Nonlinear analysis of a single-machine-quasi-infinite-busbar system

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 decreasing the frequency of excitation, it is shown that oscillatory solutions (limit-cycles) lose their stability through a series of period-doubling bifurcations leading to chaos and unbounded motions (pole-slippage). A second-order approximate solution that improves on the accuracy of the solution given by A.M.A. Hamdan and A.H. Nayfeh (Trans. on Power Systems, vol.4, p.843-9, 1989) is described. The solution accounts for the frequency shift caused by the excitation. The loss of stability of the second-order solution, which is a precursor to chaos and unbounded motions, agrees fairly well with the numerical simulations