S-shaped Region Research Articles

Analysis of extremely low water hammer pressures of draft tubes for double units in pumped storage power stations under successive load rejection conditions

With large-scale integration of intermittent energy into power systems, the operating conditions of pumped storage power stations (PSPSs) change frequently, thereby intensifying the risk of load rejections. For multiple units sharing a water conveyance system, when one or more units reject the load, other units also reject the load after a few seconds; this is defined as successive load rejection (SLR). During SLR conditions, pumped storage units produce extreme water hammer pressures, jeopardizing the safe operation of PSPSs. This study reveals the generation mechanism of extremely low draft tube pressure (DTP) during SLR, and clarifies the generating unit and corresponding occurrence moment characteristics of the minimum DTP. The results indicated an extremely low DTP, attributed to the sharp decline in the discharge owing to increased rotational speed in unit's S-shape region and the hydraulic interference owing to the increased discharge of the other unit. When the guide vane closing time (GVCT) was short, the minimum DTP occurred in the subsequent load rejection unit (SLRU) near the first peak of its rotational speed, with the discharge of initial load rejection unit (ILRU) in the rising stage. Conversely, for a large GVCT, the minimum DTP occurred in the ILRU near the second peak of its rotational speed, with SLRU discharge in the rising stage. Finally, engineering measures to improve the extremely low DTP were proposed. Overall, the findings underscore crucial engineering insights for ensuring the safety of PSPSs under extreme conditions.

Investigations into Hydraulic Instability during the Start-Up Process of a Pump-Turbine under Low-Head Conditions

To investigate the hydraulic characteristics during the start-up process of a full-flow pumped storage unit under low-head conditions, numerical simulations were conducted to study the dynamic characteristics during the process, providing a detailed analysis of the dynamic behavior of the internal flow field during the transition period as well as the associated variation in external performance parameters. Study results revealed a vortex-shedding phenomenon during the initial phase of the start-up process. These vortices restrict the flow, initiating a water hammer effect that abruptly elevates the upstream pressure within the runner. As the high-pressure water hammer dissipated, the flow rate rapidly increased, leading to a secondary but relatively weaker water hammer effect, which caused a momentary drop in pressure. This series of events ultimately resulted in significant oscillations in the unit’s head. After the guide vanes stop opening, the vortex structures at the runner inlet and outlet gradually weaken. As the runner torque continues to decline, the unit gradually approaches a no-load condition and enters the S-shaped region. Concurrently, pressure pulsations intensify, and unstable vortex formations reemerge along the leading and trailing edges of the runner blades. The escalated flow velocity at the runner’s exit contributes to the elongation of the vortex band within the draft tube, ultimately configuring a double-layer vortex structure around the central region and the pipe walls. This configuration of vortices precipitates the no-load instability phenomenon experienced by the unit.

Numerical investigation of energy dissipation and vortex characteristics on the S-shaped region of a reversible pump-turbine

In order to meet the regulation needs of power system, the pump-turbine is prone to operate in the S-shaped region during frequent start-up, leading to unit vibration and grid connection failure. In this paper, the S characteristic experiment was carried out, and the entropy production, unstable flow and vortex structure under turbine, runaway, turbine breaking, reverse pump conditions with optimum guide vane opening are detailed analyzed. The relationship between the energy dissipation and flow field characteristics is clarified. The results show that the runner entropy production is the largest in all components, and the wall entropy production is greater than the fluctuating entropy production under turbine condition. With the decrease in discharge, the fluctuating entropy production and wall entropy production first increase and then decrease, reaching the maximum values in the runaway condition. The circumferential movement trend of water enhances, and forms circumferential flow in the vaneless region. The separation vortex formed on the blade suction surface extends from the blade inlet to the middle of the flow channel, inducing a high entropy production. Under the turbine braking condition, the tangential velocity increases rapidly in the vaneless region. The circumferential flow develops into water ring, blocking the water flows into the runner. Under the reverse pump condition, the water flows in the opposite direction, with negative tangential and streamwise velocities. The absolute flow angle becomes obtuse, and a large-scale reverse vortex is formed. The runner inlet is blocked by the water ring, and the flow channel is almost completely filled with the low-speed region. The proportion of the guide vanes entropy production reaches maximum. Unstable flow leads to the increase in vorticity. Separation vortex, bypassed vortex, and reverse flow vortex leads to an increase in VST, forming a high VST region at corresponding positions. Due to the rotational motion accompanying the development of separated vortex, it leads to the increase in CFT. In addition, the circumferential flow and water ring have higher tangential velocities, which can lead to high CFT regions.

Analysis of self-oscillation stability of a pump-turbine in the S-shaped regions of characteristic curves

Abstract The hydraulic oscillation of pumped-storage power station (PSPS) affects the safe and stable operation of the power station. The S-shaped characteristic curves of pump-turbine may sometimes result in instability in speed-no-load operation. To investigate the instability mechanisms and identify the main factors that affect stability, this paper used the overall matrix method to establish a self-excited oscillation calculation model of a PSPS and analyzed the stability characteristics and influencing factors of the S-shaped regions of the speed-no-load opening. The results show that when the slope of the characteristic curve is negative, the natural frequency attenuation factors of the system are negative, demonstrating stability. When the slope of the characteristic curve is positive, the system remains stable if the slope is large. However, if the slope of the characteristic curve is below a certain value, which may lead to instability. Increasing the inlet valve resistance and appropriately changing the valve layout position can enhance the stability of the system. The damping surge chamber fluctuations have no impact on system stability. The study also found that the stability regions of the S-shaped regions are related to the slope of the characteristic curve, the unit operating discharge, and the value resistance coefficient.

FSI simulation of a high-head pump-turbine during load rejection process

Abstract High-head pump-turbine suffers large centrifugal and hydraulic forces due to large rotational speed and severe pressure pulsations during transient processes, and the strong vibration may increase the risk of runner failure. Load rejection transient process is crucial for pumped-storage hydropower stations, and the evolution laws of the runner dynamic stress during this process need profound research. In this study, the evolution of the runner dynamic stress of a prototype pump-turbine during a load rejection transient process was simulated using the one-dimensional and three-dimensional coupling (1D-3D) method and the fluid-structure interaction (FSI) method. The results of this dynamic transient process were compared to the results of the static working points. It is shown that the rotational speed dominates the mean value of stress while the fluctuating amplitude of stress is dominated by pressure fluctuations, which are larger in the S-shaped region of characteristics. Compared with the static working point solutions, the transient process solutions can better reflect the stress fluctuations and should be used for safety assessment.

Three-dimensional simulations of load rejection processes of a variable-speed pump-turbine under different initial rotational speeds

Abstract The load rejection transient process is one of the most dangerous operating conditions in pumped storage power stations. When the operating point slides through the S-shaped region quickly, the pressure fluctuations increase sharply and the unit vibrates obviously. In variable-speed units, the different initial rotational speeds have significant effects on the operating point trajectories during load rejection processes. In this paper, under the same head and guide vane opening, the load rejection processes with different initial rotational speeds were simulated by using three-dimensional methods, and the variations of rotational speed, discharge and torque were obtained and analyzed. The results show that the changes of initial rotational speeds affect the shapes of velocity triangle at the runner inlet and outlet, and causes the flow separations and vortices in the runner and draft tube, which leads to different efficiency and torque of the pump-turbine under initial steady conditions. In addition, during load rejection processes, the maximum values of macro parameters and pressure fluctuations, and the transitions of flow patterns have obvious differences because of these different initial rotational speeds.

Vortex motion in vaneless space and runner passage of pump-turbine in S-shaped region

This study examines the S-characteristic, a key factor affecting the safe grid connection and operation of pumped-storage units, and its significant impact on the safety of pumped-storage power stations. We conducted numerical simulations and model experiments to investigate vortex motion characteristics in the vaneless space and runner passage of pump-turbines operating within the S-shaped region, along with an analysis of pressure pulsation characteristics. The accuracy of these simulations was validated through laser Doppler velocimetry experiments, and particle image velocimetry experiments were used to capture vortex motion in the vaneless space. We observed that vortices generated on the guide vane side follow the flow direction, blocking the guide vane passage, while those generated by runner blades move in the opposite direction. Employing an entropy production theory and the Liutex method, we investigated vortex distribution and hydraulic loss in the S-shaped region. The results show that reduced flow rates lead to significant vortices in the vaneless space and guide vane area, which become main contributors to energy loss in this region. These vortices, along with those in the runner passage, mainly arise from flow separation on blade and guide vane surfaces due to suboptimal inflow conditions. The study also identifies pressure fluctuations in the vaneless space, induced by a rotating stall, as the most significant pressure pulsation phenomenon, which significantly impacts the performance of the unit in both upstream and downstream directions.

Reduction of Pressure Pulsation for Pump-Turbine by Variable Speed Operation

Abstract Variable speed operation has emerged as a key direction in the development of pumped storage technology. Maintaining pressure pulsation within the control range is particularly critical for ensuring operational safety of variable-speed pumped storage plants (VSPSPs). However, there is limited research on the relationship between pressure pulsation for pump-turbine and variable speed operation. This paper presents amplitude distribution diagrams of pressure pulsation, obtained from processing model test results of a real VSPSP. Different conditions of variable speed operation are simulated by a numerical model to analyze the influence of operating trajectory on pressure pulsation, and the intensity of pressure pulsation is quantitatively evaluated. According to the results, when the initial speed or speed command increases, the trajectory passes through more regions with high-amplitude pressure pulsation and gradually moves toward the S-shaped region, leading to pressure oscillations. When speed command reduces, maximum pressure pulsation at the volute inlet and in the draft tube can be reduced by 82.18% and 63.24% at most, and the evaluation score can be increased by 28.77%. The findings of this study can offer theoretical guidance for operating VSPSPs.

Dynamic modeling and favorable speed command of variable-speed pumped-storage unit during power regulation

Variable-speed pumped-storage unit (VSPSU) has advantages in flexibility, efficiency, and reliability. It has become a state-of-the-art technology in pumped-storage industry. However, there is little research about the transient process of VSPSU working at a favorable speed command during power regulation. To study the issue, a refined model considering hydraulic–mechanical and electrical subsystems is built in this work. All submodels are created by the authors as individual modules on Simulink platform, and these modules can be easily combined to model different VSPSUs. For the VSPSU that uses a doubly fed induction machine and adopts the fast power control strategy, there are several speed constraints. To satisfy the speed constraints during transient process, the speed command is adjusted to avoid exceeding the allowable speed variation range and eliminate the oscillation caused by the S-shaped region, while being guided by the optimal speed to achieve higher efficiency. The faster the speed command changes, the more rapid the power regulation could be. But fast-changing speed command also leads to larger pressure fluctuations in penstocks. Hence, different schemes of the speed command are compared, and suitable schemes are proposed by comprehensively considering the balance between rapidity and safety. The dynamic model and analysis of favorable speed command can provide support and advice for engineering practice.

S-shaped characteristics of pump turbine with large guide vane opening by experimental and numerical analysis

Pumped storage hydropower is perhaps the most reliable solution to the energy crisis, but its development and application are limited by hydraulic instability, such as S-shaped characteristics. In this paper, based on the S-shaped region pressure fluctuation test of a model pump turbine, the connection between the guide vane opening and S-shaped pressure fluctuation is established, and a guide vane opening of 28 mm is selected for numerical analysis to expand the discussion of the S-shaped pressure fluctuation characteristics to large guide vane openings. The frequency components of the vaneless space are extracted by fast Fourier transform analysis, and the rotational stall frequency is identified. Among them, the blade passage frequency and its multiplier are induced by the rotor–stator interaction, and the low-frequency component of pressure fluctuations is induced by the rotational stall and vortex rope. Based on this, the internal flow and flow rate along the S-shaped characteristic curve and their correlation with the rotational stall are analyzed. In addition, the percentage of and variation in the entropy production rate in the S-shaped region are also analyzed.

Study on S-shaped region of pump turbine based on Omega vortex analysis method and entropy production theory

Study on S-shaped region of pump turbine based on Omega vortex analysis method and entropy production theory

Variation law of pressure pulsation during variable speed operation of pumped storage units

Variable speed operation technology has become an emerging development direction in hydropower industry. Variable-speed pumped storage plants (VSPSPs) constantly undergo various transient processes, and ensuring the amplitude of pressure pulsation within the control range is critical to the safe operation of variable-speed pumped storage units (VSPSUs). However, its extreme value is usually determined by rule of thumb in design stage, and few researches focus on the relationship between pressure pulsation and variable speed operation of VSPSUs. In this paper, characteristic curves of pressure pulsation are plotted by processing model test results with Gridfit function, taking a real VSPSP as an example. The total pressure during transient processes is predicted by simulation of a numerical model. Load rejection conditions (change initial speed) and large load regulation conditions (change speed command and power command) are simulated, and the influence of operating trajectory on pressure pulsation during variable speed operation is analyzed. The results show that with the increase of initial speed or speed command, the value of pressure pulsation increases; the trajectory passes through more high-amplitude pressure pulsation region and gradually shifts to the S-shaped region, causing the pressure oscillation. This study could provide theoretical reference for the operation of VSPSUs.

Multi-Objective Optimization of Back-to-Back Starting for Pumped Storage Plants under Low Water Head Conditions Based on the Refined Model

Pumped storage plants (PSP) must switch frequently between various working conditions. Moreover, PSPs can fall easily into an S-shaped zone under low water head conditions, especially during back-to-back starting (BTBS), which reduces the stability and safety of unit operation. In this paper, a nonlinear PSP model for BTBS is established by combining an electrical subsystem with a refined hydraulic-mechanical subsystem. The influences of the hydraulic, mechanical, and electrical factors on the BTBS process are investigated quantitatively. Choosing the speed overshoot and speed stable time as the optimization objectives, and considering a variety of constraints, the multi-objective particle swarm optimization (MOPSO) algorithm is introduced to study and optimize two typical startup strategies. The results show that: (1) The parameters of a hydraulic-mechanical-electrical system have a significant impact on BTBS process, and the most unfavorable working condition corresponds to the lowest water head; (2) In the control schemes, a novel constant excitation voltage strategy is proposed based on the multi-objective optimization scheme. Compared with the constant excitation current strategy or single-objective, the optimization strategy proposed can considerably improve the speed overshoot and the speed stable time by at least 68.27% and 3.22% under the worst working conditions. (3) It is further verified that the problem of trapping in the S-shaped region under various working conditions may be avoided by the obtained optimal control scheme. The results give prominence to the effectiveness of the proposed optimization strategy for maintaining the safety and stabilization of PSP operation.

Distribution Features of Flow Patterns and Pressure Pulsations of Pump-Turbine in Five Operating Modes on the Four-Quadrant Plane

To meet the demand of the power grid for flexible regulation, pump turbines have to frequently and fleetly stop, start, and transition between different modes, causing many instability problems. To solve the problems, understanding the complex flow and pressure pulsation features in different working conditions is the prerequisite. In this study, the flow patterns, pressure pulsations, cavitation characteristics, and runner forces of a prototype pump-turbine working under the five operating modes were displayed and analyzed based on computational fluid dynamics simulations. It is shown that when working points are near the pump and turbine design working points, the flow is smooth, with small pressure pulsation and without cavitation; however, when working points deviate from the optimal ones, flow patterns become worse and cavitation appears. In the pump-brake mode, the flow hits the runner blades violently, causing obvious pressure and runner force fluctuations. In the hump region, the flow has a strong impact on the guide vanes, and the rotating stall vortices are apparent in the vane area. In the S-shaped region, pressure pulsations are the highest with prominent rotor–stator interaction and rotating stall. Under similar working conditions, a larger guide-vane opening corresponds to a larger pressure pulsation amplitude. On the spatial distribution, the largest pressure pulsations happen in the vaneless space.

Vortex Distribution and Energy Loss in S-Shaped Region of Pump Turbine

Research on the S-shaped region of pump turbines requires a detailed understanding of the vortex distribution law and energy losses under various working conditions. In this study, numerical simulations of a pump turbine model were conducted, and the results were consistent with the experimental results. The |ω|-criterion in the vortex analysis method was combined with the Q-criterion to reveal vortex distribution in the S-shaped region for each working condition along the Q11-n11 curve for all the conditions. Under the runaway and turbine break conditions, the flow field vortices were mainly the leaf channel vortex and separation vortex. Under zero-flow-rate and reverse-pump conditions, the vortices developed towards the stay-guide vanes, obstructing the flow path. Combined with the entropy production rate distribution, vorticity is closely related to energy loss. Compared to the rotation, the vorticity generated by the strong shear effect is significant.

Investigation of the Flow Instabilities of a Low Specific Speed Pump Turbine Part 1: Experimental and Numerical Analysis

Abstract This is the first part of a two-part paper focusing on the flow instabilities of pump turbines. In this first part, results of the experiments and computational fluid dynamics (CFD) simulations of the research carried out on a low specific speed model pump turbine at HSLU (Lucerne University of Applied Sciences) Switzerland are presented. The requirements of a stable and reliable pump turbine operation, under continuously expanding operating ranges, challenge the hydraulic design and demand new developments. This paper presents the results of experimental (model pump turbine at the test rig) and numerical (CFD) investigations of the pump turbine instabilities of a low specific speed (nq = 25) pump turbine in the turbine operating mode. Four-quadrant characteristics of a low specific speed pump turbine with two similar runners differentiating in the size (diameter) are measured. Testing of both runners with the same guide vane system provided information about the effects of the increased vaneless space on the pump turbine performance and stability. A CFD methodology is developed by applying several turbulence models to accurately predict the characteristics of the reversible pump turbines in the S-shaped region (speed no load conditions) as well as to analyze the flow features especially at off-design conditions. This CFD model is validated against the experimental data at 6 deg and 18 deg guide vane openings in turbine operating mode. Using the data of the unsteady pressure measurements and detailed investigation of unstable ranges on the pump turbine characteristics, flow instabilities in the low-specific speed model pump turbine are analyzed. Relevant frequencies such as rotating stall, steady and unsteady vortex formations are determined.

Three-Dimensional CFD Simulations of Start-Up Processes of a Pump-Turbine Considering Governor Regulation

The pumped-storage power station is an efficient stability regulator of the power grid. However, due to the instability of the pump-turbine in the S-shaped characteristic region, rotational speed fluctuation is easy to occur in the speed no-load condition, making synchronization with and connection to the grid difficult. To investigate the key factors of these difficult grid connections, the start-up processes of a practical pump-turbine under the lowest head condition were simulated by using the three-dimensional CFD method, in which the governor regulating equations with different regulating parameters were integrated successfully. The results show that the working points oscillate with the fluctuations of rotational speed, discharge, and torque, and different regulating parameters have a significant influence on the dynamic histories. In addition, the internal flow patterns, especially the backflows at the runner inlet, keep apparent values at the middle span (0.5 span) but have regular transitions near the shroud side (0.7–0.8 span). The faster the guide vanes adjust, the faster the backflows change, and the larger the macro parameters fluctuate. Overall, the instability of the start-up is the result of the periodical evolutions of backflows at the runner inlet, because the trend and period of the radial velocities at different inlet span locations are consistent with those of the discharge.

Investigations on Pressure Fluctuations in the S-Shaped Region of a Pump–Turbine

Hydraulic pumped storage is a special power generation and electricity shortage technology, which is usually operated with thermal power and nuclear power units, and plays a key role in ultra-high voltage and smart grid. Pressure fluctuations are the main reasons for the instability of the S-shaped region of pump–turbines, which seriously affects their lifespan and operation stability. To reveal the mechanism and propagation law of pressure fluctuations in the S-shaped region as well as numerical simulations at the turbine, the braking and the reverse pump operating conditions of a pump–turbine were carried out. Numerical results were validated using the performance experiments, and the generation mechanism and propagation law of pressure fluctuation were analyzed in detail. The analyses show that high-amplitude pressure fluctuations mainly occur in the braking and reverse pump operating conditions. Under the braking condition, a 0.49-fn low-frequency pressure fluctuation was captured, which is caused by the rotation of the backflow in the vanes. Under the reverse pump condition, a 0.19-fn low-frequency pressure fluctuation was confirmed, which is caused by the periodic rotation of the vortex between the vaneless space. This study has important guiding significance for practical engineering application.

CFD simulation of the pump trip runaway transient process of a pumped-storage power plant with head 700 m

Simulating transient processes of pumped-storage power plants is essential for the design and optimization of pump-turbine and water conveyance system. Because pressure pulsations and runner forces cannot be obtained from the traditional 1D transient simulation methods, 3D CFD simulations are necessary. In this study, the fast runaway transient process, occurring after the pump trip of a pumped-storage plant with a head of 700m, was simulated by using the CFD method that couples the 1D water conveyance system and 3D turbine. The phenomena, composed of water hammer fluctuations, pressure pulsation transitions, and flow pattern evolutions, were described and analyzed. We found that the flow patterns and pressure pulsations change violently as the working point goes through different regions. Especially, the pressure pulsations and unbalanced radial runner forces are the most severe in the S-shaped characteristic region. The strong impact on blades, large scale recirculating vortices in blade passages, obvious rotating stalls in vane and blade regions, transitional backflows at runner inlet and outlet, and strong circumferential velocity in vaneless space are the main sources. The dynamic working trajectory does not follow the measured static characteristic curve and demonstrates an undamped loop in the S-shaped region. This paper provides some evidence on the relations between flow structure and pressure pulsation features, although the mechanism of dynamic characteristics needs further investigations.

CFD analysis of flow pattern in S-Shape region for low specific speed Francis turbine

In this research, a Francis turbine with low specific speed was analyzed by unsteady numerical simulation in case of S-Shape region appearing model test. It was found that S-Shape characteristics curve was caused by an increase of head. Firstly, the head was decreased in accordance with a decrease of flow rate. However, once a centrifugal force became larger, then a reverse flow appeared between guide vane and runner and the head was increased. And then, head was decreased with flow rate decreasing. In this research, operating conditions of flow rate were defined as three regions, first half of S-Shape region, just S-Shape region and last half of S-Shape region. The operating condition, where the head was decreased in accordance with the decrease of flow rate, was defined as the first half of S-Shape region. The operating condition, where the head was just being increased in accordance with the decrease of flow rate, was defined as the just S-Shape region. The operating condition after passing of the just S-Shape region was defined as the last half of S-Shape region. It was revealed that those three operating conditions showed a spectrum distribution of pressure fluctuation differently each other. A flow visualization analysis with numerical results was conducted to investigate the difference of pressure spectrum in three operating conditions. At the first half of S-Shape region, two groups of reverse flow were caused at chamber between guide vane and runner and revolving in same direction as runner rotation. At the just S-Shape, the reverse flows were circumferentially connected to build a long curved string. At the last half of S-Shape, the reverse flows were fully connected to build a round ring shape.