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This paper develops a branch-flow-based optimal power flow (OPF) problem for multi-phase distribution networks that allows for tap selection of wye, closed delta, and open delta step-voltage regulators (SVRs). SVRs are assumed ideal and their taps are represented by continuous decision variables. To tackle the non-linearity, the branch-flow semidefinite programming framework of traditional OPF is expanded to accommodate SVR edges. Three types of non-convexity are addressed: (a) rank-1 constraints on non-SVR edges, (b) nonlinear equality constraints on SVR power flows and taps, and (c) trilinear equalities on SVR voltages and taps. Leveraging a practical phase-separation assumption on the SVR secondary voltage, novel McCormick relaxations are provided for (c) and certain rank-1 constraints of (a), while dropping the rest. A linear relaxation based on conservation of power is used in place of (b). Numerical simulations on standard distribution test feeders corroborate the merits of the proposed convex formulation. [ABSTRACT FROM AUTHOR]

The theme of this paper is three-phase distribution system modeling suitable for the Z-Bus load-flow. Detailed models of wye and delta constant-power, constant-current, and constant-impedance loads are presented. Models of transmission lines, step-voltage regulators, and transformers that build the bus admittance matrix (Y-Bus) are laid out. The Z-Bus load-flow is then reviewed and the singularity of the Y-Bus in case of certain transformer connections is rigorously discussed. Based on realistic assumptions and conventional modifications, the invertibility of the Y-Bus is proved. Last but not least, MATLAB scripts that model the components of the IEEE 37-bus, the IEEE 123-bus, the 8500-node feeders, and the European 906-bus low-voltage feeder are provided. [ABSTRACT FROM AUTHOR]

This paper derives a set of sufficient conditions guaranteeing that the load-flow problem in unbalanced three-phase distribution networks with wye and delta constant-power, constant-current, and constant-impedance loads (ZIP loads) has a unique solution over a region that can be explicitly calculated from the network parameters. It is also proved that the well-known Z-Bus iterative method is a contraction over the defined region, and hence converges to the unique solution. [ABSTRACT FROM PUBLISHER]