For an open channel with cascade pumping stations, the water level immediately upstream of the pumping station should be kept constant to ensure pumping stability and lining safety. In this study, a simple method was proposed to determine the control time of the pumping station to ensure a stable water level immediately upstream of the pumping station using reverse analysis. The variable discharge process and fixed water level were taken as the upstream and downstream boundaries of the one-dimensional open channel hydrodynamic model, and the discharge process of the pumping station was obtained under ideal conditions. The control time was determined by the equivalent water volume change considering the step change of the discharge of the pumping station. A case study was performed using the Jiaodong water diversion project from Songzhuang sluice to Huibu pumping station (G1–P1), and the effects of the initial discharge, variable discharge, and downstream water level on the control time were investigated. The results show that (1) the larger the initial discharge, the shorter the control time; (2) increasing the upstream discharge reduced the control time, while decreasing the upstream discharge increased the control time; (3) the control time decreased with the increase of the water depth immediately upstream of the pumping station.

Incorporation of Optimal Limited Ecological Curves into the Operation Chart of Cascade Hydropower Systems to Alleviate Ecological Damages in Hydrological Extremes

The increasing integration of variable renewable energy (VRE) into power grids has significantly widened the peak-to-valley difference in net load and intensified its volatility. To follow these rapid load changes, cascade hydropower plants must frequently adjust their output, operate within unstable oscillation zones, or undergo repeated start-stop cycles. This creates a growing conflict between the system’s demand for peak shaving and the actual operational capabilities of hydropower plants. To address this challenge, this paper proposes a method for reconstructing the load curve based on fuzzy recognition of peak-valley characteristics. By adaptively adjusting the number of identified features, the method transforms the highly fluctuating net load into a multi-segment linear form. This preserves essential peak and valley information while promoting output stability. Building on this reconstructed load curve, a short-term peak-shaving model for cascade hydropower is developed, aiming to minimize the standard deviation of the residual load. The model is solved using an improved progressive optimality algorithm (POA) that integrates feasible region reduction with a multi-segment, variable-step-size search strategy. The peak-shaving performance is evaluated under three VRE penetration scenarios: low (10%), medium (20%), and high (40%). A case study conducted on China’s Wujiang River demonstrates the effectiveness of the proposed method. The load curve reconstruction transforms hydropower output from hourly sawtooth-like fluctuations into a stepwise pattern, albeit with a slight reduction in the peak-to-valley difference optimization rate (PVOR). For example, in the 10% penetration scenario, the frequency of output adjustments decreases by 73.2%. As the VRE penetration rate increases, the net peak-to-valley load difference grows sharply, and the PVOR of the reconstruction scheme declines from 26.70% to 9.12%. Nevertheless, the frequency of output adjustments does not exceed 15 times, thereby maintaining stable operation. The proposed approach achieves a reasonable trade-off between peak-shaving effectiveness and operational stability, offering a practical solution for hydropower dispatch in grids with high VRE penetration rates.

Under high-intensity peak shaving and frequency regulation, the output of hydropower plants fluctuates frequently, significantly increasing the complexity of load distribution among cascade hydropower plants (LDCHP). Currently, commonly used solution methods include traditional dynamic programming and intelligent optimization algorithms. The former suffers from the "curse of dimensionality" during computation, whereas the latter typically relies on population-based evolutionary mechanisms, often resulting in low convergence efficiency and suboptimal computational performance. To address the LDCHP challenge, this study develops a model for LDCHP and applies the A* algorithm to solve the related dispatching problem. Using cascade hydropower plants in the middle reaches of the Dadu River Basin, China, as a case study, the proposed approach is empirically validated. The results indicate that, compared with the DP algorithm, the A* algorithm achieves an average computational efficiency improvement of 5,372.9 times, alongside a 1.56% decrease in energy storage utilization efficiency. Furthermore, the total energy storage loss calculated by the A* algorithm is 22.41% lower than actual operational data, demonstrating its capacity to significantly enhance solution efficiency without compromising scheduling benefits. Overall, this approach provides valuable technical support for solving complex cascade hydropower dispatching models.