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Published June 2021 | Submitted + Accepted Version
Journal Article Open

The Optimal Power Flow Operator: Theory and Computation


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.

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.

Attached Files

Accepted Version - 09292090.pdf

Submitted - 1907.02219.pdf


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August 20, 2023
October 20, 2023