Short-term optimal scheduling of cascade hydropower stations enhances their flexible regulation and power generation capabilities. However, nonlinear function relationships and multistage and hydraulic interdependencies present significant challenges, resulting in considerable solution errors, premature convergence, and high computational demands. This study proposes a progressive linear programming method that decomposes nonlinear functions to address these challenges. First, to accurately represent nonlinear functions and mitigate computational complexity, the entire feasible domain is partitioned into multiple contiguous subdomains in which nonconvex nonlinear functions within each subdomain can be equivalently replaced by linear relationships. Second, a progressive linear programming optimization algorithm is devised to prevent premature convergence, utilizing continuous subdomains rather than discrete points as state variables and incorporating the progressive optimality principle. Finally, to increase the solution efficiency, a dimensionality reduction strategy via the feasible domain state dynamic acquisition method is presented and optimized after excluding the infeasible states in each stage. The simulation of three cascade hydropower stations in a river basin in southwest China shows that the proposed method can achieve a superior peak regulation effect compared to the conventional mixed integer linear programming and progressive optimality algorithm. During the dry and wet seasons, the residual load peak–valley differences at the three stations are reduced by 612 MW and 521 MW compared to the MILP and 1889 MW and 2439 MW compared to the POA, which underscores the effectiveness of the method in optimizing the short-term scheduling of cascade hydropower stations.

Accurate forecasting of the tail water level (TWL) is of great importance for the safe and economic operation of hydropower stations. The prediction accuracy is significantly influenced by the backwater effect of downstream tributaries and the operation of adjacent hydropower stations, but the explicit quantification method of the backwater effect is lacking. In this study, a deep-learning-model-based forecasting method for TWL predictions under the backwater effect is developed and applied in the Xiangjiaba (XJB) hydropower station, which is influenced by the backwater effect of downstream tributaries, including the Hengjiang River (HJR) and the Minjiang River (MJR). Firstly, the random forest algorithm was used to analyze the influence of HJR and MJR flows with different lag times on the TWL prediction error of the XJB hydropower station. The results show that the time lags of the backwater effect of HJR and MJR run offs on the TWL of the XJB are 5~7 h and 1~2 h, respectively. Then, the run off thresholds of the HJR and MJR for impacting the TWL of the XJB station are obtained through scenario comparison, and the results show that the run off thresholds of the HJR and the MJR are 700 m³/s and 7000 m³/s, respectively. Finally, based on the analysis of the time lag and the threshold of the backwater effect, a deep learning model (LSTM)-based TWL forecasting method is established and applied to predict the TWL of the XJB station. The results show that the forecasting model has a good predictive performance, with 98.22% of absolute errors less than 20 cm. The mean absolute error over the validation dataset is 5.27 cm, and the maximum absolute error is 63.35 cm. Compared with the LSTM-based prediction model without considering the backwater effect, the mean absolute error decreased by 31%, and the maximum absolute error decreased by 71%.

The Jinsha River basin (JRB), known as China’s largest hydropower base, has been facing a surge in hydrological drought occurrences in the past several years. This study used the drought index model and soil and water assessment tool (SWAT) hydrological model to uncover the linkages between meteorological and hydrological drought using long-term datasets in the JRB. The results revealed that: (1) Over the past six decades, the JRB has experienced recurrent meteorological droughts, with the upper reaches being the most affected, accounting for a frequency of 17.5%. However, the frequency of drought in the middle and lower reaches has shown a marked increase in the last 15 years. (2) The frequency of hydrological drought in the JRB has been on the rise over the past six decades, with a particularly notable increase observed in the last two decades. Furthermore, a noticeable upward trend has been observed in the duration of these hydrological droughts. (3) The propagation durations from meteorological drought to hydrological drought exhibited noticeable seasonal differences in the JRB. The transmission duration during the flood season was shorter, whereas in the dry season, it was more protracted. Additionally, the connection between meteorological drought and hydrological drought demonstrates a weakening trend. The findings of this study hold significant implications for crafting an efficient reservoir dispatching strategy to safeguard the water security of the JRB.

Wind curtailment, caused by wind power uncertainty, has become a prominent issue with the large-scale grid connection of wind power. To fully account for the uncertainty of wind power output, a short-term hydro-wind-thermal operation method based on a wind power confidence interval is proposed. By utilizing the flexible start-stop and efficient ramp-up of cascade hydropower plants to smooth fluctuations in wind power output, a multi-objective optimal scheduling model that minimizes the cost of power generation and maximizes the consumption of clean energy is constructed. To reduce the solution’s complexity, we chunk the model according to the energy type using a hierarchical solution. The overall solution framework, which integrates a nonparametric method, a heuristic algorithm, and an improved particle swarm algorithm, is constructed to solve the model rapidly. The simulation results of a regional power grid show that the proposed method can attain an efficient solution in 83.5 seconds. Furthermore, the proposed method achieves an additional 455,600 kWh of hydropower and a reduction of ¥233,300 in the cost of coal consumption. These findings suggest that the proposed method is a good reference for the short-term operation of a hydro-wind-thermal combination in large-scale wind power access areas.

In this paper, improved reinforcement learning (IRL) is designed for the multi-objective optimization operation of a cascade reservoir system. The primary improvement of IRL is searching within limited solution space, based on the derived monotonic property: the first-order derivative relationship between individual reservoir water release decisions for mainstream use (i.e., hydropower generation) as well as tributary use (i.e., regional water supply) and the cascade system’s or a particular reservoir’s water availability, along with the synchronicity and substitutability assumption of storage distribution in the cascade system. The improved algorithm is then applied to a real-world cascade reservoir system in the Yangtze River of China. The results demonstrate the high computational efficiency and reasonable interpretability of IRL.

Accurate forecast of tail water level (TWL) is of great importance for the safe and economic operation and management of hydropower stations. The predictive performance is significantly influenced by the backwater effect of downstream hydropower stations and tributaries, but the explicit quantification method of the backwater effect is lacked. In this study, a deep learning model based forecasting framework for TWL predictions is established and applied to forecast TWL of Xiangjiaba (XJB) hydropower stations, which is influenced by the backwater effect of downstream tributaries including Hengjiang River (HJR) and Minjiang River (MJR). Firstly, the lag time of the backwater effect of HJR and MJR is analyzed based on the permutation importance. The results demonstrate that the lag time of backwater effect on the TWL of XJB is 5-7 hours for the HJR and 1-2 hours for the MJR. Then, the runoff thresholds of the HJR and MJR for impacting the TWL of the XJB station are obtained by scenario comparison, and the results show that the thresholds of HJR and MJR are 700 m3/s and 7000 m3/s respectively. Finally, the deep learning methods based TWL forecasting model is established based on the lag time and threshold analysis. The model is used to forecast the TWL in future 48 hours. The results show that the forecasting model has a good predictive performance with 98.22% of absolute errors less than 20 cm. The mean absolute error over the validation dataset is 5.27 cm and the maximum absolute error is 63.35 cm.