Optimal Tap Selection of Step-Voltage Regulators in Multi-Phase Distribution Networks

An optimal power flow (OPF) problem is formulated that allows for tap selection of various types of step-voltage regulators (SVRS) in multi-phase distribution networks. The goal of the OPF is power-import minimization while satisfying operational constraints. Variables include nodal power injections, nodal voltages, and SVR tap ratios. SVRS are modeled according to their voltage gains and their connecting transmission line parameters. A set of power flow equations that rely on the nodal admittance model of SVRS and explicitly account for the tap ratios are derived. Chordal SDP relaxations of the power flow equations are pursued for non-SVR edges. For each SVR type, novel relaxations are proposed to handle the non-convex primary-to-secondary voltage relationship. Numerical tests on the IEEE 37-bus feeder indicate the success of the proposed formulation in selecting taps of wye, closed-delta, and open-delta SVRS while keeping the incurred cost within 1% of its optimal value.