Optimal Operation of Unbalanced Three-Phase Islanded Droop-Based Microgrids

Pedro P. Vergara, Juan C. Lopez, Marcos J. Rider*, Luiz C.P. Da Silva

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

50 Citations (Scopus)


This paper presents a new mixed-integer nonlinear programming (MINLP) model for the optimal operation of unbalanced three-phase droop-based microgrids. The proposed MINLP model can be seen as an extension of an optimal power flow for microgrids operating in islanded mode, that aims to minimize the total amount of unsupplied demand and the total distributed generator (DG) generation cost. Since the slack bus concept is not longer valid, the proposed model considers the frequency and voltage magnitude reference as variables. In this case, DGs units operate with droop control to balance the system and provide a frequency and voltage magnitude reference. Additionally, a set of efficient linearizations are introduced in order to approximate the original MINLP problem into a mixed-integer linear programming (MILP) model that can be solved using commercial solvers. The proposed model has been tested in a 25-bus unbalanced three-phase microgrid and a large 124-node grid, considering different operational and time-coupling constraints for the DGs and the battery systems (BSs). Load curtailment and different modes of operation for the wind turbines have also been tested. Finally, an error assessment between the original MINLP and the approximated MILP model has been conducted.

Original languageEnglish
Article number8048577
Pages (from-to)928-940
Number of pages13
JournalIEEE Transactions on Smart Grid
Issue number1
Publication statusPublished - 2019
Externally publishedYes


  • Droop control
  • islanded microgrid
  • mixed-integer linear programming
  • three-phase optimal power flow


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