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A key issue in Low Voltage (LV) distribution systems is to identify strategies for the optimal management and control in the presence of Distributed Energy Resources (DERs). To reduce the number of variables to be monitored and controlled, virtual levels of aggregation, called Virtual Microgrids (VMs), are introduced and identified by using new models of the distribution system. To this aim, this paper, revisiting and improving the approach outlined in a conference paper, presents a sensitivity-based model of an LV distribution system, supplied by an Medium/Low Voltage (MV/LV) substation and composed by several feeders, which is suitable for the optimal management and control of the grid and for VM definition. The main features of the proposed method are: it evaluates the sensitivity coefficients in a closed form; it provides an overview of the sensitivity of the network to the variations of each DER connected to the grid; and it presents a limited computational burden. A comparison of the proposed method with both the exact load flow solutions and a perturb-and-observe method is discussed in a case study. Finally, the method is used to evaluate the impact of the DERs on the nodal voltages of the network.

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