The application of the induction electrical generator instead of the synchronous ones in the self-contained power diesel-generating plants is known to have a number of advantages. The induction generator is a simple and reliable non-contact electrical machine. The symmetric rotor possesses perfect damping features being of great importance with the asymmetric load. When operating with the frequency converter (amplifier) the generator is not loaded with the highest harmonics which makes it possible to lower the dimensions power by a factor of 1.5-2. The capacitor system is considered to be the simplest one among the available systems for voltage excitation and control. The paper considers the mathematical model of the two-phase induction machine. The model regards the residual magnetization of the magnetic circuit as well as its saturation in the nominal conditions. This makes it possible to model the self-excitation conditions, to plot the load excitation conditions, to plot the load characteristics with the varying saturation range.The type of control of the generator output voltage value through the change in the rotation frequency is considered. This type is possible when the consumer admits the frequency variation in the supply voltage over some range. Another type of the voltage control is the one through the change in the capacitance value of the capacitor battery in the excitation circuit. The type of the phase control of the excitation capacitance current value is considered. The distortions of the sinusoidal output voltage waveform are analyzed in this case. Static and dynamic load characteristics with the step change of the load are provided for each of the above cases. The results of the modeling are compared with the experimental investigations on the basis of the physical model. Some considerations concerning the design of the diesel-generating plants with the induction generators are presented.