This work considers the DC part of a hybrid AC/DC microgrid with a meshed topology. We address cost minimization, battery scheduling and the power loss minimization within the power distribution network through constrained optimization. The novelty comes from applying differential flatness properties to the microgrid components and formulating the cost and constraints in terms of the associated B-splines parametrization of the flat outputs (the voltages and currents of the system). This allows us to obtain optimal power profiles to minimize the power dissipation and the cost of the electricity purchase from the external grid. These profiles are tracked by a model predictive controller at the higher level, while at a a lower level a controller deals with the operation of the switches within the DC/DC converters. Extensive simulations under nominal and fault-affected scenarios using realistic data validate the proposed approach.