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The three-phase grid-connected inverter system with LCL filter bears lower stability due to the characteristic of gaining peak at its resonance, and the distortion of grid voltage will cause grid-connected current. To address these problem, this paper adopts the method of applying capacitor current feedback to increase system damping and restrain the peak of resonance, in which the value of the capacitor current can be obtained through estimation, aiming to avoid increasing the extra sensors, then adopts the grid voltages feedforward scheme to eliminate the influences of the distorted grid voltage, and finally proposes the feedforward function of the grid voltage of a three-phase grid-connected inverter with an LCL filter in the stationary α-β frame. Simulation and experimental results show that it is effective that the method described in this paper.