Under Uncertainty for Static Security Management

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