Chaotic motions in the two-degree-of-freedom swing equations

We analyze chaotic motions occurring on certain energy surfaces of the conservative two-degree-of-freedom (three-machine) swing equations used as models in transient stability analysis of electric power systems, and we note the implications of this chaotic behavior for first swing stability predictions using these equations. In the particular parameter range chosen for study the swing equations may be thought of as a perturbation of the equations of a forced oscillator; the parameter range bears the same relation to the general swing equations as does a special case of the restricted three body problem to the equations of motion of celestial mechanics. We also give a simplification of Melnikov's method for detecting chaotic motions which may prove useful in other examples.