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In practical applications, the rational operation rule derivation can lead to significant improvements in the middle and long-term joint operation of cascade hydropower stations. The key issue of actual optimal operation is to select effective attributions from the deterministic optimal operation results, however, there is still no general and mature method to solve this problem. Firstly, the joint optimal operation model of hydropower reservoirs considering backwater effects are established. Then, the dynamic programming and progressive optimality algorithm are applied to solve the joint optimal operation model and the deterministic optimization results are obtained. Finally, the grey relational analysis method is applied to select more effective factors from the obtained results as the input of a support vector machine for further operation rule derivation. The Xi Luo-du and Xiang Jia-ba cascade reservoirs in the upper Yangtze river of China are selected as a case study. The results show that the proposed method can obtain better input factors to improve the performance of SVM, and smallest value of root mean square error by the proposed method of Xi Luo-du and Xiang Jia-ba are 94.33 and 21.32, respectively. The absolute error of hydropower generation for Xi Luo-du and Xiang Jia-ba are 2.57 and 0.42, respectively. Generally, this study provides a well and promising alternative tool to guide the joint operation of hydropower reservoir systems.

Operation Rule Derivation of Hydropower Reservoirs by Support Vector Machine Based on Grey Relational Analysis