Design of Multifrequency Proportional–Resonant Current Controllers for Voltage-Source Converters

In recent years, the applicability of multifrequency proportional–resonant (PR) current controllers has been extensively explored. The analysis and controller design are typically performed by means of frequency response methods. In this context, the open-loop system's gain crossover frequency and the associated phase margin are most commonly used as design parameters. However, those parameters are not well defined in applications with multifrequency PR controllers, where multiple 0-dB crossings of the open-loop gain emerge. In contrast, it is shown that the system's gain margin can mostly be utilized as a reliable stability measure. Furthermore, since each resonator introduces an unwanted phase lag to its higher neighbored resonator, the desired stability margin might not be achieved by “conventional” controller designs or the system could even be destabilized. Hence, this article reviews common analytic design guidelines for PR current controllers and extends them to controllers that implement multiple resonators in either a stationary frame or a synchronous reference frame. To achieve a good compromise between the stability margin and a small steady-state control error, a recursive adjustment procedure for the controller's integral gains is proposed. The “plug-and-play” controller design is applied to a grid-connected voltage-source converter and the theoretical findings are validated by computer simulations and experiments.