Characterization of the Minimum Recovery Time Transients for Three-Phase PWM Rectifiers

Three-phase Pulse Width Modulated (PWM) rectifiers are used in a large number of applications since they can provide sinusoidal AC currents and regulate the DC-link voltage. In order to guarantee safe and reliable operation, closed-loop controllers must be implemented. Traditionally, dual-loop controllers in the synchronous reference frame (SRF) are employed. Therefore, the dynamic transient response of the system is limited and it is highly determined by the control design. Due to the limitations of linear compensators, advanced control methods have been developed to improved the system’s dynamics. However, these improvements cannot be easily evaluated and compared due to the absence of an objective tool to evaluate the system performance. In this work, the minimum recovery time transient for the three-phase rectifier in the synchronous reference frame is analyzed. In this way, these transients can be used as a theoretical limit to evaluate the dynamic performance of the converter. First, the large-signal model of the converter is developed in the SRF and described in a normalized domain to obtain general expressions valid for any combination of converter’s parameters. This model enables a graphical representation of the system’s dynamics, describing the natural evolution of the state-variables in a simple manner. In this way, the operating point is represented as circular trajectories in the geometric plane with well defined parameters. The concepts of time optimal control are applied to achieve minimum time solutions by using only the saturation limits of the control input during transients. By represented the theoretical minimum time responses in the geometric plane, the transient’s parameters can be completely analyzed and closed-form equations can be derived. Hardware-in-the-Loop results are provided to validate the theoretical analysis.