The increasing presence of renewable energy sources (RES) in power grids reduces the system inertia, which quantifies the grid's ability to contrast the frequency changes due to external disturbances. The intermittent nature of RES makes the system inertia time-varying, thus requiring the development of algorithms for the online inertia constant estimation under normal operating conditions of the power grid. In this paper, we consider one of these algorithms, which exploits the data measured online through phasor measurement units, and critically analize it, in order to efficiently apply it to the estimation of the inertia in the IEEE-14-bus power system, also with the addition of a PV power plant. The obtained results point out an increased efficiency of the online estimation of the network inertia.