The paper presents a nonlinear state-space model of a self-excited induction generator. A systematic methodology is then proposed to compute all the possible operating points and the eigenvalues of the linearized system around the operating points. In addition to a zero equilibrium, one or two operating points are typically found possible. In the first case, the zero equilibrium is unstable, resulting in spontaneous transition to the stable nonzero operating point. In the second case, the smaller of the nonzero operating points is unstable, so that only one stable operating point exists. However, the unstable operating point creates a barrier that must be overcome through triggering. The paper concludes with numerical examples and experiments illustrating the application of the theoretical results.