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1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100083;
2. 北京宇航系统工程研究所, 北京 100076

Dynamic modeling and constant power control of wind turbines with trailing-edge flaps
ZHANG Zhen1, LU Jingwei1, LIANG Yukun2
1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. Beijing Institute of Astronautical Systems Engineering, Beijing 100076, China
Received: 2016-03-14; Accepted: 2016-06-12; Published online: 2016-09-06 16:10
Foundation item: National Natural Science Foundation of China (61433011, 51575544)
Corresponding author. ZHANG Zhen, E-mail: zhangzhen@buaa.edu.cn
Abstract: The wind turbine systems with trailing-edge flaps have broad prospects in application of large-scale wind turbine system. In the smart wind turbines with variable trailing-edge flaps, the aerodynamic characteristics of the blades can be regulated by using the trailing-edge flaps, and then the purpose of the constant power output of the wind turbines can be achieved. In this paper, the aerodynamic model of wind turbine blades with variable trailing-edge flaps is presented firstly by blade element moment method. Then a nonlinear dynamic model of smart wind power system is established. The nonlinear model is linearized by dynamic inversion method. Based on the linearized model, the feedback controller is designed through Hcontrol. Finally, simulations are carried out for cases with 12-16 m/s step wind and actual wind based on four component model. Simulation results show that the control strategies are capable of controlling output power of wind power system effectively.
Key words: wind turbine     trailing-edge flaps     modeling     constant power control     dynamic inversion     robust control

1 风电系统建模 1.1 具有尾缘襟翼的风力机气动模型

1.1.1 基于BEM计算风力机功率输出

BEM将动量理论与实际叶片上发生的局部情况结合起来。将流管离散成N个高度为dr的环形单位，如图 1所示。这些单位的外侧边界由流线形成，即单位之间没有流动。

 图 1 BEM中使用的形状像环形单元的控制体积 Fig. 1 Control volume shaped as an annular element used in BEM model

1) 离散的各个叶素之间是相互独立的，即其中任意某一个叶素对其他叶素不会有影响。

2) 每个环形单元中，叶片作用在流动上的力是定常的 (该假设对应于叶片数为无穷的情况，建模时通过引入普朗特叶尖损失因子修正这一严格的假设)。

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 图 2 升力系数和升阻比随迎角的变化 Fig. 2 Variation of lift coefficient and lift-drag ratio with angle of attack

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a≤0.2时，轴向诱导因子a的表达式不变, 直接跳到步骤10。当a>0.2时，利用式 (10) 和式 (11) 相等，可以得到Glauert修正后轴向诱导因子a的表达式为

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1.1.2 气动转矩模型

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 图 3 功率系数随叶尖速比和襟翼偏转角的变化 Fig. 3 Variation of power coefficient with tip speed ratio and flap deflection angle

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1.2 发电机模型

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1.3 襟翼执行机构

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1.4 风电系统的整体模型

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2 基于动态逆方法的变襟翼控制器设计 2.1 控制问题描述

 图 4 风电系统的变襟翼控制框图 Fig. 4 Control block diagram of variable flap of wind power system
2.2 基于动态逆方法的智能风电系统的线性化

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2.3 基于LMI算法的H控制器设计

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3 仿真结果及分析

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e=ωr*-ωr，得PID控制器

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 图 5 12~16 m/s阶跃风下风力发电系统响应 Fig. 5 Response of wind power system with 12-16 m/s step wind

 图 6 实际风下风力发电系统响应 Fig. 6 Response of wind power system with actual wind
4 结论

1) 基于修正的BEM建立尾缘襟翼偏转角对风力机吸收风能的影响的模型。不同于目前使用较多的系统辨识方法，本文借助文献[15-16]的数据作为计算依据，利用修正的BEM建立了一个在叶素的径向距离比于叶片半径为65%~90%之间的位置上装有襟翼执行机构，额定功率为500 kW的变襟翼风力机模型。为以后分析其他型号的襟翼风力机拓宽了思路。

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#### 文章信息

ZHANG Zhen, LU Jingwei, LIANG Yukun

Dynamic modeling and constant power control of wind turbines with trailing-edge flaps

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(3): 464-471
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0199