Efficient Relaxations for Joint Chance Constrained AC Optimal Power Flow

Kyri Baker, Bridget Toomey

Research output: Contribution to journalArticlepeer-review

37 Scopus Citations


Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce higher levels of uncertainty and can yield optimization problems that are difficult to solve in an efficient manner. Solution methods for single chance constraints in optimal power flow problems have been considered in the literature, ensuring single constraints are satisfied with a prescribed probability; however, joint chance constraints, ensuring multiple constraints are simultaneously satisfied, have predominantly been solved via scenario-based approaches or by utilizing Boole's inequality as an upper bound. In this paper, joint chance constraints are used to solve an AC optimal power flow problem while preventing overvoltages in distribution grids under high penetrations of photovoltaic systems. A tighter version of Boole's inequality is derived and used to provide a new upper bound on the joint chance constraint, and simulation results are shown demonstrating the benefit of the proposed upper bound. The new framework allows for a less conservative and more computationally efficient solution to considering joint chance constraints, specifically regarding preventing overvoltages.
Original languageAmerican English
Pages (from-to)230-236
Number of pages7
JournalElectric Power Systems Research
StatePublished - 2017

NREL Publication Number

  • NREL/JA-5D00-68430


  • Boole's inequality
  • chance constraints
  • distribution grids
  • renewable integration
  • voltage regulation


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