This paper proposes a control structure of SST (Solid-state-transformer), which consists of MMC (Modular Multi-level Converter) based AC/DC converters and isolated DC/DC converters, to reduce the size of capacitors. The phase separated configuration requires a high capacitance needed for smoothing capacitors due to instantaneous power oscillation at the double line frequency. This paper proposes an improved method to control the DC/DC converter to achieve synchronous instantaneous power with the AC/DC converter so that the double line frequency component applied to the capacitors between the AC/DC and DC/DC converters is cancelled. This paper also proposes a control method to cancel the oscillating instantaneous power caused by unbalanced load current. The proposed control techniques were demonstrated in a 6-kVA laboratory prototype. The possible loss increase in the isolated DC/DC converter by the proposed control is also discussed.