This paper studies DC micro-grids in mesh topology where voltage regulation is performed at each node with help of storage devices interfaced through boost converters. Loads and distributed power sources are treated as arbitrary perturbations under a hierarchical control strategy. The primary level controller is characterized by its faster actuation rate and focus on the implementation of distributed voltage sources, while the secondary level uses a consensus algorithm to reach power sharing among the sources, and introduces an auxiliary loop to secure voltage regulation around the nominal value. We model the entire network, considering the switching process of each individual converter, primary and secondary level controllers, hardware and communication interconnections, as a discrete time system, in opposi- tion to the documented continuous time dynamic assumption. This leads to obtain an explicit representation of the entire grid, which is closer to its final hardware implementation, and facilitates dynamic trajectory analysis over specialized or conventional hardware. The developed convergence criteria for the discrete time closed loop system is corroborated by dynamic simulations which also show the main benefits of the discrete time modeling.