The upgrade of a pumped-storage power plant (PSPP) to allow variable speed operation offer several advantages in pumping and generating modes. However, in pumping mode at part load, both pressure and torque pulsations develop in the pump turbine runner. This paper evaluates the risk of fatigue damage in the penstock of a variable-speed PSPP due to the propagation of the pressure pulsations developing in the pump turbine runner at partial load in pumping mode. For that purpose, a simulation model of a variable-speed PSPP has been developed. The pressure and torque pulsations are generated each from a different set of sinusoidal functions calibrated from the results of a Computational Fluid Dynamic model, which was in turn validated from experimental data. A Monte Carlo simulation has been performed considering different temporal gaps between the sinusoidal functions reproducing the pressure pulsations in one and another pump turbine. The number of stress cycles that may cause fatigue damage in the penstock has been obtained from the results of the simulations and the fatigue curves defined in the Eurocode, and then transformed into the maximum number of hours per year the PSPP can operate at partial load in pumping mode to avoid fatigue damages.