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A Lagrangian Dual Approach for Identifying the Worst Contingencies in Power Systems

Brian Dandurand(bdandurand***at***anl.gov)
Kibaek Kim(kimk***at***anl.gov)
Sven Leyffer(leyffer***at***mcs.anl.gov)

Abstract: We address the problem of identifying critical contingencies in an electric grid network. The critical contingency identification is modeled as a nonconvex robust optimization problem, where the upper level must choose the most damaging attack that anticipates the lower-level decision to minimize the damage from the attacks. In general, nonconvex robust optimization problems are NP-hard, and effective solution approaches make use of the problem structure. Initially, we consider a single-level reformulation to the original problem, but we note that its convexity properties do not allow for tractable solution approaches. To address this issue, we pose a Lagrangian-based reformulation that preserves the modeling of nonlinear aspects of the power network operation, while having the desired structure amenable to the application of standard solution approaches in mixed-integer convex programming. We present computational experiments based on IEEE and Pegase cases, discuss the effectiveness of the new approach, and conclude with questions arising from the experiments that can be addressed in the future.

Keywords: Optimal power flow, nonconvex robust optimization, network contingency identification, mixed-integer convex programming

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Combinatorial Optimization (Branch and Cut Algorithms )

Category 3: Robust Optimization

Citation: Argonne National Laboratory July 2019

Download: [PDF]

Entry Submitted: 07/25/2019
Entry Accepted: 07/25/2019
Entry Last Modified: 07/25/2019

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