A Comparison Between Real and Complex Harmonic Selective Repetitive Control Schemes with Improved Stability Characteristics

When designing the control system of grid-connected inverters, engineers are faced with the requirement of tracking periodic references and rejecting periodic disturbances. In applications where these exogenous signals have high harmonic content for a well-known family of harmonic components, e. g. $6k\pm 1$ or $4k\pm 1$, real or complex harmonic selective repetitive structures are highly indicated solutions to be used as controllers. In this sense, this paper presents a structural and performance comparison between the complex controller based on the generalized delayed signal cancellation method and the real $nk\pm m$ repetitive controller with improved stability characteristics. The comparison was validated through experimental results using a three-phase active power filter.