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On Semidefiniteness of Signed Laplacians with Application to Microgrids
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
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2016 (English)In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 49, no 22, p. 97-102Article in journal (Refereed) Published
Abstract [en]

The paper investigates the positive semidefiniteness of signed Laplacians. It is noted that a symmetric signed Laplacian defines a unique resistive electrical network, wherein the negative weights correspond to negative resistances. As such, the positive semidefiniteness of the signed Laplacians is equivalent to the passivity of the associated resistive networks. By utilizing n-port circuit theory, we obtain several equivalent conditions for signed Laplacians to be positive semidefinite with a simple zero eigenvalue. These conditions characterize a set of negative weights that maintain the semidefiniteness of the Laplacian. The results are used to analyze the small-disturbance angle stability of microgrids as an application.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 49, no 22, p. 97-102
Keywords [en]
Circuit theory, Eigenvalues and eigenfunctions, Angle stability, Electrical networks, Equivalent condition, Positive semidefinite, Positive semidefiniteness, Resistive network, Semidefiniteness, Small disturbances, Laplace transforms
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-201803DOI: 10.1016/j.ifacol.2016.10.379Scopus ID: 2-s2.0-84994121128OAI: oai:DiVA.org:kth-201803DiVA, id: diva2:1075174
Note

QC 20170217

Available from: 2017-02-17 Created: 2017-02-17 Last updated: 2017-06-13Bibliographically approved

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