This study introduces a Model Predictive Control （MPC） method to construct a MPC scheme for joint optimal operation of cascade reservoirs in the downstream Jinshajiang River. The successive approximation dynamic programming algorithm is used to search the optimal solution within a closed-loop with the objective of maximizing power generation over a forecast period，and subsequently executes optimal decisions in open-loop MPC scheme. Five forecast accuracy scenarios are configured for sensitive analysis by synthesizing systematic and random error characteristics. The forecasting and operating of the cascade reservoirs are simulated across a complete hydrological year，i.e.，water supply period，main flood prevention period，and impoundment periods，and compare with current joint operation scheme. Results demonstrate that: ① Smaller forecast errors or longer forecast horizons lead to higher total hydropower generation of cascade reservoirs. ② Compared with the joint operation scheme，the MPC scheme with a 3-day forecasting error variance can significantly reduce water spillage by 5.21 billion m3 （−9.1%） and increase power generation by 2.96 billion kW·h （+1.5%）. ③ The MPC scheme exhibits profound intra-annual adaptability，which generates more power during the main flood prevention and impoundment periods while reduces spillway discharge during the refill period. The proposed MPC scheme features favorable control performance and strong robustness，and provides a new technical approach for implementing rolling "forecasting-operating-decision-making" for reservoir groups.

The regulation of upstream cascade reservoirs has significantly altered the downstream hydrologic regime and should be taken into account in design flood estimation. The current flood regional composition (FRC) methods do not consider the unfavorable situations for reservoir flood control operation. In this paper, a novel framework, the most unfavorable flood regional composition (MUFRC) method, was proposed based on flood risk analysis to estimate design flood in the cascade reservoir operation period. The cascade reservoirs in the Yalong River basin were selected as a case study. The results indicated that (1) the proposed MUFRC method would allocate more flood volume to the downstream uncontrolled sub-basin, and the precise definition of flood disaster loss could have a significant impact on the MUFRC method for the rational estimation of design flood. (2) The 1000-year design flood peak, and 3-day and 7-day flood volumes at the outlet section estimated by the MUFRC method are 15,400 m3/s, 3.91, and 8.42 billion m3, respectively, which are higher than the values estimated by other FRC methods. (3) The flood control water level in the downstream reservoir can be adjusted for the reduction in design floods in the operation period, which can additionally generate 460 million kW·h (+1.82%) of hydropower during the flood season. A comparison study and sensitivity analysis further proved that the MUFRC method can rationally allocate flood volume while balancing the flood risk and comprehensive utilization benefits, which is worth further study and practical application.

The existing trade-off between flood control and water conservation measured by flood limited water level (FLWL) during flood season hinders multi-reservoir system from realizing comprehensive benefits. To overcome this barrier, we reasonably allocated the complementary flood prevention storage based on the aggregationdecomposition technique, theoretically deduced the mathematical formula of power generation variation simplified from the cascade reservoir operation model, and dynamically operated reservoir water levels considering the inflow forecasting information. The Wudongde (WDD) - Baihetan (BHT) - Xiluodu (XLD) Xiangjiaba (XJB) cascade reservoirs in the downstream Jinsha River in China is selected as the case study. Results demonstrate that: (1) The derived power generation function monotonically increases only with the growth of the pre-discharge water volume. (2) The reduced proportion of the flood prevention storage of the WDD (or XJB) is favorable to boost the hydroelectric benefits of the WDD - BHT (or XLD - XJB) cascade reservoirs. Optimal allocation of flood prevention storage can increase 1.933 billion kW center dot h power generation annually (+2.15 %) for the WDD - BHT - XLD - XJB cascade reservoirs. (3) Further cooperated with dynamic operation of water levels, the WDD - BHT - XLD - XJB cascade reservoirs can totally generate 5.925 billion kW center dot h more hydropower annually (+6.60 %) using effective 5-day lead-time inflow forecasting information, while maintaining the design flood prevention standards.

Study region: The study region is the Yalong River basin, the largest tributary of the Jinsha River in China. Study focus: The most likely flood regional composition (MLFRC) method has been widely used to estimate the design flood of cascade reservoirs in the operation period, in which the Gumbel copula or t-copula is often selected to fit the theoretical joint distribution. However, the Gumbel copula is only suitable for 2 or 3 cascade reservoirs, while the t-copula has great uncertainty in parameter estimation. In this study, we introduce vine-copula into MLFRC framework to estimate design flood of cascade reservoirs, and comprehensively compare the universality of different copulas through statistical experiments and a case study on the cascade reservoirs in Yalong River basin. New hydrological insights for the region: The results indicated that: (1) Vine-copula significantly outperforms Gumbel copula and t-copula in terms of fitting the theoretical joint distribution. (2) The vine-copula based MLFRC method can successfully solve the different flood regional composition schemes most accurately in the simulated scenarios. (3) Compared with the design floods in construction period, the design floods in operation period in the Yalong River basin decrease significantly due to the regulation of upstream reservoirs. The 1000-year design flood at basin outlet section decrease by about 40 %.

The construction and operation of upstream reservoirs have significantly altered downstream hydrologic regime. Appropriate and quantifiable assessment method for the alteration of hydrologic regime is considerably vital and emergent for ecological protection and restoration. The Range of Variability Approach (RVA) and modified RVA methods have been widely used in practice to assess the hydrological alteration. However, these methods have failed to concurrently describe the distribution of indicator and morphological features in detail, which might inevitably lead to the misjudgment of alteration. This paper proposes a Joint Probability Density Difference Approach (JPDDA) method to address the major drawbacks of these previous methods with the introduction of Gaussian Kernel Density Estimation (KDE) and copula function. The annual average flow is selected as the reference variable to construct a proper joint probability density function between itself and other hydrological alteration indicators. The JPDDA method could describe the marginal distribution in detail through Gaussian KDE and also link the morphological features with copula function. Along with pervious methods, the hydrological alterations at Yichang hydrological station, Yangtze River are estimated based on the measured flow from 1949 to 2022. It is shown that the hydrologic regime has suffered from a moderate or even heavy alteration under the influence of massive upstream cascade reservoirs, and the JPDDA outperforms the other methods in terms of rationality and stability for practical assessments. Thus, the proposed JPDDA method is strongly advised to handle the hydrological alteration and could provide a reasonable reference for ecological operation.

Design floods are traditionally estimated based on the at-site annual maximum flood series, including historical information of hydraulic structures. Nevertheless, the construction and operation of upstream reservoirs undermine the assumption of stationarity in the downstream flood data series. This paper investigates non-stationary design flood estimation considering historical information from the Three Gorges Reservoir (TGR) in the Yangtze River. Based on the property that the distribution function of a continuous random variable increases monotonically, we proposed a novel time-varying P-III distribution coupled with the curve fitting method (referred to as the Tv-P3/CF model) to estimate design floods in the TGR operation period, and we comparatively studied the reservoir indices and parameter estimation methods. The results indicate that: (1) The modified reservoir index used as a covariate can effectively capture the non-stationary characteristics of the flood series; (2) The Tv-P3/CF model emphasizes the fitness of historical information, yielding superior results compared to time-varying P-III distribution estimated by the maximum likelihood method; (3) Compared to the original design values, the 1000-year design peak discharge Qm and 3-day and 7-day flood volumes in the TGR operation period are reduced by approximately 20%, while the 15-day and 30-day flood volumes are reduced by about 16%; (4) The flood-limited water level of the TGR can be raised from 145 m to 154 m, which can annually generate 0.32 billion kW h more hydropower (or increase by 6.8%) during flood season without increasing flood prevention risks.

The Wudongde-Baihetan-Xiluodu-Xiangjiaba cascade reservoirs in the lower Jingsha River shoulder the downstream flood control tasks jointly, and the complementary equivalent relationship between the flood prevention storage of these reservoirs is not considered during the planning and design stage.Based on the principle of water balance and the assumption of total flood prevention storage unchanged, the flood prevention storage of cascade reservoirs was aggregated and decomposed.The optimal allocation calculation formulas for two-reservoir and multi-reservoir systems were derived and solved numerically with power generation as the main objective.Results show that the Wudongde and Xiangjiaba reservoirs with relatively small storage allocate about 1.180 and 0.216 billion m3 of the flood prevention storage to the Baihetan and Xiluodu reservoirs respectively, which can generate extra 445 and 32 million kW·h hydropower from July to August for the Wudongde-Baihetan and the Xiluodu-Xiangjiaba aggregation systems.Joint and optimal allocation of flood prevention storage for the four cascade reservoirs can increase 1.037 billion kW·h hydropower annually from July to August, yielding significant economic benefits.

针对确定性水库优化调度模型难以直接应用于实际操作的局限性,建立雅砻江流域"三库七级"梯级水库电站联合优化调度模型,采用Gaussian径向基函数提取各水库的调度规则,并率定和检验拟合效果.结果表明,雅砻江梯级水库电站联合优化调度运行的年均发电量为 983.19 亿 kW·h,比设计多年平均发电量增加78.94 亿kW·h(+8.73%);两河口、锦屏I级和二滩水库的优化调度过程呈现一定规律,Gaussian 径向基函数拟合调度过程的决定系数R2 均大于 90%,能有效拟合其调度规则,且模拟调度结果相比设计值增发电量 51.27亿kW·h(+5.67%).

The equivalent relationships between flood prevention storage of a cascade reservoir system provide useful information for real-time operation. However, those relationships are implicitly hinted at in the optimized operation rules of downstream reservoirs, which may add difficultly in providing feasible operation strategies for engineering practice. In this study, we investigate the equivalent relationship between cascade reservoirs using a flood regional composition-based framework coupled with reservoir inflow and river flow routing techniques. We select the cascade reservoirs in the downstream Jinsha River and Three Gorges Reservoir (TGR) as the case study. Results reveal that (1) the equivalent relationship between flood prevention storage of cascade reservoirs in the downstream Jinsha River and TGR is approximately linear-related; (2) the conversion coefficient of equivalent relationship depends on the flood type, and the intercept term of equivalent relationship is mainly influenced by the design flood frequency; and (3) the TGR flood prevention storage (or water level) can be dynamically adjusted according to the corresponding reserved flood prevention storage of cascade reservoirs in the downstream Jinsha River, which can generate 3.56 billion kW center dot h ( +8.5%) extra hydropower during flood season without increasing flood control risks. (c) 2023 American Society of Civil Engineers.

水利水电工程兴建运行改变了下游河流的水文情势和来水来沙条件,推求梯级水库下游控制断面设计洪水成了亟需解决的难题.本文综述设计洪水地区组成法的研究进展及问题,推导概率组合离散求和法和改进离散求和法,对比分析两者的离散估计误差;结合清江水布垭～隔河岩～高坝洲梯级水库应用实例,比较讨论各种设计洪水地区组成法的优缺点和实用性.结果表明:(1)基于Copula函数的改进离散求和法可直接推导公式,且无需作独立化处理;离散求和法的总误差随着相关系数ρ的增大而显著增加;当ρ>0.2时不宜使用.(2)经水布垭～隔河岩水库调蓄后,高坝洲坝址1000年一遇设计洪峰流量削减了50%左右.(3)对于单座或2座水库,离散求和法和同频率地区组成法的适用条件分别为00.7,改进离散求和法和最可能地区组成法没有限制条件;对于3座及以上的梯级水库群,最可能地区组成法可得到唯一最佳方案解.研究成果可为我国《水利水电工程设计洪水计算规范》的修订提供参考.

The coincidence of floods in the mainstream and its tributaries may lead to a large flooding in the downstream confluence area, and the flood coincidence risk analysis is very important for flood prevention and disaster reduction. In this study, the multiple regression model was used to establish the functional relationship among flood magnitudes in the mainstream and its tributaries. The mixed von Mises distribution and Pearson Type III distribution were selected to fit the probability distribution of the annual maximum flood occurrence dates and magnitudes, respectively. The joint distributions of the annual maximum flood occurrence dates and magnitudes were established using copula function, respectively. Fuhe River in the Poyang Lake region was selected as a study case. The joint probability, co-occurrence probability and conditional probability of flood magnitudes were quantitatively estimated and compared with the predicted flood coincidence risks. The results show that the selected marginal and joint distributions can fit observed flood dataset very well. The coincidence probabilities of flood occurrence dates in the upper mainstream and its tributaries mainly occur from May to early July. It is found that the conditional probability is the most consistent with the predicted flood coincidence risks in the mainstream and its tributaries, and is more reliable and rational in practice.

The hydrologic data series are nonstationary due to climate change and local anthropogenic activities. The existing nonstationary design flood estimation methods usually focus on the statistical nonstationarity of the flow data series in the catchment, which neglect the hydraulic approach, such as reservoir flood regulation. In this paper, a novel approach to comprehensively consider the driving factors of non-stationarities in design flood estimation is proposed, which involves three main steps: (1) implementation of the candidate predictors with trend tests and change point detection for preliminary analysis; (2) application of the nonstationary flood frequency analysis with the principle of Equivalent Reliability (ER) for design flood volumes; (3) development of a nonstationary most likely regional composition (NS-MLRC) method, and the estimation of a design flood hydrograph at downstream cascade reservoirs. The proposed framework is applied to the cascade reservoirs in the Han River, China. The results imply that: (1) the NS-MLRC method provides a much better explanation for the nonstationary spatial correlation of the flood events in Han River basin, and the multiple nonstationary driving forces can be precisely quantified by the proposed design flood estimation framework; (2) the impacts of climate change and population growth are long-lasting processes with significant risk of flood events compared with stationary distribution conditions; and (3) the swift effects of cascade reservoirs are reflected in design flood hydrographs with lower peaks and lesser volumes. This study can provide a more integrated template for downstream flood risk management under the impact of climate change and human activities.