Data-Driven Distributionally Robust Optimal Power Flow for Distribution Systems

Robert Mieth, Yury Dvorkin

Research output: Contribution to journalArticlepeer-review


Increasing penetration of distributed energy resources complicate operations of electric power distribution systems by amplifying volatility of nodal power injections. On the other hand, these resources can provide additional control means to the distribution system operator (DSO). In this work we develop a data-driven distributionally robust decision-making framework in the DSO's perspective to overcome the uncertainty of these injections and its impact on the distribution system operations. We develop an ac optimal power flow formulation for radial distribution systems based on the LinDistFlow ac power flow approximation and exploit distributionally robust optimization to immunize the optimized decisions against uncertainty in the probabilistic models of forecast errors obtained from the available observations. The model is reformulated to be computationally tractable and tested on multiple IEEE distribution test systems. We also release the code supplement that implements the proposed model in Julia and can be used to reproduce our numerical results.

Original languageEnglish (US)
Pages (from-to)363-368
Number of pages6
JournalIEEE Control Systems Letters
Issue number3
StatePublished - Jul 2018


  • Power systems
  • smart grid
  • stochastic optimal control
  • uncertain systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization


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