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Time delay in the swing equation: A variety of bifurcations

Scholl, Tessina H. 1; Gröll, Lutz 1; Hagenmeyer, Veit 1
1 Institut für Automation und angewandte Informatik (IAI), Karlsruher Institut für Technologie (KIT)


The present paper addresses the swing equation with additional delayed damping as an example for pendulumlike systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased. To this end, a general formula for the first Lyapunov coefficient in second order systems with additional delayed damping and delay-free nonlinearity is given. Insofar, the paper extends the results about the stability switching of equilibria in linear time delay systems from Cooke and Grossman. In addition to the analytical results, periodic solutions are numerically dealt with. The numerical results demonstrate how a variety of qualitative behaviors are generated in the simple swing equation by only introducing time delay in a damping term.

DOI: 10.1063/1.5122784
Zitationen: 7
Web of Science
Zitationen: 5
Zitationen: 9
Zugehörige Institution(en) am KIT Institut für Automation und angewandte Informatik (IAI)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 12.2019
Sprache Englisch
Identifikator ISSN: 1054-1500, 1089-7682
KITopen-ID: 1000104293
HGF-Programm 37.06.01 (POF III, LK 01) Networks and Storage Integration
Erschienen in Chaos
Verlag American Institute of Physics (AIP)
Band 29
Heft 12
Seiten Article: 123118
Schlagwörter swing equation, pendulum equation, time delay, retarded functional differential equation, delayed damping, power system stability, first Lyapunov coefficient, bifurcation analysis, Hopf bifurcation, limit cycles
Nachgewiesen in Web of Science
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