TY - GEN

T1 - Optimal power flow over tree networks

AU - Bose, Subhonmesh

AU - Gayme, Dennice F.

AU - Low, Steven

AU - Chandy, K. Mani

PY - 2011/12/1

Y1 - 2011/12/1

N2 - 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 x n Hermitian positive semi-definite matrix is a tree, then the matrix has rank at least n - 1.

AB - 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 x n Hermitian positive semi-definite matrix is a tree, then the matrix has rank at least n - 1.

UR - http://www.scopus.com/inward/record.url?scp=84856113749&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856113749&partnerID=8YFLogxK

U2 - 10.1109/Allerton.2011.6120323

DO - 10.1109/Allerton.2011.6120323

M3 - Conference contribution

AN - SCOPUS:84856113749

SN - 9781457718168

T3 - 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

SP - 1342

EP - 1348

BT - 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

T2 - 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

Y2 - 28 September 2011 through 30 September 2011

ER -