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- Publisher Website: 10.1109/TCSI.2019.2929180
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Article: On extension of effective resistance with application to graph Laplacian definiteness and power network stability
Title | On extension of effective resistance with application to graph Laplacian definiteness and power network stability |
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Authors | |
Keywords | Effective resistance Signed graph Laplacian matrix Power network Stability |
Issue Date | 2019 |
Publisher | IEEE. The Journal's web site is located at https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919 |
Citation | IEEE Transactions on Circuits and Systems I: Regular Papers, 2019, v. 66 n. 11, p. 4415-4428 How to Cite? |
Abstract | This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the traditional definitions that only apply to a pair of nodes. The monotonicity and convexity properties are preserved by the extended definitions. The extended definitions provide new insights into graph Laplacian definiteness and power network stability. It is proved that the Laplacian matrix of a signed graph is positive semi-definite with only one zero eigenvalue if and only if the effective conductances between some specific pairs of node sets are positive. Also, the number of Laplacian negative eigenvalues is upper bounded by the number of negative weighted edges. In addition, new conditions for the small-disturbance angle stability, hyperbolicity, and type of power system equilibria are established, which intuitively interpret angle instability as the electrical antagonism between certain two sets of nodes in the defined active power flow graph. Moreover, a novel optimal power flow (OPF) model with effective conductance constraints is formulated, which significantly enhances power system transient stability. By the properties of extended effective conductance, the proposed OPF model admits a convex relaxation representation that achieves global optimality. |
Persistent Identifier | http://hdl.handle.net/10722/272185 |
ISSN | 2023 Impact Factor: 5.2 2023 SCImago Journal Rankings: 1.836 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Song, Y | - |
dc.contributor.author | Hill, DJ | - |
dc.contributor.author | Liu, T | - |
dc.date.accessioned | 2019-07-20T10:37:20Z | - |
dc.date.available | 2019-07-20T10:37:20Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | IEEE Transactions on Circuits and Systems I: Regular Papers, 2019, v. 66 n. 11, p. 4415-4428 | - |
dc.identifier.issn | 1549-8328 | - |
dc.identifier.uri | http://hdl.handle.net/10722/272185 | - |
dc.description.abstract | This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the traditional definitions that only apply to a pair of nodes. The monotonicity and convexity properties are preserved by the extended definitions. The extended definitions provide new insights into graph Laplacian definiteness and power network stability. It is proved that the Laplacian matrix of a signed graph is positive semi-definite with only one zero eigenvalue if and only if the effective conductances between some specific pairs of node sets are positive. Also, the number of Laplacian negative eigenvalues is upper bounded by the number of negative weighted edges. In addition, new conditions for the small-disturbance angle stability, hyperbolicity, and type of power system equilibria are established, which intuitively interpret angle instability as the electrical antagonism between certain two sets of nodes in the defined active power flow graph. Moreover, a novel optimal power flow (OPF) model with effective conductance constraints is formulated, which significantly enhances power system transient stability. By the properties of extended effective conductance, the proposed OPF model admits a convex relaxation representation that achieves global optimality. | - |
dc.language | eng | - |
dc.publisher | IEEE. The Journal's web site is located at https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919 | - |
dc.relation.ispartof | IEEE Transactions on Circuits and Systems I: Regular Papers | - |
dc.subject | Effective resistance | - |
dc.subject | Signed graph | - |
dc.subject | Laplacian matrix | - |
dc.subject | Power network | - |
dc.subject | Stability | - |
dc.title | On extension of effective resistance with application to graph Laplacian definiteness and power network stability | - |
dc.type | Article | - |
dc.identifier.email | Song, Y: songyue@hku.hk | - |
dc.identifier.email | Hill, DJ: dhill@eee.hku.hk | - |
dc.identifier.email | Liu, T: taoliu@eee.hku.hk | - |
dc.identifier.authority | Hill, DJ=rp01669 | - |
dc.identifier.authority | Liu, T=rp02045 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1109/TCSI.2019.2929180 | - |
dc.identifier.scopus | eid_2-s2.0-85077472093 | - |
dc.identifier.hkuros | 299180 | - |
dc.identifier.volume | 66 | - |
dc.identifier.issue | 11 | - |
dc.identifier.spage | 4415 | - |
dc.identifier.epage | 4428 | - |
dc.identifier.isi | WOS:000494680200028 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 1549-8328 | - |