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The Optimal Power Flow Operator: Theory and Computation

Zhou, Fengyu and Anderson, James and Low, Steven H. (2021) The Optimal Power Flow Operator: Theory and Computation. IEEE Transactions on Control of Network Systems, 8 (2). pp. 1010-1022. ISSN 2325-5870. doi:10.1109/TCNS.2020.3044258. https://resolver.caltech.edu/CaltechAUTHORS:20200707-114446351

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Abstract

Optimal power flow (OPF) problems are mathematical programs to determine how to distribute power over networks subject to power flow and operational constraints. In this article, we treat an OPF problem as an operator that maps user demand to generated power, and allow the problem parameters to take values in some admissible set. We formalize this operator theoretic approach, define and characterize restricted parameter sets under which the mapping has a singleton output, independent binding constraints, and is differentiable. We show that for any power network, these analytical properties hold under almost all operating conditions and can thus be relied upon in applications. We further provide a closed-form expression for the Jacobian matrix of the OPF operator and describe how various derivatives can be computed using a recently proposed scheme based on homogenous self-dual embedding. In contrast to related work in the optimization literature, our results have a clear physical interpretation.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TCNS.2020.3044258DOIArticle
https://arxiv.org/abs/1907.02219arXivDiscussion Paper
ORCID:
AuthorORCID
Zhou, Fengyu0000-0002-2639-6491
Anderson, James0000-0002-2832-8396
Low, Steven H.0000-0001-6476-3048
Additional Information:© 2020 IEEE. Manuscript received April 3, 2020; revised April 8, 2020, September 9, 2020, and September 10, 2020; accepted November 14, 2020. Date of publication December 11, 2020; date of current version August 24, 2021. This work was supported in part by the NSF under Grant CCF 1637598, Grant CPS 1739355, and Grant ECCS 1931662; in part by the PNNL under Grant 424858; and in part by the ARPA-E GRID DATA Program. Recommended by Associate Editor Y. Yuan.
Funders:
Funding AgencyGrant Number
NSFCCF-1637598
NSFCPS-1739355
NSFECCS-1931662
Battelle Memorial Institute424858
Advanced Research Projects Agency-Energy (ARPA-E)UNSPECIFIED
Subject Keywords:Analysis, linear programming, optimal power flow (OPF)
Issue or Number:2
DOI:10.1109/TCNS.2020.3044258
Record Number:CaltechAUTHORS:20200707-114446351
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200707-114446351
Official Citation:F. Zhou, J. Anderson and S. H. Low, "The Optimal Power Flow Operator: Theory and Computation," in IEEE Transactions on Control of Network Systems, vol. 8, no. 2, pp. 1010-1022, June 2021, doi: 10.1109/TCNS.2020.3044258
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104253
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Jul 2020 19:11
Last Modified:13 Sep 2021 22:51

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