Description: Water, Vol. 10, Pages 20: Studying Operation Rules of Cascade Reservoirs Based on Multi-Dimensional Dynamics Programming Water doi: 10.3390/w10010020 Authors: Zhiqiang Jiang Hui Qin Wenjie Wu Yaqi Qiao Although many optimization models and methods are applied to the optimization of reservoir operation at present, the optimal operation decision that is made through these models and methods is just a retrospective review. Due to the limitation of hydrological prediction accuracy, it is practical and feasible to obtain the suboptimal or satisfactory solution by the established operation rules in the actual reservoir operation, especially for the mid- and long-term operation. In order to obtain the optimized sample data with global optimality; and make the extracted operation rules more reasonable and reliable, this paper presents the multi-dimensional dynamic programming model of the optimal joint operation of cascade reservoirs and provides the corresponding recursive equation and the specific solving steps. Taking Li Xianjiang cascade reservoirs as a case study, seven uncertain problems in the whole operation period of the cascade reservoirs are summarized after a detailed analysis to the obtained optimal sample data, and two sub-models are put forward to solve these uncertain problems. Finally, by dividing the whole operation period into four characteristic sections, this paper extracts the operation rules of each reservoir for each section respectively. When compared the simulation results of the extracted operation rules with the conventional joint operation method; the result indicates that the power generation of the obtained rules has a certain degree of improvement both in inspection years and typical years (i.e., wet year; normal year and dry year). So, the rationality and effectiveness of the extracted operation rules are verified by the comparative analysis.