Nonlinear modal interaction analysis and vibration characteristics of a Francis hydro-turbine generator unit

Abstract The Francis hydro-turbine generator unit (FHTGU) is a typical nonlinear system with the coupling hydraulic, mechanical and electric subsystems. It is a challenge to understand the reasons for its operational failures because the major reason for failures involves complex interactions of the three subsystems. Subsystems’ model interaction with the method of normal forms has been well developed and investigated, overcoming the linear methods used in the FHTGU’s stability analysis. However, these methods have not to quantify higher-order terms in a mathematically accurate type to capture dynamic modal interactions between subsystems. Due to the accelerating expansion of hydropower stations, stability of FHTGU shows singular nonlinear oscillations and new methods have to be upgraded to cope with this new situation. In this study, the nonlinear modal method is introduced to analyze the dynamic modal interactions between subsystems, and results given by the different methods are compared to verify the method’s feasibility. The effect of the second order modes is quantified to investigate its effect on the dynamic characteristics of FHTGU, and the vibration characteristics affected by the wind generation system are also investigated. The result shows that the intensity of modes can be effectively reduced to satisfy the stable requirements. All of these results provide a theoretical guidance for the stable operation of FHTGUs.