The influence of autoparametric resonances on the stability of power systems

Formulates the equations of a two-machine infinite busbar system as two nonlinearly coupled oscillators. The authors derive conditions for the existence of two-to-one and three-to-one internal resonances. As a result of the analysis, two sets of four first-order nonlinear differential equations are obtained for the modulation of the amplitudes and phases of the two modes. Six first-order equations describing the amplitudes and phases of three machines possessing a combination autoparametric resonance of the additive type are derived. A qualitative analysis of these equations gives useful information about the regions of instability and the nature of the solutions