Distributionally robust risk-constrained optimal power flow using moment and unimodality information

Bowen Li, Ruiwei Jiang, Johanna L. Mathieu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

As we incorporate more random renewable energy into the power grid, power system operators need to ensure physical constraints, such as transmission line limits, are not violated despite uncertainty. Risk-constrained optimal power flow (RCOPF) based on the Conditional Value-at-Risk (CVaR) is a convenient modeling tool, ensuring that these constraints are satisfied with a high probability (e.g., 95%). However, in practice, it is often difficult to perfectly estimate the joint probability distribution of all uncertain variables, including renewable energy production and load consumption. In this paper, we propose a distributionally robust RCOPF approach by considering all possible probability distributions that share the same moment (e.g., mean and covariance) and unimodality properties. Moment and unimodality information can be estimated based on historical data, and so the proposed approach can be applied in a data-driven manner. In view of the computational challenges, we derive a conservative and a relaxed approximation of the problem. We reformulate these approximations as semidefinite programs (SDPs) facilitating the use of highly efficient off-the-shelf optimization solvers (e.g., CVX). We demonstrate the proposed approach based on a modified IEEE 9-bus power network.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2425-2430
Number of pages6
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Externally publishedYes
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

Fingerprint

Optimal Power Flow
Unimodality
Renewable Energy
Probability Distribution
Moment
Conditional Value at Risk
Semidefinite Program
Probability distributions
Historical Data
Transmission Line
Approximation
Data-driven
Joint Distribution
Power System
Grid
Uncertainty
Optimization
Electric lines
Operator
Modeling

ASJC Scopus subject areas

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

Cite this

Li, B., Jiang, R., & Mathieu, J. L. (2016). Distributionally robust risk-constrained optimal power flow using moment and unimodality information. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 2425-2430). [7798625] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798625

Distributionally robust risk-constrained optimal power flow using moment and unimodality information. / Li, Bowen; Jiang, Ruiwei; Mathieu, Johanna L.

2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 2425-2430 7798625.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Li, B, Jiang, R & Mathieu, JL 2016, Distributionally robust risk-constrained optimal power flow using moment and unimodality information. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7798625, Institute of Electrical and Electronics Engineers Inc., pp. 2425-2430, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7798625
Li B, Jiang R, Mathieu JL. Distributionally robust risk-constrained optimal power flow using moment and unimodality information. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 2425-2430. 7798625 https://doi.org/10.1109/CDC.2016.7798625
Li, Bowen ; Jiang, Ruiwei ; Mathieu, Johanna L. / Distributionally robust risk-constrained optimal power flow using moment and unimodality information. 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 2425-2430
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