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This paper studies the performance of the Back to Back converter to control the power flow between two interconnected AC systems under unbalance grid voltage and voltage sag conditions. The first one system is considered the electrical grid, and the second one a Double Feed Induction Generator. To maintain the power transference under these disturbances a control-block diagram based on a decupled control strategy is proposed. The control strategy is performed using the single-phase dq transformation. In the study, the behavior of the BTB converter in the linear region, as well as the analysis of the DC link stage and the active/reactive power flow are presented. The operation of the controlled BTB converter is evaluated through simulations by using a 3KVA prototype. Results show the control-block diagram proposed is a suitable option to maintain the power transference under unbalance grid voltage and voltage sag conditions.