The main advantages of multi-winding (multiphase) induction machines include reducing torque ripple, decreasing rotor harmonics losses, reducing the current per phase without increasing the voltage per phase, reducing the current harmonics of the DC voltage source, and high fault tolerance. The authors propose a theoretical description for the harmonic content of the DC-link current, magnetomotive force, and electromagnetic torque of a multi-winding induction machine (IM), and an account of the interaction of the time harmonics for the power supply and the spatial harmonics for winding functions is presented. The proposed theoretical analysis has made it possible to substantiate supply-winding schemes for the compensation of higher harmonics (6th and 12th in the DC-link current and the IM’s electromagnetic torque) and the improvement of the electromagnetic and electromechanical compatibility of the multi-winding machine, which are justified according to the proposed theoretical description. Further, a schematic solution for the multi-winding induction motor with electronic changing of the pole number is proposed to provide a reduction in speed ripples at low rotation speeds. This decrease is ensured by increasing the number of pole pairs and increasing the frequency of the supply voltage. Mathematical models of multi-winding switch control-based induction machines are developed using the method of average voltages in the integration step for an investigation of electromagnetic and electromechanical processes. It is shown that the developed models are distinguished by high speed of response and accuracy. This is confirmed by the comparative analysis using known methods and models in the Matlab environment, as well as a comparison of the simulation results with the known results of physical experiments. The results of mathematical modeling show that the use of a multi-winding IM with appropriate supply-winding schemes stands to significantly reduce the ripples of the IM’s electromagnetic torque and DC-link current in the case of using six-step voltage source inverters. This makes this type of inverter suitable for use in a frequency-controlled electric drive as an alternative to using a PWM inverter, which has a negative influence on the IM’s state.