Mixed p-z approach for time-domain analysis of voltage source inverters with periodic pulsewidth modulation

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 Z-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 values m_k and n_k. All results were visualized from the derived equations by the program MathCAD. The derived equations are validated using a 3-kW three-phase inverter.