Multi-Timescale Three-Phase Unbalanced Distribution System Operation With Variable Renewable Generations

Huaiguang Jiang, Yingchen Zhang, Eduard Muljadi, Yi Gu, Jun Zhang, Hongyu Wu

Research output: Contribution to journalArticlepeer-review

19 Scopus Citations


This paper proposes a multi-timescale operational approach for a three-phase unbalanced distribution system, which contains hourly scheduling at substation level and minutes power flow operation at feeder level. In the substation scheduling model, the objective is to minimize the system cost with variable renewable generations. The given error distribution model of renewable generation is formulated as a chance constraint, and derived into a deterministic form by Gaussian mixture model (GMM) with genetic algorithm-based expectation-maximization (GAEM). In the feeder scheduling model, the system cost is further reduced with the optimal power flow (OPF) at a timescale of minutes. Considering the nonconvexity of the three-phase unbalanced OPF problem in distribution systems, the semidefinite programming (SDP) is used to relax the problem into a convex problem, and a distributed computation approach is built based on alternating direction method of multiplier (ADMM). The IEEE 123-bus distribution system, DU (University of Denver) campus distribution system, and the IEEE 8500-bus distribution system are used as the test bench for the proposed approach. And the numerical results demonstrate the effectiveness and validity of the proposed method.
Original languageAmerican English
Pages (from-to)4497-4507
Number of pages11
JournalIEEE Transactions on Smart Grid
Issue number4
StatePublished - 2019

NREL Publication Number

  • NREL/JA-5D00-72247


  • alternating direction method of multiplier
  • chance constraint
  • distribution system
  • expectation-maximization
  • Gaussian mixture model
  • optimal power flow
  • semidefinite programming


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