Stochastic AC optimal power flow with approximate chance-constraints

Jeremias Schmidli, Line Roald, Spyros Chatzivasileiadis, Goran Andersson

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With higher shares of fluctuating electricity generation from renewables, new operational planning methods to handle uncertainty from forecast errors and short-term fluctuations are required. In this paper, we formulate a probabilistic AC optimal power flow where the uncertainties are accounted for using chance constraints on line currents and voltage magnitudes. The chance constraints ensure that the probability of limit violations remain small, but require a tractable reformulation. To achieve this, an approximate, analytical reformulation of the chance constraints is developed based on linearization around the expected operating point and the assumption of normally distributed deviations. Further, an iterative solution approach is suggested, which allows for a straightforward adaption of the method based on any existing AC OPF implementation. We evaluate the performance of our method in a case study on the 24-bus IEEE RTS96 system. The proposed algorithm is found to converge fast and substantially reduce constraint violations.
Original languageEnglish
Title of host publicationProceedings of 2016 IEEE Power and Energy Society General Meeting
Publication date2016
Pages5 pp.
Publication statusPublished - 2016
Externally publishedYes
Event2016 IEEE Power Engineering Society General Meeting - Boston, United States
Duration: 17 Jul 201621 Jul 2016


Conference2016 IEEE Power Engineering Society General Meeting
Country/TerritoryUnited States
Internet address
SeriesIeee Power and Energy Society General Meeting


  • Power system planning and layout
  • Interpolation and function approximation (numerical analysis)
  • Power transmission, distribution and supply
  • Other topics in statistics
  • iterative methods
  • linearisation techniques
  • load flow
  • power generation planning
  • probability
  • stochastic processes
  • stochastic AC optimal power flow
  • chance-constraint approximation
  • electricity generation
  • operational planning method
  • short-term fluctuation
  • line current
  • voltage magnitude
  • limit violation probability
  • analytical reformulation
  • iterative solution approach
  • AC OPF implementation
  • 24-bus IEEE RTS96 system
  • constraint violation reduction
  • Uncertainty
  • Reactive power
  • Wind power generation
  • Mathematical model
  • Generators
  • Wind forecasting
  • Load flow
  • Forecast Uncertainty
  • Chance Constrained Optimal Power Flow
  • AC Power Flow


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