Three-phase optimal power flow for networked microgrids based on semidefinite programming convex relaxation

Many autonomous microgrids have high penetration of distributed generation (DG) units. Optimal power flow (OPF) is necessary for the optimal dispatch of such networked microgrids (NMGs). Existing convex relaxation methods for three-phase OPF are only applicable to radial networks, not meshed networks. To overcome this limitation, we develop a semidefinite programming (SDP) convex relaxation model, which can be applied to meshed networks and also includes a model of three-phase DG units and on-load voltage regulators with different connection types. The proposed model has higher accuracy than other existing convex relaxation models and the SDP model effectively solves the OPF problem for three-phase meshed networks with satisfactory accuracy, as validated by real 6-bus, 9-bus, and 30-bus NMGs and the IEEE 123-bus test cases. In the SDP model, the convex symmetric-component of the three-phase DG model is shown to be more accurate than three-phase DG that is modelled as three single-phase DG units in three-phase unbalanced OPF. The optimal control variables obtained from the convex relaxation optimization can be used for both the final optimal dispatch strategy and the initial value of non-convex OPF to obtain the globally optimal solution efficiently.