Power plants are subject to introduce disturbances in the power grid, resulting from interactions with the dynamical behavior of the energy source subsystem. In the case of hydropower plants when used to compensate for variations of power generation and consumption, instabilities or undesirable disturbances may arise. They may be caused by phenomena such as part load vortex rope pulsations in the draft tube of Francis turbines. This may affect the dynamical behavior of the power plant and lead to troublesome interactions with the grid. This paper presents a case study of an existing hydropower plant that illustrates the effects of pressure pulsations due to vortex rope precession on the draft tube of Francis turbines. It also showcases possible solutions to the mitigation of the effects of this disturbing hydraulic phenomenon over the operation of the generators and electrical system. The investigated system is a 1 GW hydropower plant (4 x 250 MW units). The assessment of the power swings is performed through modal analysis combined with frequency-domain and time-domain simulations, which are then compared with on-site measurements.