The increasing integration of distributed energy resources (DERs) in distribution grids imposes an imperative need for reliable and accurate monitoring of the grids' operating condition. Consequently, electric utilities have recently started considering the deployment of Phasor Measurement Units (PMUs) in Medium Voltage Distribution Grids (MVDGs) in order to enhance and improve the monitoring capabilities of the operator. In this paper, a fast reporting measurement device is considered at a MV-LV transformer substation for enhancing the monitoring of the MVDG. A monitoring scheme is then proposed that utilizes the capabilities of this device not only for enhancing the monitoring of the MVDG, but also to simultaneously improve the monitoring of the Low Voltage Distribution Grid (LVDG). The results of the numerical simulations indicate that the proposed scheme exhibits good performance in all the considered scenarios.