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Research on Joint Probability Density of Wind Vector Based on Copula Function and Wind Speed Orthogonal Components

DOI：

 作者 单位 邮编 程正兵 北京工业大学 城市与工程安全减灾教育部重点实验室 100124 冀骁文* 北京工业大学 城市与工程安全减灾教育部重点实验室 100124

准确地表示风矢量联合概率密度对于风能的评估、风机结构设计具有重要意义，本研究将围绕提升风矢量联合概率密度表示结果准确性展开研究。首先，将风矢量表示为风速正交分量，采用混合Normal分布分别对边缘概率密度进行表示，并提出了估计混合Normal分布参数的方法。然后，基于Copula函数考虑风速正交分量间的相关性从而得到二者的联合概率密度，其中Copula参数通过最小二乘法估计，紧接着通过雅可比变换得到风矢量联合概率密度。最后，采用印度风能研究所的测点S3和S7的每小时平均风速和风向数据，与以往基于Copula函数和风速、风向变量得到的风矢量联合概率密度结果进行对比。结果表明，与以往方法相比，所提方法得到的风矢量联合概率密度结果准确性有很大的提升，本研究可为风能的开采和利用提供理论依据。

Accurately representing the joint probability density of wind vector is significant for wind energy assessment, as well as structural design of wind turbine. This study will focus on improving the accuracy of describing joint probability density of wind vector. Firstly, the wind vector is represented as orthogonal components, a mixed Normal distribution is used to represent their marginal probability density, and a method for estimating the initial values of parameters is proposed. Then, based on Copula function, the correlation between the orthogonal components of wind speed is considered to obtain their joint probability density, the Copula parameter is estimated by the Least Squares estimation, and then joint probability density of wind vector is obtained through Jacobian transformation. Finally, the hourly average wind speed and direction data in point S3 and S7 from the Indian Wind Energy Research Institute is used to compare with previous joint probability density results of wind vector obtained based on the Copula function and wind speed and direction variables. The results show that the joint probability density of wind vector obtained by proposed method is more accuracy than previous method. This study can provide a theoretical basis for the exploitation and utilization of wind energy.
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