Abstract
Many autonomous microgrids have extensive penetration of distributed generation (DG). Optimal power flow (OPF) is necessary for the optimal dispatch of networked microgrids (NMGs). Existing convex relaxation methods for three-phase OPF are limited to radial networks. In light of this, we develop a semidefinite programming (SDP) convex relaxation model which can cope with meshed networks and also includes a model of three-phase DG and under-load voltage regulators with different connection types. The SDP model solves the OPF problem of multi-phase meshed network effectively, 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 demonstrated to be more accurate than a three-phase DG modelled as three single-phase DG units in three-phase unbalanced OPF. The proposed method also has higher accuracy than the existing convex relaxation methods. The resultant optimal control variables obtained from the convex relaxation optimization can be used for both final optimal dispatch strategy and initial value of the non-convex OPF to obtain the globally optimal solution efficiently.