## 1 Introduction  
In recent decades, energy consumption has been increasing dramatically worldwide, while the excess use of fossil energy sources (especially oil, coal, and gas) leads to serious problems of climate change [1]. The human energy structure should be urgently improved, and the renewable energy must be more widely implemented to help maintain sustainable growth [2]. Over the last few decades, renewable energy sources from hydro, solar, wind, wave, tidal, and biomass have shown greater interest worldwide due to their availability, eco-friendliness, and ease in harnessing to fulfill the need of mankind [3]. Usually, the renewable energy sources such as wind, solar, wave, tidal, and biomass are intermittent in nature and hence lack in producing continuous and name plate capacities. The unpredictability of their power generation has an adverse effect on the power production, which will lead load and frequency fluctuations of power grids [4]. Hence, suitable energy storages in bulk are required. Until now, pumped hydroelectric energy storage is the only proven large-scale energy storage scheme for power system operation. Pumped-storage power plants (PSPS) can store energy and generate power according to the load fluctuations flexibly [1]. Pump-turbine is the heart of any PSPP, and it is the part responsible for the plant overall efficiency and its operational characteristics. The penetration of large amounts of intermittent energy to the power grid makes the pump-turbine frequently undergo transient operations, which has caused a series of severe stability problems [5]. In general, when the grid parameters fluctuate beyond a manageable limit, the generator of pump-turbine automatically disconnects from the power grids, resulting in load rejections [6]. If the servomotor fails to close the guide vane momentarily, the units set into runaway processes. However, the S-shaped characteristics of pump-turbine often lead to self-excited oscillations in the runaway process [7]. As a result, the fluctuations of operating parameters, such as pressure, torque, and rotational speed, cannot be converged to constants like normal Francis turbines and will lead to drastic increases in vibrations, a reduction of runner life, and even breakdown of the rotor [8; 9; 10]. Therefore, the unstable oscillation problem of pump-turbine during the runaway process needs to be solved. Generally, the oscillation stability of a pump-turbine during runaway processes is associated with many parameters of the hydraulic system, such as rotational inertia, water elasticity, and friction loss in the pipe system; however, the slope of the characteristic curve at the runaway point is the most important influence factor [11]. Various one-dimensional mathematical models based on the static characteristic curves of model pump-turbines have been developed to study the dynamic stability mechanism and the influences of different factors [12; 13; 14; 15]. Some methods, such as partly closing the main inlet valve [16] and misaligning guide-vane openings [17; 18], have been proposed to stabilize runaway processes. However, these methods are not solutions to the source of the unstable problem. [PERSON] [19] thought the formation of a fully developed vortex structure at the runner inlet should be avoided for a stable characteristic and found that the shape of the runner leading edge influences the formation of the fully developed vortex structure. [PERSON] [20] reported that two pump-turbines (BQ and XJ) share the same specific speed and nearly have the same parameters of turbines except the shape of the runner leading edge (see Figure 1), but they have distinctive differences in the runaway oscillation process. The oscillation process for the BQ pump-turbine is self-excited, while that for the XJ pump-turbine is damped. It can be reasoned that the characteristics of transient flows within the two pump-turbines may be different, and the evolution of transient flows in XJ pump-turbine is conducive to the stability of runaway oscillation.