Smart grids are incessantly contemplating new challenges about power electronics technologies, and this paper focuses on the application of solid-state transformers (SSTs) and the forthcoming perspective of hybrid AC/DC grids. In such perspective, a multilevel bidirectional four-port (MB4P) DC-DC converter is proposed to be integrated in a three-phase SST. It interfaces the SST through three independently ports, corresponding to the three-phases, and the other port is used to create a DC grid. The proposed MB4P DC-DC converter has as main features a multilevel operation with seven voltage levels as function of the voltages on both DC sides, as well as the interleaved operation, where the controlled variables have a ripple with a frequency six times higher than the switching frequency. Furthermore, it can operate in buck or boost modes, and with current or voltage control. Besides the voltage and current control, specific attention is given to the proposed PWM. The advanced attributes of the MB4P DC-DC converter are proven by computer simulations and by analytical description, both exploring steady-state and transient-state distinctive requirements.