The COVID-19 crisis is profoundly influencing the global economic framework due to restrictive measures adopted by governments worldwide. Finding real-time data to correctly quantify this impact is very significant but not as straightforward. Nevertheless, an analysis of the power demand profiles provides insight into the overall economic trends. To accurately assess the change in energy consumption patterns, in this work we employ a multi-layer feed-forward neural network that calculates an estimation of the aggregated power demand in the north of Italy, (i.e, in one of the European areas that were most affected by the pandemics) in the absence of the COVID-19 emergency. After assessing the forecasting model reliability, we compare the estimation with the ground truth data to quantify the variation in power consumption. Moreover, we correlate this variation with the change in mobility behaviors during the lockdown period by employing the Google mobility report data. From this unexpected and unprecedented situation, we obtain some intuition regarding the power system macro-structure and its relation with the overall people's mobility.