To realize high efficiency transmission and flexible voltage regulation of series-parallel DC solid state transformers in medium and low voltage DC interconnection scenarios, this paper combines the CLLLC and the Buck/Boost-CLLLC converter modules to form a new hybrid series-parallel bi-directional DC solid state transformer (HSBDCSST). It has both the bi-directional flexible voltage regulation of Buck/Boost-CLLLC converter and the bidirectional high-efficiency transmission advantage of the CLLLC converter. Synchronized square wave control of the CLLLC module and the improved virtual DC motor control (IVDCM) of the Buck/Boost-CLLLC module are also proposed, in which each CLLLC module is controlled by the same fixed frequency square wave with 50% duty cycle to ensure high efficiency. As for the Buck/Boost-CLLLC module, a link that the rated angular speed of the DC motor varies in proportion to the mechanical power is introduced on the basis of traditional VDCM control. This constitutes the IVDCM control strategy, realizes voltage regulation and improves the inertia damping characteristics of the DC transformer. This effectively improves the response speed and dynamic characteristics of the system. Finally, a Matlab/Simulink simulation model and an experimental platform of the 3-module series-parallel system are constructed to verify the effectiveness of the control method.