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Erschienen in: 4OR 3/2020

15.09.2020 | Invited Survey

Mathematical programming formulations for the alternating current optimal power flow problem

verfasst von: Dan Bienstock, Mauro Escobar, Claudio Gentile, Leo Liberti

Erschienen in: 4OR | Ausgabe 3/2020

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Abstract

Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the cost of generating power. Current can either be direct or alternating: while the former yields approximate linear programming formulations, the latter yields formulations of a much more interesting sort: namely, nonconvex nonlinear programs in complex numbers. In this technical survey, we derive formulation variants and relaxations of the alternating current optimal power flow problem.

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1
We remark that most of the power grid literature uses i to indicate current, and therefore resorts to j to indicate \(\sqrt{-1}\). We chose to keep notation in line with mathematics and the rest of the physical sciences, namely we use \(i=\sqrt{-1}\), and employ I to denote current.
 
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Metadaten
Titel
Mathematical programming formulations for the alternating current optimal power flow problem
verfasst von
Dan Bienstock
Mauro Escobar
Claudio Gentile
Leo Liberti
Publikationsdatum
15.09.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
4OR / Ausgabe 3/2020
Print ISSN: 1619-4500
Elektronische ISSN: 1614-2411
DOI
https://doi.org/10.1007/s10288-020-00455-w

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