针对水库库容特性的函数化表征问题,通过对水库的形态特征进行抽象,构建了描述水库一般性形态特征的三棱锥模型和不规则锥体模型,在此基础上采用数学积分方法推导出表征水库库容特性的三参数幂函数模型,并根据水库库容特性的数学性质,给出了三参数幂函数的参数取值范围,最后以长江中上游流域37座水库为研究对象,通过合理性分析和拟合优度评价,证明了三参数幂函数是一种适用性广、可靠性高、物理意义明确的水库库容特性表征函数。研究成果可为水电站水库发电精细化调度提供基础函数曲线支撑。
Abstract
To express the characteristics of reservoir capacity through function, we have developed two models: the triangular pyramid model and the irregular cone model. These models accurately depict the general morphological features of reservoirs. On this basis, we have devised a three-parameter power function model to represent the reservoir capacity characteristics using mathematical integration techniques. Furthermore, by considering the mathematical properties of reservoir capacity characteristics, we gave the ranges of parameter values for the three-parameter power function. Finally, through rationality analysis and evaluation of the goodness of fit, we validated the broad applicability, high reliability, and clear physical significance of this model in characterizing reservoir capacity characteristics for hydropower stations with 37 reservoirs in the middle and upper reaches of the Yangtze River as case studies. The research finding serves as a fundamental support for generating precise function curves, enabling fine dispatching of hydropower reservoirs.
关键词
水电站水库 /
水库库容特性 /
函数拟合 /
拟合优度分析 /
三参数幂函数
Key words
reservoir of hydropower station /
reservoir capacity characteristics /
function fitting /
analysis of goodness of fit /
three-parameter power function
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基金
国家自然科学基金青年基金项目(51909010)
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