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.

Key words: reservoir of hydropower station, reservoir capacity characteristics, function fitting, analysis of goodness of fit, three-parameter power function