This study was interested in the management of an energy production unit. A variable speed wind turbine (VSWT) was used as a principal source and a supercapacitor (SC) module was used as an energy storage system. Both were connected through a direct current bus. This unit was supplying a three-phase load using an inverter and an inductor and capacitor filter. In order to regulate the direct current bus voltage, the SC storage state was controlled by using a buck-boost converter according to load instructions and wind speed fluctuations. Then, a resonant controller was established to avoid any disturbances and to control the alternating line-to-line voltages of the load which may be unbalanced. This study has shown that the stability of the three-phase voltage source depends on the direct current bus power management and also on the line-to-line voltage control. Simulation results are presented to validate the efficiency of the control strategies used.