风力发电机三维阵风谱建模与仿真的向量自回归法

针对风力发电机空气动力学和结构分析的要求，提出一种新的向量自回归(vector autoregressive, VAR)三维阵风速场仿真方法。在常规自回归(autoregressive, AR)法建模的基础上，根据维纳-辛钦公式，由协方差向量和功率谱求出自回归系数向量。其中输入参数为单点Davenport阵风功率谱(power spectral density, PSD)和互相关函数。基于此，推导出多维风速时程模型。算例采用一个3 桨叶风力发电机所在风场，其中心高为H=30 m, 风力机转子半径R=11.6 m, 沿风力机叶尖扫过圆周均布12个点，取其中3点进行仿真， 并采用Burg算法进行功率谱估计。采样频率0~0.9 Hz，频率采用点数N=1 800，时间间隔0.1 s。仿真结果表明，适当选取采样频率点数与时间间隔，可以在保证模拟功率谱计算精度的同时，具有快速高效的特点，弥补了传统方法在模拟三维风速时耗时长、精度低的缺点。

VAR Approach for 3-D Gust Wind Spectral Modeling and Simulation of Wind Turbine

Focusing on the demand of wind turbine aerodynamics and structural analysis, a novel vector autoregressive method for 3-dimmentional wind speed simulation is presented. Based on the traditional AR model approach, and by Wiener-Khintchine formula, the autoregressive factor vectors were deduced from covariance and power spectral density (PSD), where the input parameters are single point Davenport gust wind PSD and correlation function. From these, a multiple dimensional wind speed model was deduced. A case study is about a wind field with a 3-blade wind turbine, where its center height H=30 m, radius of wind turbine R=11.6 m. Three points wind speed were simulated from the 12 points which were arranged along the tip circle of the blades. To evaluate the veracity of VAR model, the PSD were estimated with Burg arithmetic. The sampling frequency range is 0-0.9 Hz, the number of frequency sampling points N=1800, time interval 0.1s. The simulation results show that the proper selection of sampling frequency numbers and time interval can keep the simulation process fast, efficient and precise, which overcome the shortcomings of long time cost and low precision in the traditional method.