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Spectral Analysis of Synchronization in a Lossless Structure-Preserving Power Network Model


F. Dörfler, F. Bullo

IEEE International Conference on Smart Grid Communications, Gaithersburg, Maryland, USA, pp. 179-184

This paper considers the synchronization and transient stability analysis in a simple model of a structure-preserving power system. We derive sufficient conditions relating synchronization in a power network directly to the underlying network state, parameters, and topology. In particular, we provide a spectral condition based on the algebraic connectivity of the network and a second condition based on the effective resistance among generators. These conditions build upon the authors’ earlier results on synchronization in network-reduced power system models. Central to our analysis is the reduced admittance matrix of the network, which is obtained by a Schur complement of the network’s topological admittance matrix with respect to its bus nodes. This network-reduction process, termed Kron reduction, relates the structure-preserving and the networkreduced power system model. We provide a detailed graphtheoretic, algebraic, and spectral analysis of the Kron reduction process leading directly to the novel synchronization conditions.


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% Autogenerated BibTeX entry
@InProceedings { D_rBul:2010:IFA_4919,
    author={F. D{\"o}rfler and F. Bullo},
    title={{Spectral Analysis of Synchronization in a Lossless
	  Structure-Preserving Power Network Model}},
    booktitle={IEEE International Conference on Smart Grid Communications},
    address={Gaithersburg, Maryland, USA},
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