评估风力涡轮机传递的平均功率
此示例使用Symbolic Math Toolbox™和统计信息和机器学习工具箱™来探索和得出风力涡轮机生成的平均功率的参数分析表达式。
The parametric equation can be used for evaluating various wind turbine configurations and wind farm sites. More information see<一种href="//www.tatmou.com/fr/discovery/wind-resource-assessment.html" target="_blank">风资源评估一种>。
背景
The total power delivered to a wind turbine can be estimated by taking the derivative of the wind's kinetic energy. This results in the following expression:
(1)
一种is the swept area of turbine blades, in
ρ=空气密度,在
u =风速,在
The process of converting wind power to electrical power results in efficiency losses, as described in the diagram below.
The electrical power output of a practical wind turbine can be described using the following equation:
(2)哪里
The overall efficiency is between 0.3 and 0.5, and varies with both wind speed and rotational speed of the turbine. For a fixed rotational speed, there is a rated wind speed at which electrical power generated by the wind turbine is near its maximum (
(3)
假设固定旋转速度,可以使用以下轮廓估算风力涡轮机的电力输出:
在哪里
=额定风速
=切入速度,电力输出升高到零以上并开始产生功率的速度
=毛茸茸的风速,关闭涡轮机的速度以防止结构损坏 如图所示,我们假设输出功率在 We define a piecewise function that described turbine power.
在哪里v一种riables
得出风力涡轮机平均功率的方程式
I.定义电源的分段表达
符号
pe =
C_1 = (Per * u_c^k)/(u_c^k - u_r^k)
C_1 =
C_2 =每/((你_r^k - u_c^k)
C_2 =
II. Define external wind conditions
额定功率输出很好地表明了风力涡轮机能够产生多少功率,但是我们想估计风力涡轮机将实际提供多少功率。为了计算平均功率,我们需要考虑外部风条件。Weibull分布在对风的差异进行建模方面做得很好,因此可以使用以下概率密度函数来估计风轮廓:
(4)
In general, larger 'a' values indicate a higher median wind speed, and larger 'b' values indicate reduced variability.
我们使用<一种href="//www.tatmou.com/fr/help/stats/weibull-distribution.html" target="_blank">Statistics and Machine Learning Toolbox一种>to generate a Weibull distribution and illustrate the variability in wind at our wind farm site (a=12.5, b=2.2):
a = 12.5;b = 2.2;n = 1000;PD = Makedist('Weibull' ,,,,'一种' ,一种,'b' ,,,,b)
pd = weibulldistribution weibull分布a = 12.5 b = 2.2
r =wblrnd(a,b,[1 N])
r =1×10006.0811 4.3679 17.3751 4.1966 8.7677 18.3517 13.9761 9.9363 3.0039 2.7496 16.5233 2.5333 3.0151 10.7854 6.3169 16.9442 11.6922 4.1418 6.4460 2.9379 8.4449 21.6033 5.4887 3.6903 8.1241 6.9789 7.1974 12.1293 8.4485 16.1833 7.7371 21.9390 14.0043 20.8297 18.3668 5.9351 7.8970 13.3122 3.2335 21.7093 11.4461 12.2905 6.8609 6.3983 15.8128 10.7241 11.3478 8.5754 7.6896 7.0249
x = linspace(0,34,n);y = pdf(pd,x);情节(x,y,'行宽' ,2)保持on 直方图(R,15,'正常化' ,,,,'PDF' )holdoff 标题(“威布尔的风速分布” )Xlabel(“风速(m/s)” )
III. Calculate average power
可以使用以下积分获得风力涡轮机的平均功率输出:
(5)
当风速小于风速切割时,电源为零
(6)
等式(7)中有两个不同的积分。我们将方程式(4)插入这些积分中,并使用替换简化它们:
(7)
(8)
求解这些积分,然后用
符号
int1 =