一种求解风电机组最优轮毂高度的数学模型

A MATHEMATICAL MODEL FOR OPTIMAL HUB HEIGHT OF WIND TURBINE

旨在建立一种求解风电机组最优轮毂高度的数学模型,并给出具有普适性的轮毂高度比选方法。首先,通过选用功率曲线、风速分布和风廓线模型确定风电机组总收益,由总收益与风电机组轮毂高度的关系得到边际收益;其次,通过建立轮毂高度与塔筒质量的函数关系得到边际成本;最后,在解得最优轮毂高度的基础上给出3种最佳轮毂高度比选方法。研究结果表明:1)在可行域内,风电机组存在最优轮毂高度且值为唯一。2)当可选轮毂高度的最大值小于等于最优轮毂高度时,最大值为最佳轮毂高度;当可选轮毂高度最小值大于等于最优轮毂高度时,最小值为最佳轮毂高度。3)若可选最佳轮毂高度大于最优轮毂高度,则必定存在1个小于最优轮毂高度且收益相同的高度。4)最优轮毂高度与切变指数成正比,与风电机组塔筒单位造价成反比,与风电机组固定成本无关。

This paper establishes a mathematical model for solving the optimal hub height of wind turbines and gives a universal method of hub height comparison and selection. First,the total revenue of the wind turbine is determined by selecting models of power curve,wind speed distribution and wind profile,and then the marginal revenue is obtained from the relationship between the total revenue and the hub height of the wind turbine. Secondly,the marginal cost is obtained by establishing the function relationship between the hub height and tower mass. Finally,based on the solution of the optimal hub height,three methods of optimum hub height comparison and selection are given. The research results show that:1) Within the feasible region,an optimal hub height of wind turbine exists and the value is unique. 2) When the maximum value of optional hub height is less than or equal to the optimal hub height,the maximum value is the best. When the minimum value of optional hub height is greater than or equal to the optimal hub height,the minimum value is the best. 3) If the selectable optimum hub height is greater than the optimal hub height,there must be a height that is less than the optimal hub height and has the same beneflt. 4) The optimal hub height is directly proportional to the shear index,inversely proportional to the unit cost of the tower,and has no correlation with the flxed cost of wind turbine.