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This paper presents two control strategies for a Single-Phase Back-to-Back (SPBTB) converter for control bidirectional power transfer based on the linear operating region of the topology. The control strategies presented allow an independent control of active/reactive power. The first scheme proposes to cancel the non-linear expressions associated to the linearized model. Therefore, it is obtained a suitable steady state and dynamic response of the system. The second control strategy uses a non-linear method that ensures a better response, since it does not linearize around a specific point, obtaining a global control law for the all operating region. The performance is verified with simulation and experimental results.