Even though the modular multilevel cascaded converter with single-delta bridge-cell (MMCC-SDBC or SDBC) has been widely discussed for static synchronous compensators (STATCOM), it is basically for the reactive power compensation. In order to simultaneously compensate for the reactive power and regulate the active power, this article integrates the SDBC based STATCOM with one single-phase converter through one medium-frequency transformer operating at three times the fundamental frequency. This article especially focuses on the operation of the developed system under unbalanced grid conditions because it is relatively critical compared with the SDBC based STATCOM. Generally, the circulating current is controlled within the SDBC to address the unbalanced operation, but the considerable magnetizing inductance makes the developed system almost impossible to fulfill this control requirement. In this article, however, it is fortunately found that the task of circulating current control can be shifted to the single-phase converter so that the influence of the medium-frequency transformer is greatly reduced. Experimental results are provided to confirm the effectiveness of the proposed control method and the feasibility of the developed system under unbalanced grid conditions, namely, the low-voltage ride-through (LVRT) operation.