As a renewable energy resource, the pumped storage power station has great prospects for better balancing supply and demand, particularly with further development of intermittent power sources and the growing need for an intelligent electric grid. However, pump-turbines often involve problematic S-shaped regions in their machine characteristics and thus, while pumped storage may solve some problems in the grid, pump-turbine operation and control can lead to other problems including severe self-excited oscillation in the hydro-mechanical system. These operational challenges have been so severe that they have even led to some reported accidents. Based on two typical and complex water conveyance systems, including two pump-turbine system sharing a common tail tunnel and two pump-turbine systems sharing an upstream penstock, the mathematical equations for self-excited oscillation are deduced from the basic equations of pressurized pipe flow coupled to the pump-turbine’s characteristics; moreover, the behaviour of a single pump-turbine system is obtained through simplification of the first analysis. An analytical study is performed and the amplitude–frequency characteristic is investigated by means of both non-linear vibration theory and its corresponding analytical solution algorithm through a multi-scale method. With a given case study in detail, the results show that, for the turbines staying in the S-shaped regions for a relatively long time, self-excited oscillation inevitably occurs with severe oscillation superposed by several oscillation modes by the use of power spectral analysis module in MATLAB, and numerical results are shown to agree well with the theoretical analysis.

A higher-order elastic model of the flow in long pressurized pipelines is expected to be utilized for stability analysis of the governor-turbine-hydraulic system in hydropower stations. Because traditional elastic models are limited in lower order application because of their difficult decoupling in addition to the rigid model, a new linear elastic model of the flow in pressurized pipelines is derived on the basis of the equations of hydraulic vibration, in which each oscillatory flow with a different order has been obtained with ordinary differential equations in decoupling form. For water conveyance systems with branching pipes or parallel pipes in hydropower stations, the state equations to describe hydraulic characteristics of the governor-turbine-hydraulic system are established with the application of this new elastic model for diversion pipeline flow or tail tunnel flow. The influence of the elastic models with different order on a system’s stability are revealed in detail by two cases that illustr...

Based on the theory of hydraulic transients and the method of characteristics (MOC), a mathematic model of the differential surge tank with pressure-reduction orifices (PROs) and overflow weirs for transient calculation is proposed. The numerical model of hydraulic transients is established using the data of a practical hydropower station; and the probable transients are simulated. The results show that successive load rejection is critical for calculating the maximum pressure in spiral case and the maximum rotating speed of runner when the bifurcated pipe is converging under the surge tank in a diversion-type hydropower station; the pressure difference between two sides of breast wall is large during transient conditions, and it would be more serious when simultaneous load rejections happen after load acceptance; the reasonable arrangement of PROs on breast wall can effectively decrease the pressure difference.

Fluid–structure interaction (FSI) is a frequent and unstable inherent phenomenon in water conveyance systems. Especially in a system with a surge chamber, valve closing and the subsequent water level oscillation in the surge chamber are the excitation source of the hydraulic transient process. Water-hammer-induced FSI has not been considered in preceding research, and the results without FSI justify further investigations. In this study, an FSI eight-equation model is presented to capture its influence. Both the elbow pipe and surge chamber are treated as boundary conditions, and solved using the finite volume method (FVM). After verifying the feasibility of using FVM to solve FSI, friction, Poisson, and junction couplings are discussed in detail to separately reveal the influence of a surge chamber, tow elbows, and a valve on FSI. Results indicated that the major mechanisms of coupling are junction coupling and Poisson coupling. The former occurs in the surge chamber and elbows. Meanwhile, a stronger pressure pulsation is produced at the valve, resulting in a more complex FSI response in the water conveyance system. Poisson coupling and junction coupling are the main factors contributing to a large amount of local transilience emerging on the dynamic pressure curves. Moreover, frictional coupling leads to the lower amplitudes of transilience. These results indicate that the transilience is induced by the water hammer–structure interaction and plays important roles in the orifice optimization in the surge chamber.

A surge tank effectively reduces water hammer but experiences water level oscillations during transient processes. A double chamber surge tank is used in high head plants with appreciable variations in reservoir water levels to limit the maximum amplitudes of oscillation by increasing the volume of the surge tank near the extremes of oscillation. Thus, the volume of the chambers and the design of an orifice are the most important factors for controlling the water level oscillations in a double chamber surge tank. Further, maximum/minimum water level in the surge tank and damping of surge waves have conflicting behaviors. Hence, a robust optimization method is required to find the optimum volume of chambers and the diameter of the orifice of the double chamber surge tank. In this paper, the maximum upsurge, the maximum downsurge, and the damping of surge waves are considered as the objective functions for optimization. The worst condition of upsurge and downsurge is determined through 1-D numerical simulation of the hydropower system by using method of characteristics (MOC). Moreover, the sensitivity of dimensions of a double chamber surge tank is studied to find their impact on objective functions; finally, the optimum dimensions of the double chamber surge tank are found using non-dominated sorting genetic algorithm II (NSGA-II) to control the water level oscillations in the surge tank under transient processes. The volume of the optimized double chamber surge tank is only 44.53% of the total volume of the simple surge tank, and it serves as an effective limiter of maximum amplitudes of oscillations. This study substantiates how an optimized double chamber surge tank can be used in high head plants with appreciable variations in reservoir water levels.

This study focuses on the output variation and dynamic behavior of hydroturbines in a hydraulically coupled system under hydraulic disturbance. The theoretical formula predicting the output variation of operating turbines after hydraulic disturbance is presented, and the influential factors are discussed. To investigate the dynamic characteristics of the hydraulic turbine governing system (HTGS) and verify the accuracy of the formula, a mathematical model of the hydropower plant with multiple turbines sharing a common hydraulic system was established, and the transient process caused by partial load rejection was simulated on the basis of the operation of a real hydropower plant. The results show that the output variation of the operating turbine is in agreement with the theoretical formula, and the amplitude of overload is significant under the conventional regulating model, i.e., opening control, in the low-head hydropower plants with long headrace tunnel during hydraulic disturbance. These methods and results will provide a theoretical basis for the safe operation and control of such hydropower plants.