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An LCL-type filter is widely used in the grid-connected inverter. However, with only injected grid current control, the current harmonics and low bandwidth caused by the resonance peak cannot be tolerated. The active damping (AD) method with an extra feedback provides a high rejection of the resonance so that the dynamic is improved; however, the high-precision sensing circuit for the extra feedback increases the cost. In this paper, with the signal flow graph and response-fitting methods, an AD method based on the feedback of the injected grid current has been proposed. Then, the novel closed-loop current control requires accurately sensing the injected grid current only, while no observation is needed. Compared with the extra feedback methods, the cost and the complexity are reduced while the reliability is improved. Based on the study of the relation between the controller and the system dynamic, a straightforward design has been proposed. The robustness, harmonic rejection, and digital implementation have been studied. Compared with the conventional control methods, the proposed one promises the satisfactory performance with both analog and digital implementations. Simulations and experiments have verified the proposed control and design strategies. [ABSTRACT FROM PUBLISHER]