Placement and Sizing of Inverter-Based Renewable Systems in Multi-Phase Distribution Networks

Emiliano Dall-Anese, Mohammadhafez Bazrafshan, Nikolaos Gatsis

Research output: Contribution to journalArticlepeer-review

30 Scopus Citations


This paper develops a tractable formulation for optimal placement and sizing of inverter-based renewable systems in multi-phase distribution networks. The goal of the formulation is to minimize the cost of inverter installation, average power import, and average distributed generation curtailment. Threephase and single-phase inverter models are presented that preserve the underlying mappings between renewable uncertainty to power injection. The uncertainty of distributed generators (DGs) and loads are characterized by a finite set of scenarios. Linear multi-phase power flow approximations are used in conjunction with scenario reduction techniques to arrive at a tractable twostage stochastic formulation for optimal DG placement and sizing. First-stage decisions are locations for DG deployment and capacity sizes, and second-stage decisions include DG real power curtailment, reactive power support, as well as feeder voltage profile. The resulting formulation is a mixed-integer second-order cone program and can be solved efficiently either by existing optimization solvers or by relaxing the binary variables to the [0,1] interval. Simulation studies on standard multi-phase IEEE test feeders promise that optimal stochastic planning of DGs reduces costs during validation, compared to a scheme where uncertainty is only represented by its average value.
Original languageAmerican English
Pages (from-to)918-930
Number of pages13
JournalIEEE Transactions on Power Systems
Issue number2
StatePublished - 2019

NREL Publication Number

  • NREL/JA-5D00-70143


  • distribution networks
  • mixed-integer second order cone program
  • multi-phase power flow
  • placement and sizing of distributed generators
  • scenario reduction


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