Non-Linear Stability Analysis of a Reduced Scale Model Pump-Turbine at Off-Design Operation
Nowadays, the pump-storage power plants are a proven solution for storing electricity at large scale and offering flexibility to the power management. Therefore, the hydraulic machines are increasingly subject to off-design operation, start-up and shutdown sequences. However, the fast and frequent switching between pumping mode and generating mode presents technical challenges. In the present study, the reduced scale model of a low specific speed pump-turbine is investigated in generating mode at off-design conditions. The operation in the typical “S-shaped” curve of pump-turbine may become unstable and the machine may switch back and forth from generating mode to reverse pumping mode preventing the correct experimental survey of this part during the model testing. The instability has been solved by a testing procedure imposing a restriction of section and a control valve for being able to increase the energy losses. This procedure, commonly used in model testing of pump-turbines, significantly improves the stability of the machine and allows for the survey of the entire “S-curve”. The aim of the present investigation is to understand and explain the origin of the switch to reverse pumping mode. Thus, a hydro-acoustic test rig model was developed with the In-house EPFL SIMSEN software and a comparison between the systems with and without a restriction of section was studied. A numerical analysis indicates that the operating points of a pump-turbine system are defined by the solution of the equation relating the test rig characteristic and the energy-discharge characteristic of the hydraulic machine for a given rotational speed and a constant guide vanes opening. Furthermore, the addition of a restriction alters the curvature of the test rig characteristic and creates a new degree of freedom to achieve stable operating points in the “S-curve”. Finally, to ensure the stability of each operating points described by the numerical model, an eigenvalue study of the non-linear hydraulic system is necessary.