A SDP relaxation of an optimal power flow problem for distribution networks
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F24%3A00600099" target="_blank" >RIV/67985556:_____/24:00600099 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s11081-023-09801-3" target="_blank" >https://link.springer.com/article/10.1007/s11081-023-09801-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11081-023-09801-3" target="_blank" >10.1007/s11081-023-09801-3</a>
Alternative languages
Result language
angličtina
Original language name
A SDP relaxation of an optimal power flow problem for distribution networks
Original language description
In this work, we are interested in an optimal power flow problem with fixed voltage magnitudes in distribution networks. This optimization problem is known to be non-convex and thus difficult to solve. A well-known solution methodology consists in reformulating the objective function and the constraints of the original problem in terms of positive semi-definite matrix traces, to which we add a rank constraint. To convexify the problem, we remove this rank constraint. Our main focus is to provide a strong mathematical proof of the exactness of this convex relaxation technique. To this end, we explore the geometry of the feasible set of the problem via its Pareto-front. We prove that the feasible set of the original problem and the feasible set of its convexification share the same Pareto-front. From a numerical point of view, this exactness result allows to reduce the initial problem to a semi-definite program, which can be solved by more efficient algorithms.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA22-15524S" target="_blank" >GA22-15524S: Polynomial optimization in the design of globally optimal frame structures under dynamic loads</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Optimization and Engineering
ISSN
1389-4420
e-ISSN
1573-2924
Volume of the periodical
24
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
30
Pages from-to
2973-3002
UT code for WoS article
000973226900001
EID of the result in the Scopus database
2-s2.0-85153256678