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The solid-state transformer (SST) is one of the key elements in power electronic-based microgrid systems. The single-phase SST consists of a modular multilevel ac-dc rectifier, a modular dual active bridge (DAB) dc-dc converter with high-frequency transformers, and a dc-ac inverter stage. However, due to dc bus voltage and power unbalancing in each module, the modular SST often presents instability problems making its design difficult and causing unpredictable behavior. Moreover, the unbalanced dc-link voltages increase the stress of the semiconductor devices, and also cause high harmonic distortions of grid current, therefore, necessitating the use of a bigger ac filter. This paper presents a novel single-phase d-q vector-based common-duty-ratio control method for the multilevel rectifier, and a voltage feedforward and feedback based controller for the modular DAB converter. With the proposed control methods, the dc-link voltage and power in each module can be balanced. In addition, the low-distortion grid current, unity power factor, and bidirectional power flow can be achieved. Simulation and experimental results are presented to validate the proposed control methods.