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

Krishna Sandeep Ayyagari, Sherin Ann Abraham, Yiyun Yao, Shibani Ghosh, Francisco Flores-Espino, Adarsh Nagarajan, Nikolaos Gatsis

Research output: Contribution to conferencePaper


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 LinDist3Flow model is adopted and the effective SVR ratio is assumed to be continuous–enabling the formulation of a problem called LinDist3Flow-OPTS, which amounts to a linear program. The scalability and optimality gap of 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, LinDist3Flow-OPTS achieves an optimality gap of approximately 1% or less while significantly lowering the computational burden.
Original languageAmerican English
Number of pages10
StatePublished - 2022
Event61st IEEE Conference on Decision and Control - Cancun, Mexico
Duration: 6 Dec 20229 Dec 2022


Conference61st IEEE Conference on Decision and Control
CityCancun, Mexico

Bibliographical note

See NREL/CP-6A40-85357 for paper as published in proceedings

NREL Publication Number

  • NREL/CP-5D00-82471


  • linear approximations
  • optimal power flow
  • power distribution networks
  • step-voltage regulators


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