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资源说明：The optimal power flow (OPF) problem is nonconvex
and generally hard to solve. In this paper,we propose a semidefinite
programming (SDP) optimization, which is the dual of an equivalent
form of the OPF problem. A global optimum solution to the
OPF problem can be retrieved from a solution of this convex dual
problem whenever the duality gap is zero. A necessary and sufficient
condition is provided in this paper to guarantee the existence
of no duality gap for the OPF problem. This condition is satisfied
by the standard IEEE benchmark systems with 14, 30, 57, 118, and
300 buses as well as several randomly generated systems. Since this
condition is hard to study, a sufficient zero-duality-gap condition is
also derived. This sufficient condition holds for IEEE systems after
small resistance (
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