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In recent years, modern distribution networks are rapidly evolving toward the new concept of Smart Grid (SG) due to the increasing level of penetration of distributed generation (DG) units, storage systems and information and communication technologies. In the framework of low voltage distribution systems, SGs based on either AC or DC grids have been proposed and compared in the technical literature, evidencing their advantages and drawbacks. Only recently, hybrid SGs that include both DC and AC grids have been proposed with the aim of optimizing the whole system behavior. In this paper, an innovative hybrid low voltage SG that includes properly controlled AC and DC grids is analyzed. The DC grids - including storage systems and interconnected to the AC grid through AC/DC PWM-controlled static converters - highly contribute to improve both quality and continuity of supply to AC and DC sensitive loads. The AC grid is optimally controlled to perform several system services (i.e., minimize power losses and optimize voltage profiles at fundamental frequency and at harmonic frequencies). Time domain simulations on a 30-node low voltage hybrid SG are presented and discussed to evidence the effectiveness of the considered solution.