Power Electronics has been widely employed in many industrial areas: transportation, electrical energy conversion and distribution and power systems. Recently, the attention towards the dc grids has increased, due to the possible advantages in terms of efficiency gain due to the direct connection of power electronics without the ac-dc conversion stage. Solid state transformers are an attractive solution to enable the dc connectivity both for the medium-and low-voltage grids and to provide at the same time additional services to the ac grid. Given that the dc grids are usually power electronics comminated, a good control of the dc buses is envisaged in addition to a good grid current control. This paper shows how a full-predictive current/voltage control for the medium voltage dc-ac converter and the dc-dc converter of a three-stage solid state transformer can offer good performance in the dc bus regulation and outperforms the conventional current control methods for the grid current control.