This paper presents an analytical closed-form mathematical model and analysis of the influence of the DC-bus ripple voltage of the three-phase voltage source inverter (VSI) with the space-vector PWM (SVPWM) on the induction machine phase voltages, currents and torque pulsations. The analytical expressions for the voltage and current space-vectors as a function of the dc-bus voltage pulsation are derived. Using superposition we can determine the separate parts of the motor currents. Next, it is shown, that dc-link voltage ripple components may cause large torque pulsation. The proposed analytical method is based on the mixed p-z approach, enabling presentation of the results in lucid and closed-form. To verify the effectiveness of the proposed analytical model, experimental results based on laboratory setup were obtained.

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A new method for time-domain analysis of power converters with periodic pulsewidth modulation (PWM) is developed. The method is based on a mixed p-z description of linear periodic time-varying system. The basic of the model is explained in DC-DC converters with periodical PWM. Next, two applications of the model are shown. First, the model was used for the analysis of three-phase voltage source inverters with a space-vector PWM feeding a three-phase R-L load. Second, the same analysis has been used for the single-phase voltage source inverters with periodic PWM. But it is shown that the model is applicable for all types of converters with an explicitly determined output voltage (converters with forced commutation). The mathematical model uses the Laplace and modified -transforms. The solution is not dependent on the number of the pulses of the PWM pattern. Instead of solution of algebraic equations, the change of switching instants is reflected in the solution only by a change in two valuesand . All results were visualized from the derived equations by the program MathCAD. The derived equations are validated using a 3-kW three-phase inverter.Index Terms-Analytical model, modified -transform, pulsewidth modulation (PWM), switched network, voltage source inverter (VSI).

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