  Secondary distribution networks (SDNets) play an increasingly important role
in smart grids due to a high proliferation of distributed energy resources
(DERs) in SDNets. However, most existing optimal power flow (OPF) problems do
not take into account SDNets with center-tapped service transformers. Handling
the nonlinear and nonconvex SDNet power flow constraints is still an
outstanding problem. To meet this gap, we first utilize the second-order cone
programming relaxation and linearization to make center-tapped service
transformer constraints convex, respectively. Then, a linearized triplex
service line power flow model, including its compact matrix-vector form, is
further developed to compose the SDNet OPF model with our proposed
center-tapped service transformer model. This proposed SDNet OPF model can be
easily embedded into existing primary distribution network (PDNet) OPF models,
resulting in a holistic power system decision-making solution for integrated
primary-secondary distribution networks. Case studies are presented for two
different integrated primary-secondary distribution networks that demonstrate
the effectiveness and superiority of this model.
