Analytic conditions for spontaneous self-excitation in induction generators

Spontaneous self-excitation in induction generators is a fascinating phenomenon triggered by the instability of a zero equilibrium state. Prediction of this condition for various values of free parameters requires many computations of the eigenvalues of a 6 × 6 matrix over a large space. The paper uses a novel approach to derive analytic conditions and predict precisely when instabilities occur. The formulas give the values of the minimum load resistance, the range of capacitor values, and the range of speeds for which spontaneous self-excitation appears. The paper concludes with an illustration of the theoretical results on an example.