We are interested in this paper on the control of an electromechanical system consisting of a doubly-fed induction generator, driven by a prime mover that can supply or extract mechanical power, e.g., a flywheel inertia, and an induction motor. The stator of the induction machine is connected to the stator of the generator whose rotor voltage is regulated by a bidirectional converter. The main interest of this configuration is that it permits a bidirectional power flow between the motor, which may operate in regenerative mode, and the generator. We propose a passivity-based controller to regulate the motor mechanical speed. Since this kind of controllers achieve stabilization via energy-balancing, regulation of the power flow in the system is naturally incorporated. Simulation results are presented to illustrate the main points of our paper.