Optimal distributed control of reactive power via the alternating direction method of multipliers

Petr Šulc, Scott Backhaus, Michael Chertkov

Research output: Contribution to journalArticlepeer-review

241 Scopus citations


We formulate the control of reactive power generation by photovoltaic inverters in a power distribution circuit as a constrained optimization that aims to minimize power losses subject to finite inverter capacity and upper and lower voltage limits at all nodes in the circuit. When voltage variations along the circuit are small and losses of both real and reactive powers are small compared with the respective flows, the resulting optimization problem is convex. Moreover, the cost function is separable enabling a distributed online implementation with node-local computations using only local measurements augmented with limited information from the neighboring nodes communicated over cyber channels. Such an approach lies between the fully centralized and local policy approaches previously considered. We explore protocols based on the dual-ascent method and on the alternating direction method of multipliers (ADMMs), and find that the ADMM protocol performs significantly better.

Original languageEnglish (US)
Article number6963439
Pages (from-to)968-977
Number of pages10
JournalIEEE Transactions on Energy Conversion
Issue number4
StatePublished - Dec 1 2014
Externally publishedYes


  • Alternating direction method of multiplier (ADMM)
  • distributed algorithms
  • distributed control
  • dual-ascent method
  • photovoltaic (PV) power generation
  • power flow
  • reactive power control

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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