Hydraulic turbine generator units with long-running operation may cause the values of hydraulic, mechanic or electric parameters changing gradually, which brings a new challenge, namely that whether the operating stability of these units will be changed in the next thirty or forty years. This paper is an attempt to seek a relatively unified model for sensitivity analysis from three aspects: hydraulic parameters (turbine flow and turbine head), mechanic parameters (axis coordinates and axial misalignment) and electric parameters (generator speed and excitation current). First, a novel approach of the Pelton turbine torque is proposed, which can make connections between the hydraulic turbine governing system and the shafting system of the hydro-turbine generator unit. Moreover, the correctness of this approach is verified by comparing with other three models of hydropower stations. Second, this latter is analyzed to obtain the sensitivity of electric parameter (excitation current), the mechanic parameters (axial misalignment, upper guide bearing rigidity, lower guide bearing rigidity, and turbine guide bearing rigidity) on hydraulic parameters on the operating stability of the unit. In addition to this, some critical values and ranges are proposed. Finally, these results can provide some bases for the design and stable operation of Peltonhydropower stations. (C) 2017 Elsevier Ltd. All rights reserved.