The increasing presence of renewable energy sources (RES) in a power grid tends to reduce its inertia constant, which quantifies the grid's ability to contrast the frequency changes due to external disturbances. This led to the development of control strategies that interface the RES to the grid providing synthetic inertia, but these strategies cannot avoid oscillations of the overall system inertia, thus requiring 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 analyze it, in order to efficiently apply it to the estimation of the inertia constant 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.