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
Y1 - 2011
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
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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 -