*Self-excited Induction generators are widely-spread in autonomous electrical power generating systems and do not need external power sources for their excitation. Thus generated voltage magnitude and frequency values depend on the rotor angular speed, value of load and the value of excitation capacitors. That is why for the design of new generating systems with self-excited induction generators it is necessary to obtain its self-excitation boundaries. The self-excited induction generator is a complex nonlinear system. A necessary condition for obtaining a reliable mathematical description of the processes of electromechanical energy conversion in autonomous generation systems is the inclusion of the magnetic system saturation of self-excited induction generator. The aim of the work is to obtain a mathematical description of the processes of electromechanical energy conversion in self-excited induction generator without using the experimental idling characteristic. The paper proposes a method for taking into account the saturation of the magnetic system of the generator by using the approximated dependence of the magnetization curve in relative units obtained for a generator of a similar series for identical phase voltages. The paper compares the results of calculating the self-excitation boundaries for an induction generator with a power of 5.5 kW when operating without load and with two values of the active load. In the first case, a mathematical model was used, using the experimentally-sampled idle speed characteristic of this generator. The second series of calculations were carried out using an approximated magnetization curve of self-excited induction generator with a power of 0.37 kW with conversion to relative units. Comparison of the results shows a high accuracy of coincidence of the self-excitation boundaries. The error increases somewhat with the increase in the active load admittance. This approach avoids the experimental determination of characteristics for a wide range of generators. *

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