A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems
We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists of choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard 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 branch-and-bound 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 lower-level defender problem. Lower bounding is provided with semidefinite programming (SDP) relaxed solutions to the lower-level 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 SDP-relaxed bilevel problem which is included in a vetted list of upper-level 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 without resorting to convex relaxations of the lower-level problem. We conclude with a discussion of future extensions and improvements.
- Research Organization:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Organization:
- USDOE Office of Electricity (OE), Advanced Grid Research & Development
- Grant/Contract Number:
- AC02-06CH11357
- OSTI ID:
- 1798035
- Journal Information:
- SIAM Journal on Optimization, Vol. 31, Issue 1; ISSN 1052-6234
- Publisher:
- Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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