Unstable vortex rope structures, characterized by the coexistence of multiple frequency components, can develop in a Francis turbine. To reveal the organization and dynamics of spectrally pure coherent structures in the vortex rope, high-fidelity numerical calculations were carried out using a Detached Eddy Simulation (DES) turbulence model, accounting for the weak compressibility of water. The dominant coherent structures were then extracted via Dynamic Mode Decomposition (DMD). Good agreement between the calculated and experimental velocity contours, as well as between the calculated and measured pressure pulsations, confirmed the accuracy and reliability of the numerical simulation. Hankel-DMD of the pressure pulsations indicated that Mode 0 dominates the spectral content, corresponding to the characteristic frequency of the vortex rope. The vortex rope was further visualized using the Delta-criterion, and its three-dimensional (3D) behavior was examined. Standard DMD decomposed the 3D flow field in DT, yielding spatial modes with high spectral purity and their associated temporal coefficients. Modes 1(15 fn) and Mode 3 (15 fn) were identified as paliform vortices near the DT inlet, corresponding the runner blade configuration. Mode 2 (0.27 fn), contributing 7.5 % to the original flow field showed strong temporal coherence with pressure pulsations and aligns with vortex rope frequency. The combined mode (Mode 0 + 2) closely resembled the original vortex rope in both morphology and dynamics. The results provide a comprehensive understanding of the formation, spectral characteristics, and dynamics of coherent structures in the draft tube vortex rope.

Hydraulic turbines operating in sediment-laden flows are highly susceptible to erosive wear, which degrades safety, efficiency, and service life. However, most existing prediction methods evaluate wear rates on fixed boundaries and cannot capture the progressive evolution of wear morphology. To address this limitation, a computational fluid dynamics-discrete element method (CFD-DEM) model with dynamic wear-boundary updating is developed and experimentally validated for sediment-laden jet impingement erosion of turbine substrate materials. Numerical results agree well with experimental wear-depth distributions and wear profiles. The effects of particle concentration, size, and shape on wear evolution are systematically investigated. Under vertical jet impingement, wall wear depth exhibits a stable M-shaped radial distribution governed by jet-wall interaction and stagnation-region flow structures. Particle parameters do not alter this basic pattern, but significantly affect the location, magnitude, and extent of wear peaks. Within the investigated range, cumulative volume loss increases approximately linearly with particle concentration, whereas particle size shows a stronger nonlinear effect. At 20 min, cumulative volume loss follows a quadratic relationship with particle size, with a second-order coefficient of 0.00441. Increasing particle size from 25% to 50% relative to the baseline increases cumulative volume loss by about 8.4 mm3, while a 100% increase yields about 85.1 mm3. Sensitivity analysis indicates that particle sphericity has the greatest influence on cumulative volume loss, followed by particle size and particle concentration.

Francis turbines employed in flexible energy storage systems frequently operate under part-load conditions, where unstable Inter-Blade Cavitating Vortex (IBCV) structures are generated within the runner passages. IBCV structures exhibit strong unsteadiness and multi-frequency characteristics, their formation and evolution involve complex dynamic mechanisms. To elucidate these dynamic mechanisms, this study establishes a Reduced-Order Model (ROM) based on three-dimensional (3D) unsteady numerical simulations under cavitation conditions. The numerical simulations were qualitatively validated against the IBCV flow visualization and quantitatively verified by the model test efficiency measurements. Dynamic Mode Decomposition (DMD) is first employed to construct the ROM, allowing the dominant structures of the IBCV to be extracted. On this basis, the capability of the developed ROM to represent IBCV evolution is further examined, and its short-term extrapolative prediction performance is also assessed. The results indicate that IBCV evolution involves two distinct processes: expansion-extension and pure extension, two primary frequencies (i.e. 1.0 fn and 2.0 fn) are also captured. Although the DMD-based ROM successfully captures the 3D IBCV, the truncation rank (r) significantly affects the accuracy of the IBCV reconstruction. Furthermore, four dominant IBCV structures are identified. Among them, Mode 1 (1.0 fn) embodies the primary dynamic features of the IBCV, whose spatial morphology and frequency are consistent with the original IBCV. Mode 3 (2.0 fn) reveals the secondary vortex dynamic behavior induced by the downstream development of the primary vortex along the blade passage. In addition, the DMD-based ROM enables accurate short-term extrapolative prediction of IBCV evolution over a full runner revolution, achieving excellent agreement with Computational Fluid Dynamics (CFD) results while reducing the computational time from hours to seconds with an acceleration of approximately 9600 times. This study deepens the understanding of IBCV formation and evolution from a dynamical perspective and develops an efficient DMD-based reduced-order framework for rapid IBCV analysis, flow-field reconstruction, and short-term evolution prediction in Francis turbines.

Francis turbines operating under sediment-laden conditions suffer from cavitation and sediment erosion, whose synergistic interaction critically threatens operational stability. This study employs a three-phase numerical framework for a Francis turbine and develops a multi-objective optimization strategy integrating hydraulics enhancement, cavitation alleviation, and erosion resistance. Two inter-blade cavitation vortices and a sheet-like flow-separation cavitation are identified at different guide vane openings, causing flow blockage, velocity redistribution, and particle accumulation near vortex peripheries. Erosion is strongly correlated with these vortical structures, exhibiting high intensity at vortex boundaries due to elevated particle velocity and concentration, whereas remaining weak in vortex cores and wall-vortex interfaces. Runner optimization with increased inlet-edge twist effectively modifies the flow pattern and sediment transport. Under two inter-blade cavitation vortex conditions, optimized hydraulic efficiency increases by 2.858% and 1.846%, with cavitation volume reduced by 33.405% and 62.265%, and average blade erosion rate decreased by 19.659% and 23.363%, respectively. Under the sheet-like cavitation condition, hydraulic efficiency increases by 0.169%, accompanied by reductions of 91.898% in cavitation volume and 30.868% in erosion rate. Morphologically, high-erosion regions induced by inter-blade vortices are significantly alleviated. These findings elucidate cavitation-erosion coupling mechanisms and confirm the effectiveness of integrated optimization in suppressing cavitation and erosion.

The injector plays a critical role in energy conversion in Pelton turbines, but intense sediment erosion can lead to local deformation and endanger turbine stability. This study uses a volume of fluid-Lagrange (VOF-Lagrange) multiphase flow model to simulate injector erosion, analyzing the impact of particle parameters and needle opening on wall abrasion morphology and predicting erosion loss. Results show that particle diameter has the greatest influence on sediment discharge and component erosion, followed by sediment concentration and needle opening. Vortex positions and particle diameter significantly affect wall erosion distribution. Erosion is most severe at the nozzle contraction, inner rib trailing edges, and needle tip, with the needle’s relative erosion ratio sensitive to particle diameter, concentration, and opening changes. Larger particles increase slip velocity and wall residence time, shifting erosion from banding to sheet and intensifying asymmetry. This study offers insights into injector erosion, providing a foundation for injector optimization in Pelton turbines.

Reasonable capacity configuration is critical for co-generation systems. Existing studies inadequately characterize pumped storage flexibility. To address this, a precision model that considers the operational characteristics of pumped storage units is presented, which covers non-operable regions, transition losses, and reservoir water volume self-adaptive initial value method to accurately describe the flexibility of pumped storage units. A multi-objective optimization framework balancing economy, environmental protection, and stability is developed. This study proposes a model for optimal configuration of energy storage capacity in multi-energy co-generation system based on the precision modeling of pumped storage energy. A combination of large and small unit configurations is introduced to accommodate the different storage capacity requirements caused by the timing characteristics of renewable energy sources. Simulations demonstrate the model’s accuracy in flexibility characterization. In the case study of this paper, the Two Large + Two Small Units (2L+2S) scheme achieves 381.87 million RMB construction cost reduction relative to the Four Units with Equal Capacity (Equal-4C) scheme, while the 2L+2S scheme demonstrates lower net load fluctuation and higher utilization rate of the pumped storage units. Excluding power station infrastructure costs, the operating cost of the system is reduced by a minimum of 13.26%.

During Pelton turbine runaway, rotational speed rises rapidly and the runner flow remains highly turbulent, reducing unit stability and inducing strong hydraulic vibrations that shorten component life. This study applies the finite volume method to simulate transient flow in a six-nozzle Pelton model from rated to maximum speed. Comparison with model tests shows runaway speed errors within 5%, ensuring result reliability. The findings reveal that during runaway, as rotational speed increases, torque decreases, while the overflow velocity at the outlet edge rises from below 1 m/s to above 35 m/s, indicating intensified turbulent fluctuations in the runner region that significantly hinder the incoming jet. The amplitude of runner hydraulic thrust fluctuations rises, with the axial thrust pulsation at a 24mm opening nearly doubling that at a 12mm opening, increasing the risk of accidental impacts between adjacent components. Energy dissipation in the runner is primarily driven by Reynolds stress work and turbulent kinetic energy production, accounting for over 80% of total dissipation, As speed increases, pressure-side high-energy clusters, which is regions of rapid energy transfer and dissipation, move forward, while intensified suction-side splashing enlarges the high-energy region.

Accurately characterizing the operational status of a hybrid energy storage system is essential to optimizing its performance. This paper provides a real-time dispatch model to characterize the complementary dynamic response capabilities of the pumped hydro storage and electrochemical energy storage. This model defines the transient time and trajectory between the steady states of pumped hydro storage and adopts a 5-min dispatch interval to fully exploit the advantages of the energy storage systems. The integrated regulation ability of the hybrid energy storage system is assessed through intra-day and real-time rolling dispatch simulations for an energy base in Northwest China. Results show that the proposed model more effectively coordinates the operational transitions of pumped hydro storage and electrochemical energy storage, enhancing their joint regulation performance. The 5-min dispatch increased the average regulation power margin of the pumped hydro storage and electrochemical energy storage by 36.48 MW and 28.96 MW, respectively. This study provides a new perspective for the coordinated operation of capacity-type and power-type storage systems.

Because of high-speed jet impingement, free-surface deformation, and three-phase flow, cavitation development on Pelton turbine buckets is highly unsteady and spatially complex, making vapor-based criteria insufficient for identifying erosion-prone regions. To address this issue, this study develops a multi-criteria cavitation erosion risk assessment framework for Pelton turbine buckets based on near-wall vapor, rapid vapor collapse, low air-content conditions, and transient pressure response. A three-dimensional unsteady cavitating-flow model of a complete runner with 21 buckets was established using the VOF multiphase model, the SST k−ω turbulence model, and the Schnerr–Sauer cavitation model, and was validated against experimental efficiency data. The numerical results show good agreement with the experiments, with a maximum deviation of 1.43% and a mean absolute deviation of 0.82%. The proposed framework indicates that cavitation risk first appears on the front face of the cut-out, whereas the risk on the back side occurs later but persists longer. With increasing needle opening, the near-wall vapor area, collapse region, and cavitation erosion all increase significantly. When the needle stroke is S≤12 mm, vapor attachment is already observed on the bucket surface, but erosion risk remains weak and delayed because the required criteria are not satisfied simultaneously during the initial cavity-growth stage. Cavitation also slightly reduces the mean runner torque and enhances radial force fluctuations, reflecting its influence on the unsteady loading environment. Compared with vapor-based approaches, the proposed framework more effectively identifies high-risk cavitation erosion regions on Pelton turbine buckets and provides a useful basis for cavitation-risk evaluation, structural optimization, and operation and maintenance.

Hydropower units often operate under complex conditions caused by water head change, guide-vane regulation, and load adjustment. These condition changes make it difficult to identify gradual performance degradation from monitoring signals alone. To solve this problem, this paper proposes a condition-aware performance health index construction and multi-source signal-mapping method for hydropower units. First, active power, guide-vane opening, and water head are used as the main operating variables. After data preprocessing and steady-state screening, water head is used as a prior constraint to divide the hydraulic boundary. FCM clustering is then used in each head layer to obtain different operating regions. Second, a high-quantile performance envelope is built in each operating region. The optimal active power is used as the performance benchmark, and the performance health index HIperf is constructed by comparing actual power with optimal power. The results show that the proposed method can describe the performance deviation under comparable operating conditions. The smoothed daily HIperf shows a degradation trend before maintenance and a recovery trend after maintenance. Finally, vibration and shaft-swing signals are mapped to HIperf to construct the signal-based health index HIsig. The mapping result shows good consistency between HIsig and HIperf, and shaft-swing features show stronger sensitivity than vibration features. The proposed framework focuses on daily-scale degradation trend identification using steady-state operating samples, while transient operating events are excluded from the current analysis. The proposed method provides a useful reference for degradation trend identification and health assessment of hydropower units under complex operating conditions.

The imbalance between power supply and demand arising from the high penetration of renewable energy poses a critical challenge for both short-term coordination and long-term reliability. Traditional planning methods overlook the integration of seasonal energy storage and the coordinated optimization across time scales. Subsequent failure to adequately account for the operational characteristics of coupled units hinders the effective balance between long-term energy gaps and short-term economic benefits. This study proposes a planning methodology for hydro-wind-PV complementary systems, considering short-term and seasonal energy storage techniques, to improve the reliability and flexibility of low-carbon energy systems. A typical high renewable energy penetration scenario prevalent in western China is used to reveal the cross-seasonal energy mismatch caused by the seasonal fluctuations in renewable generation and varying load profiles. The study proposes an innovative power curve characterization method based on a dual-feature ordered clustering network to accurately describe the seasonal supply-demand variations by analyzing the annual net load ratio sequence and varying hydropower flow characteristics. Further, a cross-time-scale constraint framework is constructed, embedding the long-term scheduling results into the short-term planning. Also, a hydrogen-hydropower coupled scheduling model is developed, integrating hydrogen supply resilience indicators and bidirectional energy flow constraints for units, along with a multi-slot variable-load start-stop strategy for electrolyzers to enhance the system's resilience against perturbations. A comparative analysis is conducted using three reference scenarios, and the results indicate that the proposed hybrid energy storage planning scheme effectively reduces power shortages by 42.5% and decreases the curtailment of renewable energy by 66.4%. Additionally, the system's resilience can be dynamically adjusted using a resilience weight factor (alpha), demonstrating its ability to balance economic efficiency and flexibility in the face of seasonal fluctuations. The findings provide theoretical support and practical references for achieving multi-time-scale balance in high-penetration renewable energy power systems.

Cavitation-jet-induced erosion often leads to severe material degradation, posing critical challenges to the design and operation of hydraulic machinery. In this study, medium compressibility is incorporated into an Eulerian-Lagrangian (E-L) method to improve the prediction of impact-load intensity generated by bubble collapse, and the framework is further coupled with a novel erosion model that accounts for material equivalent deformation to assess cavitation erosion pattern on SS 316 L surfaces. Comparisons with cavitating-jet experiments show that the proposed method reproduces the main erosion-pattern characteristics on both the lower and upper disks of a nozzle. For the lower disk of the nozzle, the predicted peak cumulative equivalent erosion pit depth (EEPD) is located in the range of r= 21–23 mm. The simulations further indicate that, under the present condition, the dominant contribution to the predicted erosion arises from collapsed bubbles with diameters of 0-50 μm, while the simulated impact-load statistics exhibit an approximately power-law-like distribution over the resolved range. Most predicted cavitation pits have diameters below 40 μm, consistent with the experimentally observed predominance of small-scale pits. For the upper disk, the predicted erosion pattern exhibits two distinct rings, with an overall intensity substantially lower than that on the lower disk, and the maximum EEPD occurs in the first erosion ring. In the second erosion ring, the peak value is located in the range of 22 mm < r< 24 mm, and its intensity decreases by 65.4 % compared with that in the first erosion ring. The present study offers a useful basis for understanding cavitation erosion characteristics and provides valuable insights for structural anti-cavitation erosion design.

Water hammer with column separation is a highly dangerous phenomenon in long-distance water transmission pipelines, potentially leading to structural damage or even loss of life. During the transient process, when pressure drops below the saturation pressure of dissolved gases, dissolved gases are released. However, the classical discrete vapor cavity model (DVCM) does not fully account for this effect, causing deviations in predicting the pressure peak and phase. This study innovatively incorporates a variable-mass gas release model into the DVCM, establishing the discrete vapor cavity model with gas release (DVCM-GR). Sensitivity analyses on grid resolution, weighting factors, and semi-empirical gas release rate coefficients were conducted, with results compared to both classic DVCM and experimental data. The results indicate that the prediction of pressure wave peak by the DVCM-GR model is mainly influenced by grid resolution, while the phase of the pressure wave is affected by the combined effect of all three factors. Specifically, an increase in grid resolution and semi-empirical gas release rate coefficient enhances the released gas mass, decreasing wave speed and causing phase delay, whereas a larger weighting factor produces the opposite effect. Compared with the DVCM, the DVCM-GR mitigates phase deviation and improves both peak and waveform predictions, especially when coupled with the Vardy and Brown friction model. This study highlights the significance of gas release effects in the simulation of water hammer with column separation, providing a new model option and theoretical foundation for more accurate transient analysis in pressurized pipelines.

With the advancement of the sharing economy and increasing integration of distributed renewable energy, shared energy storage (SES) systems have emerged as strategic and independent participants in electricity markets. This study proposes a novel bi-level optimization model where SES acts as a strategic leader in joint energy and ancillary service markets under uncertainty. First, scenario generation techniques based on kernel density estimation, Copula theory, and white noise are applied to capture the stochastic behavior of wind, solar, and load profiles. Secondly, a Stackelberg game-based framework is developed. The upper-level problem optimizes SES bidding strategies, while the lower-level simulates market clearing with conventional generators and frequency regulation services. Then, case studies based on the IEEE-30 node system validate the effectiveness of SES participation in the spot market. Results show that SES units predominantly participate in frequency regulation ancillary services, with participation rates exceeding 90 %-reaching 98.8 % in transitional seasons and 90.4 % during volatile periods. Revenue analysis highlights significant differences in earnings from the frequency regulation ancillary services market (23.7 % and 83.7 % for the two units). The proposed model shortens the cost recovery period by 2-3 years and increases overall revenue by approximately 33.5 %. Overall, the model enables SES units to formulate rational bids aligned with actual market dynamics, enhancing competitiveness and promoting efficient resource allocation.

High-pressure turbines are subjected to extreme thermal loads, with the rotor tip being the most vulnerable region to thermal failure. This study presents a novel blade tip design method based on the traditional squealer tip, incorporating two new pressure-side rim modeling: (i) the Shelf tip, part of the pressure rim is shifted towards the suction section to form a vertical platform, and (ii) the Incline tip, the shelf is inclined towards the suction surface to create an inclined platform. A detailed aerothermal performance analysis reveals distinct behaviors between the two designs. Compared to the baseline squealer tip, the Shelf tip increases tip leakage and results in a 0.106 % reduction in efficiency, along with a 0.85 % increase in the average heat transfer coefficient (HTC) in the tip region. In contrast, the Incline tip reduces leakage, leading to a 0.155 % gain in efficiency, while increasing the average HTC by 3.90 %. Although the Shelf tip causes a slight decline in aerothermal performance, both designs show potential benefits when coupled with an appropriate film cooling strategy, improving the overall thermal management of the blade tip. Subsequently, the effects of geometric parameters-cavity depth and platform width-on performance were investigated. Results show that increased cavity depth and platform width degrade the Shelf tip performance but enhance that of the Incline tip. Furthermore, integrating film cooling hole arrangements with the novel tip designs significantly improves cooling efficiency. Notably, the Shelf tip with optimized film hole layout achieves a maximum relative improvement of 71.10 % in average film cooling effectiveness. This study also proposes a parametric design method for inclined blade tips and establishes an integrated framework that combines geometric modeling, aerothermal performance analysis, and cooling evaluation. The findings demonstrate that optimal aerothermal performance can be achieved by combining inclined tip geometry with film cooling, especially under conditions of increased cavity depth and platform width-offering a promising direction for advanced high-pressure turbine blade tip design.

As a flexible regulating power source, pumped storage units play a crucial role in enabling the large-scale integration of renewable energy into power grids. Through interregional regulation, they balance the generation and consumption of renewable energy across different regions, thereby enhancing overall utilization efficiency. However, during this process, units frequently traverse or directly operate within the S-shaped characteristic region (S region), which may induce operational instability. When a high-head pump turbine enters the S region, large-scale flow separation and complex vortex inevitably develop within the flow components. The dynamic evolution of these unsteady structures induces high-amplitude pressure fluctuations and force pulsations, posing significant threats to the safe and stable operation of the unit. To elucidate the mechanisms of pressure fluctuation and force evolution in the S region, this study investigates a high-head model pump turbine through unsteady numerical simulations at representative operating points with a 12 degrees guide vane opening. The analysis focuses on internal flow characteristics, pressure fluctuations, and runner force pulsations. The results show that unstable vortex structures, including circumferential and cross flows, develop near the runner inlet, leading to pronounced pressure fluctuations. Time-frequency analysis reveals that cross flow within the runner generates low-frequency components at 0.3 fn and 0.4 fn, while rotating stall in the vaneless space causes low-frequency fluctuations at 0.6 fn and 0.7 fn. In contrast, rotor-stator interaction produces high-frequency components at 9.0 fn. Further analysis confirms that rotating stall and cross flow are the primary sources of flow instability in the S region of pump turbines. Moreover, the runner force results demonstrate that vortex structures induced by cross flow significantly affect the radial force distribution, whereas the axial force is predominantly governed by rotor-stator interaction. These findings provide a theoretical basis for optimizing the hydraulic design and enhancing the operational stability of pumped storage units.

The power system with a high proportion of renewable energy installed capacity requires large-scale power supply adjustment to ensure stable operation. Pumped storage, as a typical large-scale flexible power supply, can effectively stabilize the output fluctuations of renewable energy. This study aims to enhance the flexibility of novel power systems by exploring the regulation potential of pumped storage under extreme scenarios. Extreme scenarios with low, medium, and high renewable penetration rates are generated using Gaussian Mixture Model (GMM) clustering. These scenarios enable an in-depth analysis of flexibility regulation demands and capabilities on both the supply and demand sides. A scheduling optimization model is developed to assess the flexibility regulation capacity and economic benefits of pumped storage. The model quantifies the flexibility regulation capacity and the total daily electricity cost of pumped storage under different scenarios. The results show that in the medium penetration scenario, the total transferable load and its peak periods are reduced. In the high penetration scenario, the flexibility regulation capacity of pumped storage becomes more pronounced. When the ratio of renewable energy, pumped storage, and thermal power is 2:1:1, pumped storage provides enhanced flexibility regulation and minimizes the total electricity cost.

While finite control set model predictive torque control (FCS-MPTC) offers fast response and direct torque control for permanent magnet synchronous motors (PMSMs), its reliance on manually tuned weighting factors in cost functions limits adaptability and robustness. To address this, a priority ranking-based voltage vector selection scheme is introduced to eliminate the need for weighting factors. Firstly, the limitations of traditional FCS-MPTC approaches are analyzed, emphasizing the necessity of replacing empirical weight tuning. Secondly, a sliding mode observer is designed to estimate torque, with Lyapunov-based analysis ensuring stability and robustness to parameter variations. Finally, a dual-priority ranking mechanism is applied to evaluate candidate voltage vectors based on dynamic performance and torque ripple, achieving effective control without increasing computational complexity. Finally, simulation is conducted on a three-phase PMSM to verify the effectiveness of the proposed FCS-MPTC strategy.

In the context of flexible grid regulation, Francis turbines often operate under off-design conditions with frequent load transitions, during which cavitation vortices pose serious stability challenges. This study investigates the evolution of cavitating vortex structures during load reduction using dynamic mesh-based numerical simulations. Two distinct vortex types are identified: blade flow-separation cavitation vortices near the suction side leading edge, and inter-blade cavitation vortices extending from the runner crown to the trailing edge. As the load decreases, the former weakens and vanishes, while the latter intensifies and dominates the runner cavitation pattern. The reduced flow velocity aggravates blockage, and vortex cores are enveloped by high-speed regions. Hankel-Dynamic Mode Decomposition (DMD) analysis shows that Mode 0, reflecting the pressure trend, governs pressure fluctuations across all stages, alongside notable energy contributions from guide vane passing frequency and low-frequency modes. To suppress cavitation vortices, a blade optimization strategy targeting hydraulic efficiency and minimum pressure is proposed. The optimized blade, featuring a reverse C-shaped at the blade leading edge, reduces cavitation volume by 91.28 % and 83.15 %, and pressure amplitudes by 91.85 % and 80.73 % at two cavitation vortex conditions. These findings provide insights and solutions to enhance the operational stability of Francis turbines under transient conditions.