A multi-objective optimization model of cascade reservoirs was developed to maximize the power generation and minimizie the appropriate ecological flow shortage index (AEFSI) downstream from the reservoir. Additionally, the non-dominated sorting genetic algorithm (NSGA-II) was used to search for multi-objective Pareto optimal solutions. The paper took the Three Gorges-Gezhouba cascade reservoirs as a case study. After validating the model, data from three typical years were used in the optimization. The results indicated that maximizing power generation by adjusting the optimal rules increased power generation by 1.07%, 0.91%, and 1.03% in normal, wet, and dry hydrological years, respectively, while increasing the AEFSI by 22.12%, 11.78%, and 14.67% (compared to real operations). The AEFSI was improved (decreased) by 21.90%, 10.27%, and 18.52% when the optimal rules favored the downstream ecology, but power generation decreased by 1.61%, 1.06%, and 2.29%, respectively, in the different hydrological years. Moreover, the results provide a set of well-distributed optimal solutions along the Pareto front that allow decision-makers to easily determine the best compromised solutions based on the trade-offs between the economic and ecological benefits. The results of this study provide guidance for decision-makers to improve the comprehensive benefits of the Three Gorges-Gezhouba cascade reservoirs.

To explore the influence of the Xiluodu-Xiangjiaba cascade reservoir system on the appropriate environmental flow (AEF) of the Jinsha River, a multiobjective optimal cascade reservoir model was established with the aim of maximizing power generation while minimizing the downstream degree of AEF alteration. The AEF was determined using the range of variability approach (RVA). The optimal model was solved using an improved version of NSGA-II called INSGA2-DS. Inflows in typical normal and dry years were selected for optimization. The results show that in a normal year, power generation can be increased by 1.28% compared with that under the current regular operation conditions by prioritizing the maximization of power generation, in which case the degree of AEF alteration will increase by 13.86%. In contrast, the degree of AEF alteration will decrease by 22.53% if ecological protection is prioritized, but power generation will decrease by 0.62%. Similarly, in a dry year, power generation can be increased by 1.76% compared with that under the current regular operation conditions to maximize economic benefit, in which case, the degree of AEF alteration will increase by 4.95%. By contrast, the degree of AEF alteration can be decreased by 13.70% if the objective is AEF minimization, but power generation will decrease by 0.48%. These research results provide useful information for the formulation of ecological operation schemes involving cascade reservoirs on the Jinsha River.

To quantitatively calculate the spatiotemporal differences in the effect of the water supply from the Three Gorges Reservoir, three typical falling modes were proposed: falling in advance, uniform falling, and falling at a high water level. Based on a one-dimensional and two-dimensional model coupled hydrodynamic model, the spatial and temporal distributions of the Dongting Lake water level were compared with the ecological water level, which was assessed using a hydrological method, and the power generation of the Three Gorges Hydropower station under different scenarios was also analyzed. The results showed that the water supply effect of the falling in advance and falling at high water level scenarios on the Dongting Lake water level exhibited obvious spatial and temporal heterogeneity, but the effects were mainly concentrated in the northern part of eastern Dongting Lake, whereas limited effects were observed for the southern and western Dongting Lake. In scenario 1 (falling in advance), the water level at Chenglingji increased by 0.12 m on average and power generation was reduced by 0.30%. In scenario 3 (falling at a high water level), the water level at Chenglingji decreased by 0.09 m on average; and power generation increased by 0.28%.