On the exactness of convex relaxation for optimal power flow in tree networks

Author

Lingwen Gan ; Na Li ; Topcu, Ufuk ; Low, Steven

Author_Institution

Div. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA, USA

fYear

2012

fDate

10-13 Dec. 2012

Firstpage

465

Lastpage

471

Abstract

The optimal power flow problem is nonconvex, and a convex relaxation has been proposed to solve it. We prove that the relaxation is exact, if there are no upper bounds on the voltage, and any one of some conditions holds. One of these conditions requires that there is no reverse real power flow, and that the resistance to reactance ratio is non-decreasing as transmission lines spread out from the substation to the branch buses. This condition is likely to hold if there are no distributed generators. Besides, avoiding reverse real power flow can be used as rule of thumb for placing distributed generators.

Keywords

concave programming; convex programming; distributed power generation; power transmission lines; trees (mathematics); branch buses; convex relaxation exactness; distributed generators; optimal power flow problem; resistance-to-reactance ratio; transmission lines; tree networks; Generators; Optimized production technology; Power transmission lines; Reactive power; Resistance; Substations; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2012 IEEE 51st Annual Conference on

Conference_Location

Maui, HI

ISSN

0743-1546

Print_ISBN

978-1-4673-2065-8

Electronic_ISBN

0743-1546

Type

conf

DOI

10.1109/CDC.2012.6426045

Filename

6426045