The paper presents the analysis and numerical calculation of the dynamic stability of a hydrogenerator under conditions of disturbances in the incident transmission network. The occurrences of three-pole, two-pole and single-pole short circuits and sudden load loss are considered. In the event of short circuits, the influence of automatic reconnection (APU) on the dynamic stability of the generator is analyzed, as well as the duration of the fault itself. The hydrogenerator is modeled together with the turbine regulation and excitation regulation systems (including PSS and OEL and UEL elements). The model is implemented using the Matlab Simulink environment. In addition, the paper provides theoretical foundations for modeling a complete hydropower plant (hydraulic installation, turbine, turbine regulator) with the possibility of simplification and neglect within the complete model. Different designs of generator excitation systems are also described and then the so-called standard IEEE models of generator excitation systems are presented.