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Brian Dandurand (bdandurandanl.gov) Abstract: We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upperlevel binary maximization problem consists in choosing an attack that is treated as a parameter in the lowerlevel defender minimization problem. Instances of the lowerlevel global minimization problem by themselves are NPhard due to the nonconvex AC power flow constraints, and bilevel solution approaches commonly apply a convex relaxation or approximation to allow for tractable bilevel reformulations at the cost of underestimating some power system vulnerabilities. Our main contribution is to provide an alternative branchandbound algorithm whose upper bounding mechanism (in a maximization context) is based on a reformulation that avoids relaxation of the AC power flow constraints in the lowerlevel defender problem. Lower bounding is provided with semidefinite programming (SDP) relaxed solutions to the lowerlevel problem. We establish finite termination with guarantees of either a globally optimal solution to the original bilevel problem, or a globally optimal solution to the SDPrelaxed bilevel problem which is included in a vetted list of upperlevel attack solutions, at least one of which is a globally optimal solution to the bilevel problem. We demonstrate through computational experiments applied to IEEE case instances both the relevance of our contribution, and the effectiveness of our contributed algorithm for identifying power system vulnerabilities whose value is underestimated when using standard convex relaxations of the lower level problem. We conclude with a discussion of future extensions and improvements. Keywords: Optimal power flow, nonconvex robust optimization, network contingency identification, nonlinear mixedinteger 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 May 2020 Download: [PDF] Entry Submitted: 07/25/2019 Modify/Update this entry  
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