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This paper presents a new sliding mode current control (SMCC) of three-phase grid-connected voltage source converters (VSCs). The proposed SMCC strategy employs a nonlinear sliding mode control scheme to directly calculate the required converter control voltage so as to eliminate the line current errors in the stationary reference frame without involving any synchronous coordinate transformation. Constant converter switching frequency is achieved by using space vector modulation (SVM) which eases the design of the ac harmonic filter. Simulation results on a 3 kVA grid-connected VSC system are provided to validate the feasibility of the proposed SMCC strategy during normal and faulted grid voltage conditions.