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...

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.

For the different types of throttled surge tanks used in hydropower systems, it is important to comprehensively know the throttle's head loss characteristics for exact surge analysis and transient control. Herein, a general and complete experimental setup was designed to steadily reproduce the 12 typical flow regimes occurring at the surge tank and thus conduct comprehensive experimental research on throttle head loss coefficients. Furthermore, an extended mathematical model for the surge tank was derived by inputting experimental data on the throttle's head loss coefficients to surge analysis. Through experimental research, the throttle's head loss coefficients were determined by fitting formulae relative to the different flow regimes and discharge ratios; via a detailed case analysis, the differences in the head loss characteristics for different throttle types were accurately determined. It was demonstrated that the throttle's head loss coefficient varies with discharge ratio under different flow regimes and found that the experimentally obtained flow coefficients for different throttle types are more accurate and clearly reveal the difference of throttles’ head loss characteristics. The extended mathematical model for the throttled surge tank can provide more accurate simulation results and guidance for its engineering design and layout.

To understand the hydraulic vibration characteristics in a traditional hydropower system and identify possible exciting sources that may induce serious hydraulic vibrations in the flow passage, experimental tests and numerical calculations were conducted for different operating conditions. The experimental results show that the pressure fluctuations are mainly related to the vortex rope phenomena in the draft tube, and the dominant frequency of pressure fluctuation is 0.2~0.4 times the runner rotational frequency (f_n). The numerical results show all the attenuating factors are negative, which indicates the system itself is stable on the condition that all the hydraulic elements have steady operating performance. The free vibration analyses confirm that the frequency range of the vortex rope in the draft tube partly overlaps the natural frequencies of the hydropower system. Apart from the vortex rope, the runner rotational frequency is another common frequency that is approximately equal to the frequency of the 10th vibration mode. From the vibration mode shapes, it is inferred that a small disturbance in its frequency close or equal to a specific natural frequency of the vibration mode could induce large pressure oscillations in the tail tunnel. In light of the system’s response to different forcing frequencies, the vortex rope formed under off-design conditions and runner rotational frequency is verified to be the potential exciting source of a traditional hydropower system, and the frequency 0.2 f_n is much more dangerous than other disturbances to the system.