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.

许多自主微电网具有分布式发电 (DG) 单元的高渗透率。最佳潮流 (OPF) 是此类联网微电网 (NMG) 的最佳调度所必需的。现有的三相 OPF 凸松弛方法仅适用于径向网络，不适用于网状网络。为了克服这个限制，我们开发了一个半定规划 (SDP) 凸松弛模型，该模型可应用于网格网络，还包括三相 DG 单元和具有不同连接类型的有载电压调节器的模型。所提出的模型比现有的其他凸松弛模型具有更高的精度，并且 SDP 模型以令人满意的精度有效解决了三相网状网络的 OPF 问题，经真实 6 总线、9 总线和 30 总线 NMG 验证， IEEE 123 总线测试用例。在 SDP 模型中，三相 DG 模型的凸对称分量显示出比在三相不平衡 OPF 中建模为三个单相 DG 单元的三相 DG 更准确。凸松弛优化得到的最优控制变量既可以用于最终的最优调度策略，也可以用于非凸OPF的初始值，从而有效地获得全局最优解。