Model validation and stochastic stability of a hydro-turbine governing system under hydraulic excitations

This paper addresses the stability of a hydro-turbine governing system under hydraulic excitations. During the operation of a hydro-turbine, water hammer with different intensities occurs frequently, resulting in the stochastic change of the cross-sectional area (A) of the penstock. In this study, we first introduce a stochastic variable u to the cross-sectional area (A) of the penstock related to the intensity of water hammer. Using the Chebyshev polynomial approximation, the stochastic hydro-turbine governing model is simplified to its equivalent deterministic model, by which the dynamic characteristics of the stochastic hydro-turbine governing system can be obtained from numerical experiments. From comparisons based on an operational hydropower station, we verify that the stochastic model is suitable for describing the dynamic behaviors of the hydro-turbine governing system in full-scale applications. We also analyze the change laws of the dynamic variables under increasing stochastic intensity. Moreover, the differential coefficient with different values is used to study the stability of the system, and stability of the hydro-turbine flow with the increasing load disturbance is also presented. Finally, all of the above numerical results supply some basis for modeling efficiently the operation of large hydropower stations.