  The adoption of distributed energy resources such as photovoltaics (PVs) has
increased dramatically during the previous decade. The increased penetration of
PVs into distribution networks (DNs) can cause voltage fluctuations that have
to be mitigated. One of the key utility assets employed to this end are
step-voltage regulators (SVRs). It is desirable to include tap selection of
SVRs in optimal power flow (OPF) routines, a task that turns out to be
challenging because the resultant OPF problem is nonconvex with added
complexities stemming from accurate SVR modeling. While several convex
relaxations based on semi-definite programming (SDP) have been presented in the
literature for optimal tap selection, SDP-based schemes do not scale well and
are challenging to implement in large-scale planning or operational frameworks.
This paper deals with the optimal tap selection (OPTS) problem for
wye-connected SVRs using linear approximations of power flow equations.
Specifically, the $\textit{LinDist3Flow}$ model is adopted and the effective
SVR ratio is assumed to be continuous--enabling the formulation of a problem
called $\textit{LinDist3Flow-OPTS}$, which amounts to a linear program. The
scalability and optimality gap of $\textit{LinDist3Flow-OPTS}$ are evaluated
with respect to existing SDP-based and nonlinear programming techniques for
optimal tap selection in three standard feeders, namely, the IEEE 13-bus,
123-bus, and 8500-node DNs. For all DNs considered,
$\textit{LinDist3Flow-OPTS}$ achieves an optimality gap of approximately $1\%$
or less while significantly lowering the computational burden.
