The Solid State Transformer (SST) is an attractive solution for highly flexible, cost-effective, compact and efficient power transfer among different grids. Furthermore, a three-port topology is proven as a suitable solution to integrate energy storage resources, the key functionality of emerging SST concept. Among other alternatives, the resonant LLC series resonant converter (SRC) is the cost-effective solution to implement the DC-transformer functionality, which is a core part of the SST. This paper addresses the power sharing characteristics and the zero-voltage switching (ZVS) conditions of a galvanically isolated three-port SRC, operated in DC-transformer mode. A mathematical model, which effectively decouples principal from circulating currents and power flows, is proposed and developed. This new mathematical framework eases the analysis; and reveals a constant power sharing characteristic tightly dominated by the resonant tank parameters even though some degrees of freedom are allowed thanks to the introduction of a differential voltage at the input terminals. Subsequently, design aspects and assessments of working operation conditions are also reported. The accuracy of the proposed model is verified by experimental validation on a lab-scale prototype.