To overcome the problems of natural decreases in power quality, and to eliminate wind speed fluctuation due to wind shear and tower shadow effect arising from wind turbine structural parameters, an improved prediction model accounting for the dual effect of wind shear and tower shadow is, in this paper, built. Compared to the conventional prediction model, the proposed model contains a new constraint condition, which makes the disturbance term caused by the tower shadow effect always negative so that the prediction result is closer to the actual situation. Furthermore, wind turbine structural parameters such as hub height, rotor diameter, the diameter of the tower top, and rotor overhang on wind shear and tower shadow effect are also explored in detail. The results show that the wind shear effect became weaker with the increase in hub height. The hub height is independent of the tower shadow effect. The rotor diameter is positively correlated with the wind shear and tower shadow effect. The tower shadow effect is positively correlated with the diameter of the tower top and negatively correlated with the rotor overhang.

Wind speed is an important factor affecting the output power of horizontal axial wind turbine (HAWT). In addition to the mutation and uncertainty of natural wind, the periodic fluctuation of wind speed through blade surfaces caused by wind shear and the tower shadow effect cannot be ignored. Therefore, accurately predicting the wind speed under the action of wind shear and tower shadow effect, and analyzing the influence of structural parameters such as hub height, rotor diameter, the diameter of the tower top, and rotor overhang on the wind speed, are of great significance for optimizing the structural size, weakening the power fluctuation of the wind turbine, and slowing down the effect of the power grid.

Extensive studies have been conducted on the wind shear and tower shadow effect for HAWT. Dolan et al. [

The above studies evaluate the wind shear and tower shadow effect of HAWT in detail. The disturbance term due to wind shear can be approximated by a third-order Taylor series in the references [

The rest of the manuscript is organized as follows. In

Wind shear coefficient is used to illustrate the wind speed distribution along the vertical direction. There is a large velocity gradient at different spanwise positions of the blade during the rotor rotation for a large-scale HAWT, as shown in

Tower shadow effect refers to the phenomenon that when the incoming wind flows through the tower, the spatial variation in the flowfield will affect the wind direction and reduce the inflow velocity in the upstream and downstream of the tower. The tower will cause fluctuations in the aerodynamic performance of the wind turbine due to interference with the airflow flowing through the blade. Meanwhile, the generator performance will be reduced subsequently. It is fully a negative effect for power quality and stability. According to the wind energy handbook [

According to

In

The wind speed fluctuation caused by wind shear and the tower shadow effect changes with rotor azimuth angle. The wind speed through the blade element significantly varies with different azimuth angles and spanwise positions. The dual effect of wind shear and tower shadow effect aggravates the periodic fluctuation of blade aerodynamic load. According to the blade azimuth angle

Area 1: The blade is located in the upper half swept area, and it is only subjected to wind shear effect. The mathematical model is created in the way of [

Area 2: The blade is located in the lower half swept area, and its azimuth angle is between the critical azimuth angles

The calculation methods for critical azimuth

Area 3: The blade is located in the lower half swept area, but the blade azimuth angle is beyond the critical azimuth angles

To test the model accuracy in this study, the proposed model is used to calculate the wind speed at the blade tip for 5-MW HAWT from the National Renewable Energy Laboratory (NREL). The Gross properties chosen for the NREL 5-MW baseline wind turbine are listed in

Structural parameters | Numerical values | Wind turbine model |
---|---|---|

Rated power, rated rotational speed | 5 MW, 12.1 rpm | |

Rotor, tower top diameter, hub height | 126, 3.87, 90 m | |

Rotation direction, number of blades, wind shear coefficient | Upwind, 3, 0.2 | |

Cut-in, cut-out, and rated wind speed | 3, 25, 11.4 m/s | |

Airfoils | NACA64_A17, DU series | |

Blade set angle, rotor cone angle, tilt angle | 0°, 2.5°, 5° | |

Blade weight, rotor weight | 17,740, 110,000 kg |

To study the influence of structural parameters of a wind turbine such as hub height, rotor diameter, the diameter of tower top, and overhang on wind shear and tower shadow effect, wind speed of blade tip under different structural parameters are explored using the improved model. The detailed wind turbine structural parameters are shown in

Numbers | Hub heights | Rotor diameters | Diameters of tower top | Rotor overhangs |
---|---|---|---|---|

1 | 85 m | 116 m | 3.00 m | 4 m |

2 | 90 m | 126 m | 3.87 m | 5 m |

3 | 95 m | 136 m | 4.50 m | 6 m |

An improved model accounting for the wind shear and tower shadow effect is established in the way of unified cylindrical coordinate using the fourth-order Taylor series, and the boundary of rotor swept area is further refined. Compared to the conventional model, the proposed model more realistically reflects the influence of the tower shadow effect on the incoming wind speed.

Wind shear effect becomes weaker with the increase of hub height. It causes the maximum wind speed of the blade tip decreases, the minimum wind speed tends to increase, and the range of wind speed tends to decrease. The hub height is independent of the tower shadow effect.

The larger the rotor diameter, the greater the difference between the maximum and minimum wind speed. The rotor diameter is positively correlated with the wind shear and tower shadow effect.

Beyond the critical azimuth angles of 175.5° and 184.5°, the diameter of the tower top and rotor overhang does not affect the wind speed of the blade tip. Between the two critical azimuth angles, the wind speed decreases sharply with the increase in the diameter of the tower top but grows with the increase of rotor overhang. This is mainly because there is no correlation between wind shear and the diameter of the tower top, while the tower shadow effect is positively correlated with the diameter of the tower top, and negatively correlated with the rotor overhang.

This study focused on the relationship between wind turbine structural parameters with wind shear and the tower shadow effect. The future work will further analyze the influence of structural parameters on the rotor power and operation performance of wind turbines.

wind speed at height

wind speed at the height of rotor hub

hub height

vertical height from the ground

wind shear coefficient related to surface roughness

disturbance term of wind shear on wind speed

azimuth angle

critical azimuth angles

local radius of blade

wind speed at hub height

spatial average wind speed

tower top radius

tower base radius

distance from the blade element to the tower axis in the direction of

the horizontal distance between the rotor centre and the tower centerline

disturbance term for tower shadow on wind speed in Cartesian coordinate system

disturbance term for tower shadow on wind speed in cylindrical coordinate system

rotor radius

equal to

tower shadow on the wind speed written as a cylindrical coordinate, it is equal to