Abstract
We investigate some of the instabilities in a single-machine quasi-infinite busbar system. The system's behavior is described by the so-called swing equation, which is a nonlinear second-order ordinary-differential equation with additive and multiplicative harmonic terms having the frequency Ω. When Ω≈ω0, where ω0 is the linear natural frequency of the machine, we use digital-computer simulations to exhibit some of the complicated responses of the machine, including period-doubling bifurcations, chaotic motions, and unbounded motions (loss of synchronism). To predict the onset of these complicated behaviors, we use the method of multiple scales to develop an approximate first-order closed-form expression for the period-one responses of the machine. Then, we use various techniques to determine the stability of the analytical solutions. The analytically predicted period-one solutions and conditions for its instability are in good agreement with the digital-computer results.
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Nayfeh, M.A., Hamdan, A.M.A. & Nayfeh, A.H. Chaos and instability in a power system — Primary resonant case. Nonlinear Dyn 1, 313–339 (1990). https://doi.org/10.1007/BF01865278
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DOI: https://doi.org/10.1007/BF01865278