Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Synchronous solutions of power systems: existence, uniqueness and stability

Author: Sherwin J. Skar
Journal: Quart. Appl. Math. 38 (1980), 331-342
MSC: Primary 93D05; Secondary 34D05
DOI: https://doi.org/10.1090/qam/592200
MathSciNet review: 592200
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Abstract: This paper contains a study of the asymptotic stability and uniqueness of equilibrium solutions of multi-dimensional Hamiltonian-like systems. The results are applied to the swing equations, the classical model for power systems. By developing some results in matrix theory, it is shown that asymptotically stable equilibrium solutions may exist even though most rotor angle pairs are more than $ {90^ \circ }$, some even $ {180^ \circ }$, out of phase. In contrast to the numerical criteria usually used, an analytic criterion for the existence of asymptotically stable equilibrium solutions of the swing equations is given.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/592200
Article copyright: © Copyright 1980 American Mathematical Society

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