The effect of nonlinearities on the response of asingle-machine-quasi-infinite busbar system

A single-machine quasi-infinite busbar power system is formulated taking into consideration quadratic and cubic nonlinearities. The model equation contains parametric (time-varying coefficients) and external (inhomogeneous terms) excitations. The method of multiple scales is used to approximate the response of the system to simultaneous principal parametric resonances and subharmonic resonances of order one-half. In contrast with the linear analysis, the nonlinear analysis shows that the response can exhibit: (1) limit cycles instead of infinite motions; (2) multivaluedness that can lead to jumps; (3) subcritical instabilities; and (4) constructive and destructive interference of resonances