This paper presents a hydrogen powered hybrid solid oxide fuel cell-steam turbine (SOFC-ST) system and studies its optimal operating conditions. This type of installation can be very appropriate to complement the intermittent generation of renewable energies, such as wind generation. A dynamic model of an alternative hybrid SOFC-ST configuration that is especially suited to work with hydrogen is developed. The proposed system recuperates the waste heat of the high temperature fuel cell, to feed a bottoming cycle (BC) based on a steam turbine (ST). In order to optimize the behavior and performance of the system, a two-level control structure is proposed. Two controllers have been implemented for the stack temperature and fuel utilization factor. An upper supervisor generates optimal set-points in order to reach a maximal hydrogen efficiency. The simulation results obtained show that the proposed system allows one to reach high efficiencies at rated power levels.