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

Baker, Kyri; Bernstein, Andrey

doi:10.1109/TSG.2019.2903767

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

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Abstract

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.

Authors:

Baker, Kyri ^[1]; Bernstein, Andrey ^[2]

Univ. of Colorado, Boulder, CO (United States)
National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Publication Date:: Thu Mar 07 00:00:00 EST 2019

Research Org.:: National Renewable Energy Lab. (NREL), Golden, CO (United States)

Sponsoring Org.:: USDOE National Renewable Energy Laboratory (NREL), Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1506618

Report Number(s):: NREL/JA-5D00-73517
Journal ID: ISSN 1949-3053

Grant/Contract Number:: AC36-08GO28308

Resource Type:: Accepted Manuscript

Journal Name:: IEEE Transactions on Smart Grid

Additional Journal Information:: Journal Volume: 10; Journal Issue: 6; Journal ID: ISSN 1949-3053

Publisher:: IEEE

Country of Publication:: United States

Language:: English

Subject:: 24 POWER TRANSMISSION AND DISTRIBUTION; optimization; uncertainty; upper bound; voltage control; Monte Carlo methods; estimation; power systems

Citation Formats


                    Baker, Kyri, and Bernstein, Andrey. Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds through Learning.  United States: N. p., 2019. 
Web.  doi:10.1109/TSG.2019.2903767.

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                    Baker, Kyri, & Bernstein, Andrey. Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds through Learning.  United States.  https://doi.org/10.1109/TSG.2019.2903767

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                    Baker, Kyri, and Bernstein, Andrey. Thu .  
"Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds through Learning".  United States.  https://doi.org/10.1109/TSG.2019.2903767.  https://www.osti.gov/servlets/purl/1506618.

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@article{osti_1506618,

  title        = {Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds through Learning},

  author       = {Baker, Kyri and Bernstein, Andrey},

  abstractNote = {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.},

  doi          = {10.1109/TSG.2019.2903767},

  journal      = {IEEE Transactions on Smart Grid},

  number       = 6,

  volume       = 10,

  place        = {United States},

  year         = {Thu Mar 07 00:00:00 EST 2019},

  month        = {Thu Mar 07 00:00:00 EST 2019}

}

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