Correlation between pump-turbine S characteristics and transients in pumped-storage stations

The hydraulic transient simulations of pumped-storage stations greatly depend on pump-turbine S-shape characteristics. However, during the early design stage, the characteristic curves of a pump-turbine with same specific speed but different S-shaped characteristics might be chosen to be the boundary condition of the transient simulation, which may rise a series of problems. By linearization of the braking area and the differential equations of water hammer, it is arranged into a nonlinear plane quadratic system. The characteristics of the nonlinear system with stable extreme value (limit cycle) are analyzed. By changing the slope of the braking area, the correlation between the maximum value of water hammer and the system parameters is analyzed, and the fitting relationship between the extreme value of water hammer and the slope of the braking area is obtained. An engineering example verifies the validity of the fitting formula, the conclusions provide references for the design of pump-turbines and theoretical guidelines for the selection of turbine characteristics during the early design stage.