湍流风场模拟与风力发电机组载荷特性研究
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摘要
大型风力发电机组所处的外部环境复杂多变,建立合理且正确的湍流风场模型、空气动力学模型和结构动力学模型,不但能准确获取风力发电机组的结构动力响应特性,同时也是其设计的前提条件。风力发电机组风轮叶片在风场中做周期性的运动,使得湍流风场的建模和气动载荷的计算需要考虑风轮的旋转效应,而旋转湍流风速激励下机组的随机载荷脉动和响应需要在频域范围内进行分析。复杂外部环境条件和各种影响因素下风力发电机组的动态响应特性和载荷特性的研究对改善风电机组的结构,优化控制策略,保证机组安全运行起着至关重要的作用。本课题在国家高技术研究发展计划(863)项目“风电场、光伏电站集群控制系统研究与开发(No.2011AA05A104)"的资助下,完成了以下研究工作。
(1)建立了三维湍流风场模型,详细推导了改进的Von Karman谱,归纳了影响三维湍流风场的塔影效应和尾流效应的计算模型。介绍了风力发电机组的叶素动量理论,并分析了叶素动量理论的不足。为了考虑风轮空气动力的三维效应,引入了叶尖轮毂损失修正、推力系数修正、攻角修正和风切变速度修正。总结了现有的几种结构建模方法,对比了三种结构建模方法的优缺点。
(2)推导了旋转Fourier自谱和互谱准确的解析表达式,分析了旋转Fourier谱的物理本质,旋转Fourier谱为无数个源谱经过旋转频率的整数倍平移再乘以相应的加权系数的叠加,其中加权系数为平移之后旋转频率的n阶模态即相干函数的Fourier展开系数。旋转Fourier自谱本身既包含幅频特性,也包含相频特性。风轮的旋转效应主要通过相干函数和时滞参数体现出来,相干函数体现幅值谱的变化,时滞参数体现相位变化。相干函数的选取对旋转Fourier谱的分布具有重要的影响。对传统的Davenport指数相干函数进行修正可以消除旋转Fourier谱在旋转频率的整数倍频处出现的跌落。风切变改变了平均风速在垂直平面上的分布,从而改变了源谱谱值的大小和旋转采样点的选取。
(3)基于谱表示方法分别模拟了塔架和风轮叶片上不同点的湍流风速时程,提出了引入相位延迟因子的湍流风谱谱表示方法。对比了多时间尺度的旋转采样点和静止采样点模拟得到的风速时程。旋转效应导致旋转叶片上计算点的风速时程脉动频率明显要高于静止叶片上对应点的风速时程。计算谱与目标谱变化规律具有高度的一致性,结果表明：旋转Fourier谱和引入相位延迟因子的谱表示方法能够准确有效地模拟旋转风轮叶片上的风速时程。
(4)在频域里推导了风力发电机组在湍流风作用下的动态载荷谱,指出了载荷谱旋转模态与感应系数和旋转Fourier谱各阶模态的相关关系。得到了其挥舞运动的幅频谱和旋转叶片的载荷谱以及考虑叶片挥舞运动的单叶片、双叶片和三叶片风轮的载荷谱。风力发电机组随随机高斯湍流风输入的响应为线性系统时,频谱分析可以获得系统的各种统计特性。通过弯矩功率谱可以预估疲劳载荷,通过雨流计数法则可以预估机组的疲劳寿命。
(5)计算分析了风力发电机组在各种外部环境条件和机组状态下的极限载荷和疲劳载荷以及重要工况下的动态响应和疲劳载荷特性。机组正常发电时,叶尖位移、叶根面外弯矩、轮毂中心推力、塔顶位移和塔架各法兰处的弯矩在额定风速下的值大于切出风速下的值,并不是风速越大,对应的动态响应越大。机组遇到故障而紧急停机时,各部件的响应易产生突变,并产生振荡。机组在停机工况下存在明显的谐振现象。通过雨流计数和等效载荷方法把随机交变载荷转化成等效疲劳载荷,获得了疲劳载荷谱。
The external environment that large-scale wind turbine undergoes is complicated, establishing the reasonable and accurate turbulent wind field model, aerodynamic model and structure dynamic model of wind turbine can not only obtain accurate structure dynamic response characteristics of wind turbine, but also be the precondition for wind turbine designing. Rotational effects of the rotor should be taken into account for the modeling turbulent wind field and calculating aerodynamic loads since large-scale periodic rotation of the blades in wind fileds. Stochastic load fluctuations and response of wind turbine actuated by rotational turbulent wind velocity need to be analysed within the frequency domain. The research of dynamic responsed characteristics and load characteristics of wind turbines within complicated external environments and variable influencing factors plays a crucial role for improving sturcture of wind turbine, optimazing control strategy, and insuring operation under safe conditons. This task is financially supported by the National High-Tech Research and Development Program of China(863Program)"Research and development of collective control systems of wind farm and photo voltaic plants (Grant No.2011AA05A104)". The main works are as follows.
(1)3-D turbulent wind field model is established, the improved Von Karman spectrum is deduced in detail, Calculating models of the tower shadow and wake effects which effect3-D turbulent wind field are summarized. The Blade Element Momentum (BEM) of wind turbine is introduced systematically, and the deficiencies are analysed. In order to considering the3-D effect of turbine rotor aerodynamics, the blade tip and hub loss corrections, the thrust coefficient correction, the angle of attack correction and wind shear velocity correction are introduced. Several structure modeling methods are summarized and advantages and disadvantages of three modeling methods are compared.
(2) Accurate analytical expression of auto power spectral density(APSD) and cross power spectral density(CPSD) of the rotational Fourier spectrum are derived, the physical nature of rotational Fourier spectrum is analyzed, which is summation of numerous source spectra those have been multiplied by corresponding weighting coeffients after translation with integer multiple rotational frequencies, The weighting coefficient is the nth mode after translation, which is also Fourier expression coefficient of coherence function. The APSD of rotational Fourier spectrum contains both amplitude-frequency characteristics and phase-frequency characteristics. Rotational effects of rotor are mainly reflected by the coherence function and delay parameter, wherein the coherence function is the reflection of the changes in the amplitude spectrum, the delay parameter reflects the phase change. The selection of the coherence function is of vital influence to the rotational Fourier spectrum distribution. The revision of traditional Davenport's exponential coherence function can eliminate the dips at integer multiple rotational frequencies of rotational Fourier spectrum. Wind shear can change the source value of spectrum and the selection rotating sampling points by changing the magnitude of the average wind velocities in the vertical plane of rotor.
(3) Turbulent wind velocity time series of different points on the tower and rotor blades of wind turbine are simulated based on spectrum representation method, and spectrum representation formula which introduces phase lag factor is proposed. The simulated wind velocity time histories of multi-time scale rotational sampling points and still sampling points are compared. The fluctuating frequencis of wind velocity time histories at the calculated points of the rotating blades are significantly higher than those at the corresponding points of the stationary blades. The change laws of the calculated spectrum and the target spectrum are of high degree uniformity, which proved the theories and algorithms used in this paper can simulate the wind velocity time histories on the rotating rotor blades more accurately and efficiently.
(4) The dynamic load spectrum actuated by turbulent wind is derived in the frequency domain and the physical nature of rotational modal is revealed. The spectrum of flapping motion amplitudes, load spectra of rotational blades as well as load spectra of flapping-blade rotors with single blade, two blades and three blades are obtained. When the system with Gaussian random turbulent wind input and response of wind turbine is a linear system, all of the statistical characteristics of the system can obtained by spectral analysis. Also fatigue loads can be estimated using spectral moments. It is most common to estimate fatigue damage rates by rainflow counting method.
(5) The extreme loads and fatigue loads of wind turbine experienced all of external environment conditions and states of wind turbine are calculated, and dynamic response and fatigue load characteristics of wind turbine operated under important designed load cases are also analysed. The values of blade tip deflection, out of plane bending at blade root, thrust at hub center, tower top deflection and bending moments at tower flanges of wind turbine operated with rated wind velocity are larger than those with cut out wind velocity when it is operated with normal power produciton. It is inverse that the higher wind velocity result in greater corresponding dynamic response. The responses of components produce saltation and oscillation when wind turbine emergency stop with faults. Resonance phenomenon occures at situation of parked or idling, which results in resonant problem of wind turbine is one of main factors for turbine safe at high wind velocity. Equivalent fatigue loads of wind turbine can be calculated by rain flow counting method and the equivalent load method through transforming the random cyclic loads into equivalent fatigue loads, and then fatigue load spectra can be established, finally fatigue life of wind turbine is obtained.
(1)建立了三维湍流风场模型,详细推导了改进的Von Karman谱,归纳了影响三维湍流风场的塔影效应和尾流效应的计算模型。介绍了风力发电机组的叶素动量理论,并分析了叶素动量理论的不足。为了考虑风轮空气动力的三维效应,引入了叶尖轮毂损失修正、推力系数修正、攻角修正和风切变速度修正。总结了现有的几种结构建模方法,对比了三种结构建模方法的优缺点。
(2)推导了旋转Fourier自谱和互谱准确的解析表达式,分析了旋转Fourier谱的物理本质,旋转Fourier谱为无数个源谱经过旋转频率的整数倍平移再乘以相应的加权系数的叠加,其中加权系数为平移之后旋转频率的n阶模态即相干函数的Fourier展开系数。旋转Fourier自谱本身既包含幅频特性,也包含相频特性。风轮的旋转效应主要通过相干函数和时滞参数体现出来,相干函数体现幅值谱的变化,时滞参数体现相位变化。相干函数的选取对旋转Fourier谱的分布具有重要的影响。对传统的Davenport指数相干函数进行修正可以消除旋转Fourier谱在旋转频率的整数倍频处出现的跌落。风切变改变了平均风速在垂直平面上的分布,从而改变了源谱谱值的大小和旋转采样点的选取。
(3)基于谱表示方法分别模拟了塔架和风轮叶片上不同点的湍流风速时程,提出了引入相位延迟因子的湍流风谱谱表示方法。对比了多时间尺度的旋转采样点和静止采样点模拟得到的风速时程。旋转效应导致旋转叶片上计算点的风速时程脉动频率明显要高于静止叶片上对应点的风速时程。计算谱与目标谱变化规律具有高度的一致性,结果表明：旋转Fourier谱和引入相位延迟因子的谱表示方法能够准确有效地模拟旋转风轮叶片上的风速时程。
(4)在频域里推导了风力发电机组在湍流风作用下的动态载荷谱,指出了载荷谱旋转模态与感应系数和旋转Fourier谱各阶模态的相关关系。得到了其挥舞运动的幅频谱和旋转叶片的载荷谱以及考虑叶片挥舞运动的单叶片、双叶片和三叶片风轮的载荷谱。风力发电机组随随机高斯湍流风输入的响应为线性系统时,频谱分析可以获得系统的各种统计特性。通过弯矩功率谱可以预估疲劳载荷,通过雨流计数法则可以预估机组的疲劳寿命。
(5)计算分析了风力发电机组在各种外部环境条件和机组状态下的极限载荷和疲劳载荷以及重要工况下的动态响应和疲劳载荷特性。机组正常发电时,叶尖位移、叶根面外弯矩、轮毂中心推力、塔顶位移和塔架各法兰处的弯矩在额定风速下的值大于切出风速下的值,并不是风速越大,对应的动态响应越大。机组遇到故障而紧急停机时,各部件的响应易产生突变,并产生振荡。机组在停机工况下存在明显的谐振现象。通过雨流计数和等效载荷方法把随机交变载荷转化成等效疲劳载荷,获得了疲劳载荷谱。
The external environment that large-scale wind turbine undergoes is complicated, establishing the reasonable and accurate turbulent wind field model, aerodynamic model and structure dynamic model of wind turbine can not only obtain accurate structure dynamic response characteristics of wind turbine, but also be the precondition for wind turbine designing. Rotational effects of the rotor should be taken into account for the modeling turbulent wind field and calculating aerodynamic loads since large-scale periodic rotation of the blades in wind fileds. Stochastic load fluctuations and response of wind turbine actuated by rotational turbulent wind velocity need to be analysed within the frequency domain. The research of dynamic responsed characteristics and load characteristics of wind turbines within complicated external environments and variable influencing factors plays a crucial role for improving sturcture of wind turbine, optimazing control strategy, and insuring operation under safe conditons. This task is financially supported by the National High-Tech Research and Development Program of China(863Program)"Research and development of collective control systems of wind farm and photo voltaic plants (Grant No.2011AA05A104)". The main works are as follows.
(1)3-D turbulent wind field model is established, the improved Von Karman spectrum is deduced in detail, Calculating models of the tower shadow and wake effects which effect3-D turbulent wind field are summarized. The Blade Element Momentum (BEM) of wind turbine is introduced systematically, and the deficiencies are analysed. In order to considering the3-D effect of turbine rotor aerodynamics, the blade tip and hub loss corrections, the thrust coefficient correction, the angle of attack correction and wind shear velocity correction are introduced. Several structure modeling methods are summarized and advantages and disadvantages of three modeling methods are compared.
(2) Accurate analytical expression of auto power spectral density(APSD) and cross power spectral density(CPSD) of the rotational Fourier spectrum are derived, the physical nature of rotational Fourier spectrum is analyzed, which is summation of numerous source spectra those have been multiplied by corresponding weighting coeffients after translation with integer multiple rotational frequencies, The weighting coefficient is the nth mode after translation, which is also Fourier expression coefficient of coherence function. The APSD of rotational Fourier spectrum contains both amplitude-frequency characteristics and phase-frequency characteristics. Rotational effects of rotor are mainly reflected by the coherence function and delay parameter, wherein the coherence function is the reflection of the changes in the amplitude spectrum, the delay parameter reflects the phase change. The selection of the coherence function is of vital influence to the rotational Fourier spectrum distribution. The revision of traditional Davenport's exponential coherence function can eliminate the dips at integer multiple rotational frequencies of rotational Fourier spectrum. Wind shear can change the source value of spectrum and the selection rotating sampling points by changing the magnitude of the average wind velocities in the vertical plane of rotor.
(3) Turbulent wind velocity time series of different points on the tower and rotor blades of wind turbine are simulated based on spectrum representation method, and spectrum representation formula which introduces phase lag factor is proposed. The simulated wind velocity time histories of multi-time scale rotational sampling points and still sampling points are compared. The fluctuating frequencis of wind velocity time histories at the calculated points of the rotating blades are significantly higher than those at the corresponding points of the stationary blades. The change laws of the calculated spectrum and the target spectrum are of high degree uniformity, which proved the theories and algorithms used in this paper can simulate the wind velocity time histories on the rotating rotor blades more accurately and efficiently.
(4) The dynamic load spectrum actuated by turbulent wind is derived in the frequency domain and the physical nature of rotational modal is revealed. The spectrum of flapping motion amplitudes, load spectra of rotational blades as well as load spectra of flapping-blade rotors with single blade, two blades and three blades are obtained. When the system with Gaussian random turbulent wind input and response of wind turbine is a linear system, all of the statistical characteristics of the system can obtained by spectral analysis. Also fatigue loads can be estimated using spectral moments. It is most common to estimate fatigue damage rates by rainflow counting method.
(5) The extreme loads and fatigue loads of wind turbine experienced all of external environment conditions and states of wind turbine are calculated, and dynamic response and fatigue load characteristics of wind turbine operated under important designed load cases are also analysed. The values of blade tip deflection, out of plane bending at blade root, thrust at hub center, tower top deflection and bending moments at tower flanges of wind turbine operated with rated wind velocity are larger than those with cut out wind velocity when it is operated with normal power produciton. It is inverse that the higher wind velocity result in greater corresponding dynamic response. The responses of components produce saltation and oscillation when wind turbine emergency stop with faults. Resonance phenomenon occures at situation of parked or idling, which results in resonant problem of wind turbine is one of main factors for turbine safe at high wind velocity. Equivalent fatigue loads of wind turbine can be calculated by rain flow counting method and the equivalent load method through transforming the random cyclic loads into equivalent fatigue loads, and then fatigue load spectra can be established, finally fatigue life of wind turbine is obtained.
引文
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