The Smart Transformer, a solid-state transformer with control and communication functionalities, can be the ideal solution for integrating storage into the grid. By leveraging the knowledge of the grid state of distribution grids thanks to smart meters and/or dedicated remote terminal units, in the paper, it is proposed a control strategy for a MV/LV smart transformer (ST) with integrated storage to achieve: i) dispatched-by-design operation of the LV network by controlling the ST active power set-point on the MV power converter, and ii) voltage regulation of both MV and LV networks by controlling the reactive power injections of both LV and MV converter. The former is achieved by dispatching the active power flow of the LV network according to a profile established the day before the operation, called \emph{dispatch plan}, with the objective of reducing the amount of regulating power required to operate the grid. It is based on the use of forecast to compute a dispatch plan, and a tracking problem to compensate in real-time the mismatch between realization and dispatch plan by taking advantage of the storage capacity. The latter is achieved by using sensitivity coefficients, which are calculated from the state of the grid and integrating the information on the network topology. The problem formulation is given in the paper, and the proof-of-concept is shown by simulation using the IEEE 34 nodes test feeder and the CIGRE Low Voltage reference network.