Convexity of Solvability Set of Power Distribution Networks
Name
1803.11197v1.pdf
Description
Accepted version
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591.8 KB
Format
Adobe PDF
Checksum (MD5)
ab3110728152dfb4d446165c59006838
Author(s)
Dymarsky, Anatoly
Turitsyn, Konstantin
Date Issued
January 2019
Journal
IEEE Control Systems Letters
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
A. Dymarsky and K. Turitsyn, "Convexity of Solvability Set of Power Distribution Networks," in IEEE Control Systems Letters, vol. 3, no. 1, pp. 222-227, Jan. 2019, doi: 10.1109/LCSYS.2018.2877442.
Version
Author's final manuscript
Abstract
The solvability set of a power network-the set of all power injection vectors for which the corresponding power flow equations admit a solution-is central to power systems stability and security, as well as to the tightness of optimal power flow relaxations. Whenever the solvability set is convex, this allows for substantial simplifications of various optimization and risk assessment algorithms. In this letter, we focus on the solvability set of power distribution networks and prove convexity of the full solvability set (real and reactive powers) for tree homogeneous networks with the same r/x ratio for all elements. We also show this result can not be improved: once the network is not homogeneous, the convexity is immediately lost. It is nevertheless the case that if the network is almost homogeneous, a substantial practically important part of the solvability set is still convex. Finally, we prove convexity of real solvability set (only real powers) for any tree network as well as for purely resistive networks with arbitrary topology.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-ShareAlike
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DOI of Published Version
https://doi.org/10.1109/lcsys.2018.2877442
