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Hierarchical spectral clustering of power grids

Hierarchical spectral clustering of power grids
Hierarchical spectral clustering of power grids
A power transmission system can be represented by a network with nodes and links representing buses and electrical transmission lines, respectively. Each line can be given a weight, representing some electrical property of the line, such as line admittance or average power flow at a given time. We use a hierarchical spectral clustering methodology to reveal the internal connectivity structure of such a network. Spectral clustering uses the eigenvalues and eigenvectors of a matrix associated to the network, it is computationally very efficient, and it works for any choice of weights. When using line admittances, it reveals the static internal connectivity structure of the underlying network, while using power flows highlights islands with minimal power flow disruption, and thus it naturally relates to controlled islanding. Our methodology goes beyond the standard k-means algorithm by instead representing the complete network substructure as a dendrogram. We provide a thorough theoretical justification of the use of spectral clustering in power systems, and we include the results of our methodology for several test systems of small, medium and large size, including a model of the Great Britain transmission network.
clustering, power system analysis computing
0885-8950
1-9
Sanchez-Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Fennelly, Max
a04ae0e5-8945-40e5-bdab-c0fe765b5d54
Norris, Sean
e046c8ac-4cef-4763-adaf-1c647962088a
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Bialek, Janusz
9ebf1d00-97d0-4383-951c-6f27a7aef767
Sanchez-Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Fennelly, Max
a04ae0e5-8945-40e5-bdab-c0fe765b5d54
Norris, Sean
e046c8ac-4cef-4763-adaf-1c647962088a
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Bialek, Janusz
9ebf1d00-97d0-4383-951c-6f27a7aef767

Sanchez-Garcia, Ruben, Fennelly, Max, Norris, Sean, Wright, Nick, Niblo, Graham, Brodzki, Jacek and Bialek, Janusz (2014) Hierarchical spectral clustering of power grids. IEEE Transactions on Power Systems, 1-9. (doi:10.1109/TPWRS.2014.2306756).

Record type: Article

Abstract

A power transmission system can be represented by a network with nodes and links representing buses and electrical transmission lines, respectively. Each line can be given a weight, representing some electrical property of the line, such as line admittance or average power flow at a given time. We use a hierarchical spectral clustering methodology to reveal the internal connectivity structure of such a network. Spectral clustering uses the eigenvalues and eigenvectors of a matrix associated to the network, it is computationally very efficient, and it works for any choice of weights. When using line admittances, it reveals the static internal connectivity structure of the underlying network, while using power flows highlights islands with minimal power flow disruption, and thus it naturally relates to controlled islanding. Our methodology goes beyond the standard k-means algorithm by instead representing the complete network substructure as a dendrogram. We provide a thorough theoretical justification of the use of spectral clustering in power systems, and we include the results of our methodology for several test systems of small, medium and large size, including a model of the Great Britain transmission network.

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TPWRS2306756.pdf - Version of Record
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More information

Accepted/In Press date: 9 February 2014
e-pub ahead of print date: 17 March 2014
Published date: September 2014
Keywords: clustering, power system analysis computing
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 363140
URI: https://eprints.soton.ac.uk/id/eprint/363140
ISSN: 0885-8950
PURE UUID: 6aef0ac2-9f4e-495f-a550-cf853a2d15ca
ORCID for Ruben Sanchez-Garcia: ORCID iD orcid.org/0000-0001-6479-3028
ORCID for Nick Wright: ORCID iD orcid.org/0000-0003-4884-2576
ORCID for Graham Niblo: ORCID iD orcid.org/0000-0003-0648-7027

Catalogue record

Date deposited: 20 Mar 2014 16:18
Last modified: 03 Dec 2019 02:03

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