A SDP relaxation of an optimal power flow problem for distribution networks

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A SDP relaxation of an optimal power flow problem for distribution networks

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

A SDP relaxation of an optimal power flow problem for distribution networks

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-15524S" target="_blank" >GA22-15524S: Polynomiální optimalizace v návrhu globálně optimálních rámových konstrukcí namáhaných dynamickým zatížením</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Optimization and Engineering

ISSN

1389-4420

e-ISSN

1573-2924

Svazek periodika

24

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

30

Strana od-do

2973-3002

Kód UT WoS článku

000973226900001

EID výsledku v databázi Scopus

2-s2.0-85153256678