Direct evaluation for the output frequency and the magnetizing reactance of three-phase isolated self-excited induction generators

For an induction generator to be self excited a capacitor with a sufficient value has to be connected to its stator terminal. Under steady state conditions and for a given capacitor value, two unknowns have to be found to resolve the machine unknowns: the output frequency and the magnetizing reactance. Finding these two unknowns requires simultaneous solution of two high degree polynomials. Numerical techniques are usually involved. It is typical, however, for the induction generator to have a small but negative slip. This fact is used in this paper to derive simple approximate closed expressions for both the output frequency and the magnetizing reactance