Low-voltage flexible direct currect (LV-FDC) technology represents a vital technical approach to addressing the issues of heavy overloading and power supply reliability in end-user distribution networks. The core technological foundation of LV-FDC systems lies in their efficient operation under steady-state conditions and rapid switching control during transient states. This paper analyzes and summarizes the typical decentralized networking modes of LV-FDC systems, encompassing system topologies, connection schemes, and voltage levels. Aiming at the heavy overloading issue in transformer zones caused by uneven spatial and temporal load distributions, a set of steady-state load balancing control logic is proposed. For the issue of system operation mode switching during fault transients, an adaptive switching control based on local voltage information is proposed, which reduces the system's dependence on communication and achieves seamless switching between operating modes through the design of the slave control unit's control loop. Furthermore, an integrated design for steady-state and transient operation control based on master-slave control is analyzed in the context of multi-terminal flexible interconnection applications, ensuring efficient coordination and reliable operation of the system under both steady and transient conditions. Finally, the correctness of all control logic strategies is verified through PSCAD time-domain simulations and RT-LAB hardware-in-the-loop experiments.