Optimal operations of high-dimensional hydropower systems (HDHSs) with dozens or hundreds of plants face a serious challenge called “Curse of dimensionality” because the computational time and storage memory grow exponentially with the plant number. This study develops an efficient method to alleviate the dimensionality challenge. A random sampling (RS) technique is exploited to select representative water level states at each period by considering discrepant weights for different solution ranges. The RS can dynamically adjust sampling size and times with the selected samples. Moreover, acceptability and reliability parameters are introduced into the RS optimization to ensure a reasonable reliability level of the results. A feasible region identification (FRI) method is well designed to narrow the search range by transforming various operation constraints into equivalent water level limits and integrating them with water level range got from hundreds of simulation calculations. Furthermore, this method can use the water levels obtained in last iteration to dynamically update feasible regions during the calculation process. Three case studies involving a large-scale hydropower system with 21 plants are presented to verify the validity, efficiency, and sensitivity of the proposed method. Compared to dynamic programming (DP), discrete differential dynamic programming (DDDP) and progressive optimality algorithm (POA), the method requires only 0.85%, 1.27% and 3.14% of the computational effort to produce almost the same results. Moreover, a sensitivity analysis indicates that the reliability parameter in this method has a larger impact on the computational time than other parameters.

具有数十或数百个工厂的高维水电系统（HDHS）的最佳运行面临着一个严峻的挑战，即“维数诅咒”，因为计算时间和存储内存随工厂数量呈指数增长。这项研究开发了一种缓解尺寸挑战的有效方法。通过考虑不同解决方案范围的权重不同，利用随机采样（RS）技术选择每个时段的代表性水位状态。RS可以根据所选样本动态调整采样大小和时间。此外，将可接受性和可靠性参数引入RS优化中，以确保结果的合理可靠性水平。一种可行的区域识别（FRI）方法经过精心设计，可以通过将各种操作约束转换为等效水位限制并将它们与数百次模拟计算得出的水位范围相集成来缩小搜索范围。此外，该方法可以使用上次迭代中获得的水位在计算过程中动态更新可行区域。提出了三个案例研究，涉及一个拥有21个电厂的大型水电系统，以验证该方法的有效性，效率和敏感性。与动态规划（DP），离散差分动态规划（DDDP）和渐进最优算法（POA）相比，该方法只需要0.85％，1.27％和3.14％的计算工作量即可产生几乎相同的结果。而且，