Wind Speed Distribution Fitting and Annual Electricity Generation Estimation of Wind Turbine Based on Improved Mixture Gaussian Model

doi:10.12096/j.2096-4528.pgt.23125

Abstract

Abstract:

Objectives To address the significant errors in low wind speed section, high wind speed section, and peak and trough sections of the mixture Gaussian model, this paper proposes an improved mixture Gaussian model. Methods In the improved model, all subcomponents have the same shape parameter, and the wind speed sample values are used to replace the position parameters. Meanwhile, the nonlinear least squares method is employed to optimize and adjust the shape parameters and the weights of the subcomponents, allowing the model to accurately approximate the probability density distribution, including local points of wind speed samples. Based on four sets of wind speed distribution data from both domestic and international sources, the fitting performance of this model is compared with that of the mixed kernel density model and the Gaussian mixture model. The goodness of fit of the three models is evaluated using two error metrics and the Chi-square test coefficient. Results The improved Gaussian mixture model significantly enhances the fitting performance for complex wind speed distributions, and it can accurately fit the wind speed distribution probabilities in low wind speed section, high wind speed section, and peak and trough sections. Additionally, by comparing the annual electricity generation estimation of wind turbines based on the three models, the effectiveness and advantages of the improved model are further verified. Conclusions The proposed wind speed distribution probability model of higher precision helps accurately evaluate the power generation potential and economic benefits of wind farms, providing crucial guidance for wind farm planning and design.

Key words: wind power generation, wind speed probability distribution, mixture Gaussian model, nonlinear least squares method, fitting performance, wind turbine, annual electricity generation

CLC Number:

TK 81

Lingzhi WANG, Xinbo ZHANG. Wind Speed Distribution Fitting and Annual Electricity Generation Estimation of Wind Turbine Based on Improved Mixture Gaussian Model[J]. Power Generation Technology, 2025, 46(1): 103-112.

Figures/Tables 11

Fig. 1 Effect of three parameters of Gaussian mixture model on the distribution shape

Tab. 1 Relevant parameters of VASTAS80-2.0 MWwind turbine

参数	数值
额定功率/kW	2 000
风轮直径/m	80
切入风速/(m⋅s^-1)	4
切出风速/(m⋅s^-1)	25
额定风速/(m⋅s^-1)	14

Fig. 2 Output power curve of VASTAS80-2.0 MW wind turbine

Fig. 3 The first set of wind speed samples

Fig. 4 The second set of wind speed samples

Fig. 5 The third set of wind speed samples

Fig. 6 The fourth set of wind speed samples

Tab. 2 Sum of squared errors of three mixture models

风速样本	误差平方和
风速样本	混合核密度	混合高斯	改进混合高斯
样本1	$3.465 4 × 10 - 4$	$1.577 6 × 10 - 4$	$5.788 7 × 10 - 29$
样本2	$1.442 2 × 10 - 4$	$8.119 4 × 10 - 5$	$1.552 1 × 10 - 28$
样本3	$2.682 7 × 10 - 4$	$1.031 4 × 10 - 4$	$2.532 8 × 10 - 29$
样本4	$8.480 1 × 10 - 4$	$1.190 5 × 10 - 4$	$1.277 6 × 10 - 29$

Tab. 2 Sum of squared errors of three mixture models

风速样本	误差平方和
风速样本	混合核密度	混合高斯	改进混合高斯
样本1	$3.465 4 × 10 - 4$	$1.577 6 × 10 - 4$	$5.788 7 × 10 - 29$
样本2	$1.442 2 × 10 - 4$	$8.119 4 × 10 - 5$	$1.552 1 × 10 - 28$
样本3	$2.682 7 × 10 - 4$	$1.031 4 × 10 - 4$	$2.532 8 × 10 - 29$
样本4	$8.480 1 × 10 - 4$	$1.190 5 × 10 - 4$	$1.277 6 × 10 - 29$

Tab. 3 Root mean square errors of three mixture models

风速样本	均方根误差
风速样本	混合核密度	混合高斯	改进混合高斯
样本1	$2.838 8 × 10 - 3$	$1.915 4 × 10 - 3$	$1.160 3 × 10 - 15$
样本2	$2.122 9 × 10 - 3$	$1.592 9 × 10 - 3$	$2.202 3 × 10 - 15$
样本3	$2.990 3 × 10 - 3$	$1.854 1 × 10 - 3$	$2.905 6 × 10 - 15$
样本4	$4.604 3 × 10 - 3$	$1.725 2 × 10 - 3$	$1.787 2 × 10 - 15$

Tab. 3 Root mean square errors of three mixture models

风速样本	均方根误差
风速样本	混合核密度	混合高斯	改进混合高斯
样本1	$2.838 8 × 10 - 3$	$1.915 4 × 10 - 3$	$1.160 3 × 10 - 15$
样本2	$2.122 9 × 10 - 3$	$1.592 9 × 10 - 3$	$2.202 3 × 10 - 15$
样本3	$2.990 3 × 10 - 3$	$1.854 1 × 10 - 3$	$2.905 6 × 10 - 15$
样本4	$4.604 3 × 10 - 3$	$1.725 2 × 10 - 3$	$1.787 2 × 10 - 15$

Tab. 4 Chi-square test coefficients of three mixture models

风速样本		卡方检验系数
风速样本	混合核密度	混合高斯	改进混合高斯
样本1	$4.034 3 × 10 - 2$	$5.530 4 × 10 - 3$	$4.662 9 × 10 - 8$
样本2	$1.350 8 × 10 - 2$	$3.866 0 × 10 - 3$	$3.896 6 × 10 - 9$
样本3	$3.260 1 × 10 - 2$	$9.861 9 × 10 - 2$	$4.411 9 × 10 - 9$
样本4	$9.804 4 × 10 - 2$	$8.970 7 × 10 - 3$	$7.204 3 × 10 - 9$

Tab. 4 Chi-square test coefficients of three mixture models

风速样本		卡方检验系数
风速样本	混合核密度	混合高斯	改进混合高斯
样本1	$4.034 3 × 10 - 2$	$5.530 4 × 10 - 3$	$4.662 9 × 10 - 8$
样本2	$1.350 8 × 10 - 2$	$3.866 0 × 10 - 3$	$3.896 6 × 10 - 9$
样本3	$3.260 1 × 10 - 2$	$9.861 9 × 10 - 2$	$4.411 9 × 10 - 9$
样本4	$9.804 4 × 10 - 2$	$8.970 7 × 10 - 3$	$7.204 3 × 10 - 9$

Tab. 5 Annual electricity generation estimation of wind turbines based on three models

风速样本	模型	年发电量/(kW⋅h)	误差/(kW⋅h)
样本1	样本真实值	1.657 5×10⁷	—
	混合核密度	1.676 8×10⁷	1.926 5×10⁵
	混合高斯	1.660 0×10⁷	2.490 2×10⁴
	改进混合高斯	1.657 5×10⁷	5.9
样本2	样本真实值	1.265 4×10⁷	—
	混合核密度	1.280 9×10⁷	-1.552 2×10⁵
	混合高斯	1.265 6×10⁷	2.077 3×10³
	改进混合高斯	1.265 4×10⁷	-212.254 7
样本3	样本真实值	2.864 4×10⁷	—
	混合核密度	2.945 2×10⁷	-8.072 7×10⁵
	混合高斯	2.863 9×10⁷	5.061 2×10³
	改进混合高斯	2.864 4×10⁷	59.521 8
样本4	样本真实值	2.951 6×10⁷	—
	混合核密度	3.140 8×10⁷	-1.891 4×10⁶
	混合高斯	2.966 1×10⁷	-1.443 7×10⁵
	改进混合高斯	2.951 6×10⁷	-3.826 3

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