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Published in: 4OR 3/2020

15-09-2020 | Invited Survey

Mathematical programming formulations for the alternating current optimal power flow problem

Authors: Dan Bienstock, Mauro Escobar, Claudio Gentile, Leo Liberti

Published in: 4OR | Issue 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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Appendix
Available only for authorised users
Footnotes
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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Metadata
Title
Mathematical programming formulations for the alternating current optimal power flow problem
Authors
Dan Bienstock
Mauro Escobar
Claudio Gentile
Leo Liberti
Publication date
15-09-2020
Publisher
Springer Berlin Heidelberg
Published in
4OR / Issue 3/2020
Print ISSN: 1619-4500
Electronic ISSN: 1614-2411
DOI
https://doi.org/10.1007/s10288-020-00455-w

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