Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published September 2011 | public
Book Section - Chapter

Optimal power flow over tree networks


The optimal power flow (OPF) problem is critical to power system operation but it is generally non-convex and therefore hard to solve. Recently, a sufficient condition has been found under which OPF has zero duality gap, which means that its solution can be computed efficiently by solving the convex dual problem. In this paper we simplify this sufficient condition through a reformulation of the problem and prove that the condition is always satisfied for a tree network provided we allow over-satisfaction of load. The proof, cast as a complex semi-definite program, makes use of the fact that if the underlying graph of an n × n Hermitian positive semi-definite matrix is a tree, then the matrix has rank at least n-1.

Additional Information

© 2011 IEEE. This work was supported by NSF through NetSE grant CNS 0911041, Southern California Edison, Cisco, and the Okawa Foundation. A special thank you to Christopher Clarke of Southern California Edison for providing insightful comments and a number of interesting discussions.

Additional details

August 19, 2023
October 17, 2023