Power system modeling that captures the dynamic behavior of the different components interacting in an electric grid is useful in understanding some observed phenomena that have not been easy to reproduce by simulation. Therefore, this thesis focuses on the modeling of hydro-dominant power system to study the origin of some very low frequency oscillations (VLFOs) that have not been explained or reproduced; for example, VLFOs in the Colombian Power System have been detected in the 0.05Hz range and their origin have not been clarified. Within this work modeling guidelines for hydro-electric power plants to capture the effects of the hydraulic coupling of turbines, their control strategies, and nonlinearities in the controls and actuators will be developed. This level of modeling will enable to reproduce oscillatory observation by simulation as the ones in the Colombian system for further analysis. Finally, robust control is proposed to damp oscillatory modes to account the effect of the dynamic behavior of coupled systems and nonlinearities in their controls.