A Voltage Sourced Inverter (VSI) intended to inject active power to the grid is presented. The VSI is designed with an LCL output filter. This objective is done by means of a sliding mode control, which is a widely used technique to control systems where a fast dynamic response, robustness and accuracy are required. However, variable switching frequency appears when the sliding mode control is implemented with a fixed-band hysteretic modulator, and consequently, a ripple current is spread all over the bandwidth. This leads to a cumbersome output system filter design. In addition, sensitivity to switching interferences between phases appear in three-phase systems. A solution to these limitations is proposed by means of a current sliding mode control where feedforward variables to create a variable hysteresis envelope are used. The surface derivation and principle of decoupling between phased is presented in this paper, furthermore, an analysis of frequency stabilization method and simulation results are shown.