Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
Volume 63, Issue 5, Pages 650-660Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2016.2529281
Keywords
Convex relaxation; global solution; optimal power flow; power system optimization
Categories
Ask authors/readers for more resources
Recently, there has been significant interest in convex relaxations of the optimal power flow (OPF) problem. A semidefinite programming (SDP) relaxation globally solves many OPF problems. However, there exist practical problems for which the SDP relaxation fails to yield the global solution. Conditions for the success or failure of the SDP relaxation are valuable for determining whether the relaxation is appropriate for a given OPF problem. To move beyond existing conditions, which only apply to a limited class of problems, a typical conjecture is that failure of the SDP relaxation can be related to physical characteristics of the system. By presenting an example OPF problem with two equivalent formulations, this paper demonstrates that physically based conditions cannot universally explain algorithm behavior. The SDP relaxation fails for one formulation but succeeds in finding the global solution to the other formulation. Since these formulations represent the same system, success (or otherwise) of the SDP relaxation must involve factors beyond just the network physics. The lack of universal physical conditions for success of the SDP relaxation motivates the development of tighter convex relaxations capable of solving a broader class of problems. Tools from polynomial optimization theory provide a means of developing tighter relaxations. This paper uses the example problem to illustrate relaxations from the Lasserre hierarchy for polynomial optimization and a related mixed semidefinite/second-order cone programming hierarchy.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available