The Smart Transformer (ST) is a solid-state transformer with control and communication functionalities, interfacing medium voltage and low voltage (LV) grids. The ST can work in both ways: it can operate in a radial network independently, and it also provides meshed operation. In particular, a meshed ST-fed grid is able to optimize the power flow of the network, therefore largely avoiding the reinforcement of utilities. Though the ST can address system-level issues, challenges in terms of control and stability are encountered. The modeling as well as stability analysis of ST converter and its control for meshed operation have rarely been studied. More importantly, the interactions between ST and grid-interfaced converters during meshed operation have not yet been investigated. To ensure reliable ST-fed grid, this paper develops a complete model of ST LV converter considering all the key elements for the meshed operation. System stability is assessed based on the developed model for different scenarios. The interactions between the ST and local grid converters are examined to provide comprehensive design guidelines for the meshed ST-fed grid. The control strategy and the theoretical analysis are validated by the simulation and experimental results.