Abstract
The response of a single-machine quasi-infinite busbar system to the simultaneous occurrence of principal parametric resonance and subharmonic resonance of order one-half is investigated. By numerical simulations we show the existence of oscillatory solutions (limit cycles), period-doubling bifurcations, chaos, and unbounded motions (loss of synchronism). The method of multiple scales is used to derive a second-order analytical solution that predicts (a) the onset of period-doubling bifurcations, which is a precursor to chaos and unbounded motions (loss of synchronism), and (b) saddle-node bifurcations, which may be precursors to loss of synchronism.
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Nayfeh, M.A., Hamdan, A.M.A. & Nayfeh, A.H. Chaos and instability in a power system: Subharmonic-resonant case. Nonlinear Dyn 2, 53–72 (1991). https://doi.org/10.1007/BF00045055
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DOI: https://doi.org/10.1007/BF00045055