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This paper presents a control scheme for full-scale back to back converter used for connecting the synchronous generator-based variable speed wind turbine to grid. The new control concept is based on the q-d reference modulation indices of the Discontinuous Pulse Width Modulation (DPWM) technique. The converter consists of a six-diode rectifier and a six-IGBT voltage source inverter with a dc-link in between. Modeling of the whole system is presented in PSCAD/EMTDC software and steady-state and fault conditions of the system are investigated. Results show that the controller can appropriately control the converter of the wind turbine system in steady-state and fault conditions.