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A stochastic programming with recourse model requires the consequences of recourse actions be modeled for all possible realizations of the stochastic variables. Continuous stochastic variables are approximated by scenario trees. This paper evaluates the impact of scenario tree reduction on model performance for hydropower operations and suggests procedures to determine the optimal level of scenario tree reduction. We first establish a stochastic programming model for the optimal operation of a cascaded system of reservoirs for hydropower production. We then use the neural gas method to generate scenario trees and employ a Monte Carlo method to systematically reduce the scenario trees. We conduct in-sample and out-of-sample tests to evaluate the impact of scenario tree reduction on the objective function of the hydropower optimization model. We then apply a statistical hypothesis test to determine the significance of the impact due to scenario tree reduction. We develop a stochastic programming with recourse model and apply it to real-time operation for hydropower production to determine the loss in solution accuracy due to scenario tree reduction. We apply the proposed methodology to the Qingjiang cascade system of reservoirs in China. The results show: (1) the neural gas method preserves the mean value of the original streamflow series but introduces bias to variance, cross variance, and lag-one covariance due to information loss when the original tree is systematically reduced; (2) reducing the scenario number by as much as 40% results in insignificant change in the objective function and solution quality, but significantly reduces computational demand.

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Transboundary river water resources allocation is important in water resources management. Conflicts often arise when different water users compete for a limited water supply. This study proposes a two-level asymmetric Nash-Harsanyi Leader-Follower game model to resolve conflicts of interest in transboundary river water resources allocation problems. In the proposed model, we use bankruptcy theory to derive disagreement points and determine the bargaining weights considering the principles of equity and efficiency. For comparison, a model that does not consider disagreement points and bargaining weights are also used to demonstrate the importance of disagreement points and bargaining weights. The proposed model is applied to a real case of the Huaihe River basin in China, which is facing water shortages. In the case study, the watershed management agency serves as the leader, three provinces (Henan, Anhui and Jiangsu) serve as followers, and successive linear programming is used to solve the model for followers. The results show that the proposed disagreement points can guarantee basic water demand, and the bargaining weights can better balance the economic development levels among followers.

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The research of joint optimization operation of complex flood control systems is still in the process of development. This paper introduces a decomposition-coordination model for solving the multiobjective optimization problem for real-time flood control operation in reservoir group and flood storage basin. The multi-objective programming is established for maximum safety of the reservoir group and minimum losses of flood storage basin, according to the real-time flood control requirements. Then, a third-order hierarchical optimization decomposition-coordination model is proposed for solving the multi-objective programming problem, based on the decompositioncoordination principle of large scale system theory. It takes advantage of an objective coordination method and model coordination method to accomplish global optimization and combines progressive optimality algorithm to solve the subsystem local optimization. Finally, the model is applied for simulating the storm flood in July 2007 in the middle reaches of the Huaihe River Basin in China. Results show that the proposed decomposition-coordination model can efficiently calculate the reservoir group optima release strategy and flood storage basin diversion process, and meet the safety discharge at the downstream control section.