Distributed optimal power flow for smart microgrids

Emiliano Dall'Anese, Hao Zhu, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review


Optimal power flow (OPF) is considered for microgrids, with the objective of minimizing either the power distribution losses, or, the cost of power drawn from the substation and supplied by distributed generation (DG) units, while effecting voltage regulation. The microgrid is unbalanced, due to unequal loads in each phase and non-equilateral conductor spacings on the distribution lines. Similar to OPF formulations for balanced systems, the considered OPF problem is nonconvex. Nevertheless, a semidefinite programming (SDP) relaxation technique is advocated to obtain a convex problem solvable in polynomial-time complexity. Enticingly, numerical tests demonstrate the ability of the proposed method to attain the globally optimal solution of the original nonconvex OPF. To ensure scalability with respect to the number of nodes, robustness to isolated communication outages, and data privacy and integrity, the proposed SDP is solved in a distributed fashion by resorting to the alternating direction method of multipliers. The resulting algorithm entails iterative message-passing among groups of consumers and guarantees faster convergence compared to competing alternatives.

Original languageEnglish (US)
Article number6502290
Pages (from-to)1464-1475
Number of pages12
JournalIEEE Transactions on Smart Grid
Issue number3
StatePublished - 2013
Externally publishedYes


  • Distributed optimization
  • distribution feeders
  • microgrids
  • optimal power flow
  • semidefinite relaxation

ASJC Scopus subject areas

  • Computer Science(all)


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