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This paper proposes the application of fuzzy sliding mode controller for grid-connected voltage-sourced inverters (VSIs) under unbalanced network conditions. To realize this control scheme, sliding mode controller (SMC) is modified by adding fuzzy function to determine reference components of the VSI voltage in the stationary reference frame. Integration of fuzzy function into SMC achieves several advantages including suppression of chattering phenomenon, high tracking precision, and desirable robustness to uncertainties. Moreover, this control strategy requires neither phase locked loop function (PLL) nor synchronous coordinate transformation, which results in simple implementation. Simulation results for two cases of unbalanced grid voltages including non-identical amplitudes and unbalanced phase angles for three phase voltages are presented. The VSI is first controlled by modified SMC with power compensation feedbacks and then by fuzzy SMC. The results confirm that in comparison with modified SMC with power compensation feedbacks, employing fuzzy SMC not only leads to remarkable reduction of active and reactive power pulsations, but also decreases total harmonic distortion of the grid currents. IMPROVING THE PERFORMANCE OF GRID-CONNECTED VOLTAGE-SOURCED INVERTERS UNDER UNBALANCED NETWORK CONDITIONS USING A FUZZY SLIDING MODE- BASED APPROACH