CaltechAUTHORS
Published December 2012 | Version public
Book Section - Chapter Metadata-only

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

Creators

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon University of Pennsylvania

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.

Additional Information

© 2012 IEEE. This work was supported by Bell Labs of Alcatel-Lucent, NSF NetSE grant CNS 0911041, ARPA-E grant DE-AR0000226, Southern California Edison, National Science Council of Taiwan, R.O.C, grant NSC 101-3113-P-008-001, Resnick Institute, Okawa Foundation, Boeing Corporation, Cisco, and AFOSR award number FA9550-12-1-0302.

Additional details

Identifiers

Eprint ID
43112
Resolver ID
CaltechAUTHORS:20131220-094526108

Funding

Bell Labs of Alcatel-Lucent
NSF
CNS-0911041
ARPA-E
DE-AR0000226
Southern California Edison
National Science Council (Taipei)
NSC 101-3113-P-008-001
Resnick Sustainability Institute
Okawa Foundation
Boeing Corporation
Cisco
Air Force Office of Scientific Research (AFOSR)
FA9550-12-1-0302

Dates

Created
2013-12-23
Created from EPrint's datestamp field
Updated
2021-11-10
Created from EPrint's last_modified field

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Resnick Sustainability Institute