A semidefinite programming method with graph partitioning technique for optimal power flow problems

A new semidefinite programming (SDP) method with graph partitioning technique to solve optimal power flow (OPF) problems is presented in this paper. The non-convex OPF problem is converted into its convex SDP model at first, and then according to the characters of power system network, the matrix variable of SDP is re-arranged using the chordal extension of its aggregate sparsity pattern by the graph partitioning technique. A new SDP-OPF model is reformulated with the re-arranged matrix variable, and can be solved by the interior point method (IPM) for SDP. This method can reduce the consumption of computer memory and improve the computing performance significantly. Extensive numerical simulations on seven test systems with sizes up to 542 buses have shown that this new method of SDP-OPF can guarantee the global optimal solutions within the polynomial time same as the original SDP-OPF, but less CPU times and memory.

► We present a new semidefinite programming (SDP) method with graph partitioning technique to solve OPF problems.
► The matrix variable of SDP is re-arranged using the chordal extension of its aggregate sparsity pattern.
► The new SDP-OPF model is equivalent as the original one and can be solved by IPM for SDP.
► This method can reduce the consumption of computer memory and improve the computing performance significantly.
► This new method of SDP-OPF can guarantee the global optimal solutions, but less CPU times and memory than the original one.