Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds Through Learning

Andrey Bernstein, Kyri Baker

Research output: Contribution to journalArticlepeer-review

50 Scopus Citations


This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance constraints, which satisfy multiple constraints simultaneously with a prescribed probability, are one way to incorporate uncertainty across sets of constraints, leading to a chance-constrained optimal power flow problem. Departing from the computationally heavy scenario-based approaches or approximations that transform the joint constraint into conservative deterministic constraints; this paper develops a scalable, data-driven approach which learns operational trends in a power network, eliminates zero-probability events (e.g., inactive constraints), and accurately and efficiently approximates bounds on the joint chance constraint iteratively. In particular, the proposed framework improves upon the classic methods based on the union bound (or Boole's inequality) by generating a much less conservative set of single chance constraints that also guarantees the satisfaction of the original joint constraint. The proposed framework is evaluated numerically using the IEEE 37-node test feeder, focusing on the problem of voltage regulation in distribution grids.

Original languageAmerican English
Article number8662704
Pages (from-to)6376-6385
Number of pages10
JournalIEEE Transactions on Smart Grid
Issue number6
StatePublished - Nov 2019

Bibliographical note

Publisher Copyright:
© 2010-2012 IEEE.

NREL Publication Number

  • NREL/JA-5D00-73517


  • Optimization
  • power systems
  • support vector machines


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