Abstract: Discrete representation of the stage-capacity curve of a reservoir in a power generation dispatching model usually leads to difficulty in mathematical analysis and low efficiency in model solution. However, this relationship lacks a unified function expression and we need to examine its curve fitting. Using discrete data points of reservoir stage and capacity measured in-situ, this study derives the relationship for three different curves through linear and nonlinear least square fitting, and evaluates comprehensively their goodness of fit and the effect in practical application. A case study of 23 reservoirs in the upper Yangtze basin shows that in describing the relationship, stage-capacity curves of the power function have wide applicability and good reliability and can be used as a general curve type. The study can help promote a unified analytical expression of reservoir stage-capacity relationship and improve the solution efficiency of hydropower generation scheduling and optimization models.

Key words: hydropower reservoir, reservoir stage-capacity curve, reservoir capacity characteristic curve, curve fitting, power function