Assessing the Optimality of LinDist3Flow for Optimal Tap Selection of Step Voltage Regulators in Unbalanced Distribution Networks

TL;DR

This paper proposes a linear programming approach using LinDist3Flow for optimal tap selection of step-voltage regulators in unbalanced distribution networks, offering a scalable and near-optimal solution compared to SDP-based methods.

Contribution

It introduces a linear approximation model for optimal tap selection, demonstrating improved scalability and minimal optimality gap in large distribution networks.

Findings

Achieves approximately 1% or less optimality gap.

Significantly reduces computational burden.

Validated on IEEE standard feeders with consistent results.

Abstract

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.