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Achieving SDP Tightness Through SOCP Relaxation with Cycle-Based SDP Feasibility Constraints for AC OPF. (arXiv:1804.05128v2 [math.OC] UPDATED)
来源于:arXiv
In this paper, we show that the standard semidefinite programming (SDP)
relaxation of altering current optimal power flow (AC OPF) can be equivalently
reformulated as second-order cone programming (SOCP) relaxation with maximal
clique- and cycle-based SDP feasibility constraints. The formulation is based
on the positive semi-definite (PSD) matrix completion theorem, which states
that if all sub-matrices corresponding to maximal cliques in a chordal graph
are PSD, then the partial matrix related to the chordal graph can be completed
as a full PSD matrix. Existing methods in [1] first construct a chordal graph
through Cholesky factorization. In this paper, we identify maximal cliques and
minimal chordless cycles first. Enforcing the submatrices related to the
maximal cliques and cycles PSD will guarantee a PSD full matrix. Further, we
conduct chordal relaxation for the minimal chordless cycles by adding virtual
lines and decompose each chordless cycle to 3-node cycles. Thus, the entire
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