A key issue in LV distribution system management and control is to increase the flexibility of the existing networks so as to allow a large spread of Distributed Energy Resources (DERs). In this perspective, virtual levels of aggregation, called Virtual Microgrids (VMs), are introduced, which are composed of parts of the distribution networks including different types of DERs and their control systems. To identify the VMs it is necessary to model the impact of DERs on the voltages and power flows of the LV distribution networks and to aggregate them on the basis of their impact on specific control actions. This paper proposes, as the first step, a new model of the LV distribution system derived from the DistFlow equations. The model expresses the variations of the electrical variables of the LV network as linear functions of the DERs injections, thus proving to be suitable for the VM definition. In a case study, a comparison of the results given by the proposed model with the load flow solutions is discussed and the evaluation of the impact of the DERs on the nodal voltages of a LV distribution system is analyzed.