Minimum Recovery Time Transients for Three-Phase Converters in the Synchronous Reference Frame

Three-phase pulsewidth-modulated converters require closed-loop controllers to meet the performance requirements and to achieve reliable responses over the entire operating range. Conventionally, by using the synchronous reference frame (SRF) representation, different linear and nonlinear control strategies have been proposed to improve the converter's dynamic performance. However, the achieved improvements cannot be objectively assessed due to the absence of a performance limit standard reference of the converter's dynamics. In this article, the theoretical minimum time solutions for three-phase converters in the SRF are derived and analyzed, providing an objective reference point for the system's dynamic performance evaluation. The normalized dynamic model of the converter in the SRF is derived and combined with the time-optimal control principle to find the theoretical minimum transient time solutions. The state-plane representation of these minimum time responses enables a straightforward and comprehensive interpretation of the converter's dynamic behavior, and it simplifies the derivation of closed-form expressions that characterize the minimum time transient parameters. The introduced analysis, minimum time dynamic responses, derived transient's expressions, and dynamic performance evaluation are validated by simulation and experimental results.