Oscillatory solutions of a model system of nonlinear swing equations

Abstract Oscillatory solutions of augmented swing equations are studied. Recent work of Abed and Varaiya on the loss of stability of solutions of augmented swing equations via Hopf bifurcation is extended — particularly the case of two armatures with no infinite bus connected by a lossy transmission line. Precise details of the Hopf bifurcation are obtained, and in particular a closed expression for the parameter that determines the stability of the bifurcating solutions is obtained. For certain parameter values, stable bifurcating solutions exist. With other mathematical methods (averaging) completely different (and evidently more physically relevant) oscillatory solutions are studied. With a combination of analytic and numerical methods, a fairly completely picture of the dynamics is obtained.