Optimal tap setting of voltage regulation transformers in unbalanced distribution systems

Brett A. Robbins, Hao Zhu, Alejandro D. Dominguez-Garcia

Research output: Contribution to journalArticlepeer-review


In this paper, we propose a method to optimally set the tap position of voltage regulation transformers in distribution systems. We cast the problem as a rank-constrained semidefinite program (SDP), in which the transformer tap ratios are captured by 1) introducing a secondary-side 'virtual' bus per transformer, and 2) constraining the values that these virtual bus voltages can take according to the limits on the tap positions. Then, by relaxing the non-convex rank-1 constraint in the rank-constrained SDP formulation, one obtains a convex SDP problem. The tap positions are determined as the ratio between the primary-side bus voltage and the secondary-side virtual bus voltage that result from the optimal solution of the relaxed SDP, and then rounded to the nearest discrete tap values. To efficiently solve the relaxed SDP, we propose a distributed algorithm based on the alternating direction method of multipliers (ADMM). We present several case studies with single- and three-phase distribution systems to demonstrate the effectiveness of the distributed ADMM-based algorithm, and compare its results with centralized solution methods.

Original languageEnglish (US)
Article number7039295
Pages (from-to)256-267
Number of pages12
JournalIEEE Transactions on Power Systems
Issue number1
StatePublished - Jan 2016


  • Decentralized control
  • Distributed algorithms
  • Power system analysis computing
  • Relaxation methods
  • Transformers

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


Dive into the research topics of 'Optimal tap setting of voltage regulation transformers in unbalanced distribution systems'. Together they form a unique fingerprint.

Cite this