Optimal Power Flow for Integrated Primary-Secondary Distribution Networks with Center-Tapped Service Transformers

TL;DR

This work tackles the challenge of optimal power flow for integrated primary-secondary distribution networks that include center-tapped service transformers and triplex service lines in SDNets. It introduces convex relaxation (SOCP-ST) and linearization (L-ST) for transformer constraints, along with a linearized triplex service-line model (L-TSL) and a graph-based compact representation to enable scalable SDNet power flow. The integrated PDNet-SDNet OPF minimizes SDNet losses while respecting both networks' constraints and their coupling, with case studies showing accurate SDNet voltage and power-flow estimates and effective DER dispatch. The approach enhances empirical fidelity in distribution networks by explicitly modeling SDNets and transformer effects, supporting more reliable voltage control and planning in smart grids.

Abstract

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.

Figures (10)

• Figure 1: Integrated Primary-Secondary Distribution Network Illustration
• Figure 2: The secondary distribution network $SDNet(n_J,\phi_J)$, connected to bus $n_J$ of PDNet by a phase-$\phi_{J}$ lateral line $Lat(n_J,\phi_{J})$.
• Figure 3: A modified 12-bus PDNet system with 12 SDNets
• Figure 4: A real utility primary-secondary distribution network in U.S.
• Figure 5: Voltage distributions calculated by Models 1, 2, and 3 in the modified 12-bus PDNet with 12 SDNets.