Load power sensitivity to voltage changes continuously in the distribution grid due to the increased variability of the load demand (e.g., electric vehicles charging) and generation production (e.g., photovoltaic). Classical sensitivity identification methods do not respect the fast dynamics of such changes: they require long data history and/or high computational power to update the load sensitivity. The proposed On-Line Load sensitivity Identification (OLLI) approach is able to identify the load sensitivity in real time (e.g., every minute). This paper demonstrates that the OLLI can be achieved not only with the advanced Smart Transformer metering system, but also with commercial industrial metering products. It is shown that OLLI is able to identify correctly the load sensitivity also in presence of noise or fast stochastic variation of power consumption. The industrial metering-based OLLI application has be proven by means of a power-hardware-in-loop evaluation applied on an experimental microgrid.