$H_{\infty }$ Active Damping Filter Design for LCL-Type Grid-Tied Inverter Under Additive and Multiplicative Perturbations

Filter-based active damping (AD) is an effective method to solve the resonance problem of
LCL
filter in grid-tied inverters as it is easy to implement and does not require additional sensors. However, parameter uncertainties and grid impedance variations may lead to the damping failure and challenge the stability of the grid-tied inverter. Therefore, this article proposes
$H_{\infty }$
AD filter design for
LCL
-type grid-tied inverter under additive and multiplicative perturbations. First, the
$H_{\infty }$
robust control mechanisms of additive and multiplicative perturbations are shown, and then the design procedures and characteristics analysis of the AD filters are presented. Second, the essence of the stability robustness of the
$H_{\infty }$
AD filter systems is found to come from the phase delay. The phase delay can be compensated by the phase lead compensator in the modified repetitive controller to ensure the stability of the grid-tied inverter. Moreover, this article explores the positive effective of the control action weight function introduced in multiplicative perturbation AD filter. Finally, the stability robustness of the design AD filters is verified on a 2-kW single-phase grid-tied inverter prototype.