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The Optimal Power Flow Operator: Theory and Computation

Zhou, Fengyu and Anderson, James and Low, Steven H. (2019) The Optimal Power Flow Operator: Theory and Computation. . (Unpublished)

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Optimal power flow problems (OPFs) are mathematical programs used to determine how to distribute power over networks subject to network operation constraints and the physics of power flows. In this work, we take the view of treating an OPF problem as an operator which maps user demand to generated power, and allow the network parameters (such as generator and power flow limits) to take values in some admissible set. The contributions of this paper are to 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. In contrast to related results in the optimization literature, we do not rely on introducing auxiliary slack variables. Indeed, our approach provides results that have a clear interpretation with respect to the power network under study. 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. Our framework of treating a mathematical program as an operator allows us to pose sensitivity and robustness questions from a completely different mathematical perspective and provide new insights into well studied problems.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Zhou, Fengyu0000-0002-2639-6491
Anderson, James0000-0002-2832-8396
Low, Steven H.0000-0001-6476-3048
Additional Information:This work was funded by NSF grants CCF 1637598, CPS 1739355, and ECCS 1619352, PNNL grant 424858, ARPA-E NODES through grant dear0000699, and through the ARPA-E GRID DATA program.
Funding AgencyGrant Number
Battelle Memorial Institute424858
Advanced Research Projects Agency-Energy (ARPA-E)DE-AR0000699
Subject Keywords:Analysis, optimal power flow, linear programming
Record Number:CaltechAUTHORS:20200707-114446351
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104253
Deposited By: Tony Diaz
Deposited On:07 Jul 2020 19:11
Last Modified:07 Jul 2020 19:11

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