Please use this identifier to cite or link to this item: http://localhost/handle/Hannan/717001
Title: Convexity of Solvability Set of Power Distribution Networks
Other Titles: IEEE Control Systems Letters
Authors: Anatoly Dymarsky|Konstantin Turitsyn
subject: power systems|Algebraic/geometric methods
Year: -1-Uns- -1
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 <inline-formula xmlns:mml= http://www.w3.org/1998/Math/MathML xmlns:xlink= http://www.w3.org/1999/xlink ><tex-math notation= LaTeX >$r/x$</tex-math></inline-formula> 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.
URI: http://localhost/handle/Hannan/717001
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Appears in Collections:New Ieee 2019

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Title: Convexity of Solvability Set of Power Distribution Networks
Other Titles: IEEE Control Systems Letters
Authors: Anatoly Dymarsky|Konstantin Turitsyn
subject: power systems|Algebraic/geometric methods
Year: -1-Uns- -1
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 <inline-formula xmlns:mml= http://www.w3.org/1998/Math/MathML xmlns:xlink= http://www.w3.org/1999/xlink ><tex-math notation= LaTeX >$r/x$</tex-math></inline-formula> 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.
URI: http://localhost/handle/Hannan/717001
ISBN: 
volume: Volume
issue: Issue
Appears in Collections:New Ieee 2019

Files in This Item:
File Description SizeFormat 
08502879.pdf520.76 kBAdobe PDFThumbnail
Preview File
Title: Convexity of Solvability Set of Power Distribution Networks
Other Titles: IEEE Control Systems Letters
Authors: Anatoly Dymarsky|Konstantin Turitsyn
subject: power systems|Algebraic/geometric methods
Year: -1-Uns- -1
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 <inline-formula xmlns:mml= http://www.w3.org/1998/Math/MathML xmlns:xlink= http://www.w3.org/1999/xlink ><tex-math notation= LaTeX >$r/x$</tex-math></inline-formula> 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.
URI: http://localhost/handle/Hannan/717001
ISBN: 
volume: Volume
issue: Issue
Appears in Collections:New Ieee 2019

Files in This Item:
File Description SizeFormat 
08502879.pdf520.76 kBAdobe PDFThumbnail
Preview File