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.

中文翻译：

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基于灰色关联分析的支持向量机水电水库运行规律推导

在实际应用中，合理推导运行规则可以显着提高梯级水电站的中长期联合运行。实际优化操作的关键问题是从确定性的优化操作结果中选择有效的属性，然而，目前还没有通用的、成熟的方法来解决这个问题。首先，建立了考虑回水效应的水电站水库联合优化运行模型。然后应用动态规划和渐进优化算法求解联合最优运行模型，得到确定性优化结果。最后，应用灰色关联分析方法，从得到的结果中选取更有效的因素作为支持向量机的输入，进一步推导运算规则。以长江上游西洛渡和向家坝梯级水库为例。结果表明，所提出的方法能够获得更好的输入因子以提高SVM的性能，西洛杜和向家坝提出的方法的均方根误差最小值分别为94.33和21.32。西洛渡和向家坝水力发电绝对误差分别为2.57和0.42。总的来说，这项研究为指导水电水库系统的联合运行提供了一个很好的、有前景的替代工具。以长江上游西洛渡和向家坝梯级水库为例。结果表明，所提出的方法能够获得更好的输入因子以提高SVM的性能，西洛杜和向家坝提出的方法的均方根误差最小值分别为94.33和21.32。西洛渡和向家坝水力发电绝对误差分别为2.57和0.42。总的来说，这项研究为指导水电水库系统的联合运行提供了一个很好的、有前景的替代工具。以长江上游西洛渡和向家坝梯级水库为例。结果表明，所提出的方法能够获得更好的输入因子以提高SVM的性能，西洛杜和向家坝提出的方法的均方根误差最小值分别为94.33和21.32。西洛渡和向家坝水力发电绝对误差分别为2.57和0.42。总的来说，这项研究为指导水电水库系统的联合运行提供了一个很好的、有前景的替代工具。西洛杜和向家巴提出的方法得到的均方根误差和最小值分别为94.33和21.32。西洛渡和向家坝水力发电绝对误差分别为2.57和0.42。总的来说，这项研究为指导水电水库系统的联合运行提供了一个很好的、有前景的替代工具。西洛杜和向家巴提出的方法得到的均方根误差和最小值分别为94.33和21.32。西洛渡和向家坝水力发电绝对误差分别为2.57和0.42。总的来说，这项研究为指导水电水库系统的联合运行提供了一个很好的、有前景的替代工具。