Modeling turbine wakes and power losses within a wind farm using LES: An application to the Horns Rev offshore wind farm

A modeling framework is proposed and validated to simulate turbine wakes and associated power losses in wind farms. It combines the large-eddy simulation (LES) technique with blade element theory and a turbine-model-specific relationship between shaft torque and rotational speed. In the LES, the turbulent subgrid-scale stresses are parameterized with a tuning-free Lagrangian scale-dependent dynamic model. The turbine-induced forces and turbine-generated power are modeled using a recently developed actuator-disk model with rotation (ADM-R), which adopts blade element theory to calculate the lift and drag forces (that produce thrust, rotor shaft torque and power) based on the local simulated flow and the blade characteristics. In order to predict simultaneously the turbine angular velocity and the turbine-induced forces (and thus the power output), a new iterative dynamic procedure is developed to couple the ADM-R turbine model with a relationship between shaft torque and rotational speed. This relationship, which is unique for a given turbine model and independent of the inflow condition, is derived from simulations of a stand-alone wind turbine in conditions for which the thrust coefficient can be validated. Comparison with observed power data from the Horns Rev wind farm shows that better power predictions are obtained with the dynamic ADM-R than with the standard ADM, which assumes a uniform thrust distribution and ignores the torque effect on the turbine wakes and rotor power. The results are also compared with the power predictions obtained using two commercial wind-farm design tools (WindSim and WAsP). These models are found to underestimate the power output compared with the results from the proposed LES framework.     

Experimental identification of modal parameters of an industrial 2‐MW wind turbine

This contribution presents modal testing of a 2‐MW wind turbine on a 100‐m tubular tower with a 93‐m rotor developed by W2E Wind to Energy GmbH. This research is part of the DYNAWIND project of the University of Rostock and W2E. Beside classical modal analysis schemes, this contribution mainly focusses on the application of operational modal analysis techniques to a wind turbine. Specific problems are addressed, and hints for modal testing on wind turbines are given. Furthermore, an effective measurement setup is proposed for identification of the modal parameters of a wind turbine. The measurement campaign is divided in two parts. First, a measurement campaign using 8 sensor positions on a rotor blade was done while the rotor is lying on ground. Second, a detailed measurement campaign was done on the entire wind turbine with the rotor locked in Y position using 61 sensor positions on the tower, the mainframe, the gearbox, the generator, and the low‐voltage unit. While the rotor blade was tested by classical and operational modal analysis techniques, the entire wind turbine was tested by operational modal analysis techniques only. The mode shapes and eigenfrequencies of the wind turbine identified within the measurement campaigns are within the expected range of the design values of the wind turbine. But in contrast, the damping ratios differ strongly from those given in guidelines and literature. Furthermore, a strong influence of aerodynamic damping compared to structural damping is observed for the first tower mode even for a parked wind turbine.     

Modeling,control, and simulation of dual rotor wind turbine generator system

A new wind turbine generator system (WTGS) is introduced, and its mathematical model, blade pitch control scheme, and nonlinear simulation software for the performance prediction are presented. The notable feature of WTGS is that it consists of two rotor systems positioned horizontally at upwind and downwind locations, and a generator installed vertically inside the tower. In this paper, this new WTGS is treated as a constrained multi-body system, and the equations of motion are obtained by using the multi-body dynamics approach. Aerodynamic forces and torques generated from each of rotor blades are calculated using the blade element theory. Various pitch control schemes depending on the wind speed and the main rotor's rotational speed are implemented. A relatively simple model for the load torque is obtained by using the test data of the doubly fed induction generator adopted in the new WTGS. Finally, FORTRAN and Matlab/Simulink-based hybrid simulation software is developed and used to predict and analyze the performance of the WTGS.     

Helical vortex theory and blade element analysis of multi-bladed windmills

Multi-bladed windmills usually pump water for agriculture and domestic consumption, often in remote locations. Although they have been around for over 150 years, their aerodynamic performance is still poorly understood. This paper describes the use of helical vortex theory (HVT) and blade element momentum (BEM) analysis to predict windmill thrust, torque, and extracted power. We emphasize the unusual features of windmills: low Reynolds numbers and tip speed ratios and high solidity, all related to the generation of high torque at low wind speeds. Wind tunnel tests on a model rotor with 3, 6, 12, and 24 circular-arc, constant-chord blades determined the thrust, torque, and extracted power over a range of tip speed ratio that extended to runaway. For comparison, BEM was implemented with a correction for finite blade number derived from HVT, as well as the classical Prandtl tip loss factor. The HVT correction predicted the rotor power coefficient to within 3% of the test data on the average. At low tip speed ratios and smaller blade numbers, HVT was consistently more accurate than the Prandtl factor. At all blade numbers, the measured rotor torque exceeded the BEM predictions at the lowest tip speed ratios indicating stall delay which became more important (and more beneficial for windmill performance) as the blade number increased. The Prandtl formulation predicted the thrust to within a mean accuracy of 13% and was more accurate than the HVT method.     

CFD simulation of a floating offshore wind turbine system using a variable-speed generator-torque controller

Prediction and control of rotor rotational velocity is critical for accurate aerodynamic loading and generator power predictions. A variable-speed generator-torque controller is combined with the two-phase CFD solver CFDShip-Iowa V4.5. The developed code is utilized in simulations of the 5 MW floating offshore wind turbine (FOWT) conceptualized by the National Renewable Energy Laboratory (NREL) for the Offshore Code Comparison Collaboration (OC3). Fixed platform simulations are first performed to determine baseline rotor velocity and developed torque. A prescribed platform motion simulation is completed to identify effects of platform motion on rotor torque. The OC3’s load case 5.1, with regular wave and steady wind excitation, is performed and results are compared to NREL’s OC3 results. The developed code is shown to functionally control generator speed and torque but requires controller calibration for maximum power extraction. Generator speed variance is observed to be a function of unsteady stream-wise platform motions. The increased mooring forces of the present model are shown to keep the turbine in a more favorable variable-speed control region. Lower overall platform velocity magnitudes and less rotor torque are predicted corresponding to lower rotor rotational velocities and a reduction in generated power. Potential improvements and modifications to the present method are considered.     

Open‐loop frequency response analysis of a wind turbine using a high‐order linear aeroelastic model

Wind turbine controllers are commonly designed on the basis of low‐order linear models to capture the aeroelastic wind turbine response due to control actions and disturbances. This paper characterizes the aeroelastic wind turbine dynamics that influence the open‐loop frequency response from generator torque and collective pitch control actions of a modern non‐floating wind turbine based on a high‐order linear model. The model is a linearization of a geometrically non‐linear finite beam element model coupled with an unsteady blade element momentum model of aerodynamic forces including effects of shed vorticity and dynamic stall. The main findings are that the lowest collective flap modes have limited influence on the response from generator torque to generator speed, due to large aerodynamic damping. The transfer function from collective pitch to generator speed is affected by two non‐minimum phase zeros below the frequency of the first drivetrain mode. To correctly predict the non‐minimum phase zeros, it is essential to include lateral tower and blade flap degrees of freedom. Copyright © 2013 John Wiley & Sons, Ltd.     

Aerodynamic loads calculation and analysis for large scale wind turbine based on combining BEM modified theory with dynamic stall model

The aerodynamic loads for MW scale horizontal-axis wind turbines are calculated and analyzed in the established coordinate systems which are used to describe the wind turbine. In this paper, the blade element momentum (BEM) theory is employed and some corrections, such as Prandtl and Buhl models, are carried out. Based on the B-L semi-empirical dynamic stall (DS) model, a new modified DS model for NACA63-4xx airfoil is adopted. Then, by combing BEM modified theory with DS model, a set of calculation method of aerodynamic loads for large scale wind turbines is proposed, in which some influence factors such as wind shear, tower, tower and blade vibration are considered. The research results show that the presented dynamic stall model is good enough for engineering purpose; the aerodynamic loads are influenced by many factors such as tower shadow, wind shear, dynamic stall, tower and blade vibration, etc, with different degree; the single blade endures periodical changing loads but the variations of the rotor shaft power caused by the total aerodynamic torque in edgewise direction are very small. The presented study approach of aerodynamic loads calculation and analysis is of the university, and helpful for thorough research of loads reduction on large scale wind turbines.     

MW级风力发电机组联合仿真运动分析

根据在Adams系统中建立的MW级风力发电机组的机械模型和Adams与Matlab之间的接口,在Matlab环境中建立了偏航运动、转子运转和变桨运动的控制方法。根据给定机组的参数,研究了机组偏航运动、转子运转和变桨运动在启动阶段的特性。研究发现:在启动过程中,由于变桨运动、偏航运动和发电机转子旋转同时存在,将产生陀螺效应和惯性力,并施加在运动副上;即使对发电机施加冲击和干扰,控制模型都能够保证风力发电机组稳定运行;由于牵连运动、相对运动和惯性力的影响,转子角速度、偏航运动和变桨运动均不可能做到匀加速或匀减速运动。     

Development of an aeroelastic code based on three‐dimensional viscous–inviscid method for wind turbine computations

Aerodynamic and structural dynamic performance analysis of modern wind turbines are routinely estimated in the wind energy field using computational tools known as aeroelastic codes. Most aeroelastic codes use the blade element momentum (BEM) technique to model the rotor aerodynamics and a modal, multi‐body or the finite‐element approach to model the turbine structural dynamics. The present work describes the development of a novel aeroelastic code that combines a three‐dimensional viscous–inviscid interactive method, method for interactive rotor aerodynamic simulations (MIRAS), with the structural dynamics model used in the aeroelastic code FLEX5. The new code, called MIRAS‐FLEX, is an improvement on standard aeroelastic codes because it uses a more advanced aerodynamic model than BEM. With the new aeroelastic code, more physical aerodynamic predictions than BEM can be obtained as BEM uses empirical relations, such as tip loss corrections, to determine the flow around a rotor. Although more costly than BEM, a small cluster is sufficient to run MIRAS‐FLEX in a fast and easy way. MIRAS‐FLEX is compared against the widely used FLEX5 and FAST, as well as the participant codes from the Offshore Code Comparison Collaboration Project. Simulation tests consist of steady wind inflow conditions with different combinations of yaw error, wind shear, tower shadow and turbine‐elastic modeling. Turbulent inflow created by using a Mann box is also considered. MIRAS‐FLEX results, such as blade tip deflections and root‐bending moments, are generally in good agreement with the other codes. Copyright © 2017 John Wiley & Sons, Ltd.     

New vortex‐lift and tangential‐force models for HAWT aerodynamic load prediction

Horizontal axis wind turbines (HAWTs) experience three‐dimensional rotational and unsteady aerodynamic phenomena at the rotor blades sections. These highly unsteady three‐dimensional effects have a dramatic impact on the aerodynamic load distributions on the blades, in particular, when they occur at high angles of attack due to stall delay and dynamic stall. Unfortunately, there is no complete understanding of the flow physics yet at these unsteady 3D flow conditions, and hence, the existing published theoretical models are often incapable of modelling the impact on the turbine response realistically. The purpose of this paper is to provide an insight on the combined influence of the stall delay and dynamic stall on the blade load history of wind turbines in controlled and uncontrolled conditions. New dynamic stall vortex and nonlinear tangential force coefficient modules, which integrally take into account the three dimensional rotational effect, are also proposed in this paper. This module along with the unsteady influence of turbulent wind speed and tower shadow is implemented in a blade element momentum (BEM) model to estimate the aerodynamic loads on a rotating blade more accurately. This work presents an important step to help modelling the combined influence of the stall delay and dynamic stall on the load history of the rotating wind turbine blades which is vital to have lighter turbine blades and improved wind turbine design systems.     

垂直对称四叶片风力机气动特性仿真研究

采用CFD计算软件对垂直轴风力机气动性能进行计算.首先,使用ICEM软件对模型进行前处理,通过Fluent软件进行数值模拟,分析不同计算时间步长和湍流模型对风力机气动特性仿真结果的影响,确定符合该研究模型的计算方法.随后,对顺流垂旋型垂直轴风力机在不同叶尖速比下进行计算,发现该风力机在叶尖速比为0.42时获得最大功率系...     

基于CFD的二维垂直轴风力机性能计算

采用计算流体力学方法(CFD)针对垂直轴风力发电机,开展简化的二维绕流特性研究。首先,基于开放型转子和增强型转子,研究网格节点数和壁面y+、计算时间步长和湍流模型等的变化对计算结果的影响,对计算模型和方法进行确认。随后,计算分析增强型垂直轴风力机与开放型垂直轴风力机的特性。结果表明,与开放性垂直轴风力发电机相比,增强型垂直轴风力发电机的功率系数和转矩系数有明显增加,且达到最大值的位置向叶尖速比增大的方向移动。然后对增强型垂直轴风力机发电机在不同来流风速下进行计算,发现增强型垂直轴风力发电机的转子转矩随来流风速增加,而转矩系数和功率系数与来流风速无关。最后,针对定子叶片在不同的方向开展计算研究。结果表明,定子叶片在不同方向时,增强型垂直轴风力机的转子转矩不同,且转矩到达峰值的位置也不同;在当前3个方向角中,叶片处于0°方向角时风力机具有最高的转矩系数,即具有最佳的功率系数。     

Control strategy of a wind turbine drive by an integrated model

In this paper, an integrated equivalent circuit is defined to analyse the operation of a wind generator–rectifier system connected to a DC link, with the electric machine consisting of a surface‐mounted permanent magnet synchronous generator (SPMG) directly coupled to the wind turbine. Such circuit is defined by integrating the models related to the electromechanical equations implemented into a Simulink® code, where the SPMG parameters are derived by the elaboration of sequences of magnetostatic FEM analyses. The integrated equivalent circuit can be very useful to examine the wind generator dynamics because of wind speed variations, and to analyse the influence of the electromechanical parameters on the energy output in order to identify the appropriate control strategies involving the regulation of the rotor speed, the DC link current and the blade pitch angle. In particular, a sensorless algorithm is implemented to estimate the main mechanical quantities (output torque and rotor speed) and to determine the wind speed by means of only electrical measurements. The comparison with an anemometer‐based solution shows that similar performances can be achieved in different operating conditions. The control strategies set up by the circuit model are verified on a 20 kW‐rated SPMG with outer rotor, comparing the sensor and sensorless approaches in terms of capability of energy production, dynamic promptness and sensitivity to parameter disturbances, also with wind turbulence. Copyright © 2008 John Wiley & Sons, Ltd.     

Estimating the angle of attack from blade pressure measurements on the National Renewable Energy Laboratory phase VI rotor using a free wake vortex model: yawed conditions

Wind turbine design codes for calculating blade loads are usually based on a blade element momentum (BEM) approach. Since wind turbine rotors often operate in off‐design conditions, such as yawed flow, several engineering methods have been developed to take into account such conditions. An essential feature of a BEM code is the coupling of local blade element loads with an external (induced) velocity field determined with momentum theory through the angle of attack. Local blade loads follow directly from blade pressure measurements as performed in the National Renewable Energy Laboratory (NREL) phase IV campaign, but corresponding angles of attack cannot (on principle) be measured. By developing a free wake vortex method using measured local blade loads, time‐dependent angle of attack and induced velocity distributions are reconstructed. In a previous paper, a method was described for deriving such distributions in conjunction with blade pressure measurements for the NREL phase VI wind turbine in axial (non‐yawed) conditions. In this paper, the same method is applied to investigate yawed conditions on the same turbine. The study considered different operating conditions in yaw in both attached and separated flows over the blades. The derived free wake geometry solutions are used to determine induced velocity distributions at the rotor blade. These are then used to determine the local (azimuth time dependent) angle of attack, as well as the corresponding lift and drag for each blade section. The derived results are helpful to develop better engineering models for wind turbine design codes. Copyright © 2008 John Wiley & Sons, Ltd.     

Aerodynamic design optimization of wind turbine rotors under geometric uncertainty

Presented is a robust optimization strategy for the aerodynamic design of horizontal axis wind turbine rotors including the variability of the annual energy production because of the uncertainty of the blade geometry caused by manufacturing and assembly errors. The energy production of a rotor designed with the proposed robust optimization approach features lower sensitivity to stochastic geometry errors with respect to that of a rotor designed with the conventional deterministic optimization approach that ignores these errors. The geometry uncertainty is represented by normal distributions of the blade pitch angle, and the twist angle and chord of the airfoils. The aerodynamic module is a blade‐element momentum theory code. Both Monte Carlo sampling and the univariate reduced quadrature technique, a novel deterministic uncertainty analysis method, are used for uncertainty propagation. The performance of the two approaches is assessed in terms of accuracy and computational speed. A two‐stage multi‐objective evolution‐based optimization strategy is used. Results highlight that, for the considered turbine type, the sensitivity of the annual energy production to rotor geometry errors can be reduced by reducing the rotational speed and increasing the blade loading. The primary objective of the paper is to highlight how to incorporate an efficient and accurate uncertainty propagation strategy in wind turbine design. The formulation of the considered design problem does not include all the engineering constraints adopted in real turbine design, but the proposed probabilistic design strategy is fairly independent of the problem definition and can be easily extended to turbine design systems of any complexity. Copyright © 2014 John Wiley & Sons, Ltd.     

叶片转角对小型Savonius风机气动性能的影响

Savonius风机是一种典型的垂直轴风力发电机,通过对其进行流固耦合分析,研究叶片转角对风机气动性能的影响。利用ANSYS的CFX流体模块,流体湍流模型选择基于RANS的标准k-ε湍流模型,对风轮进行流固耦合分析,从而获得叶片产生的力矩情况,并计算了风机的功率特性。利用求解结果,得到了力矩系数与叶片转角之间的关系。分析了风机叶片在旋转一周中所产生的最大扭矩以及负扭矩所处的位置和范围。通过分析转角对风机性能的影响,可为今后的Savonius风机叶片形状优化和效率提升提供参考。     

Wind turbine load reduction by rejecting the periodic load disturbances

For the cost per kilowatt hour to be decreased, the trend in offshore wind turbines is to increase the rotor diameter as much as possible. The increasing dimensions have led to a relative increase of the loads on the wind turbine structure; thus, it is necessary to react to disturbances in a more detailed way, e.g. each blade separately. The disturbances acting on an individual wind turbine blade are to a large extent deterministic; for instance, tower shadow, wind shear, yawed error and gravity are depending on the rotational speed and azimuth angle and will change slowly over time. This paper aims to contribute to the development of individually pitch‐controlled blades by proposing a lifted repetitive controller that can reject these periodic load disturbances for modern fixed‐speed wind turbines and modern variable‐speed wind turbines operating above‐rated. The performance of the repetitive control method is evaluated on the UPWIND 5 MW wind turbine model and compared with typical individual pitch control. Simulation results indicate that for relatively slow changing periodic wind disturbances, this lifted repetitive control method can significantly reduce the vibrations in the wind turbine structure with considerably less high‐frequent control action. Copyright © 2012 John Wiley & Sons, Ltd.     

Augmented LQG controller for enhancement of online dynamic performance for WTG system

Operation of variable speed wind turbine generator (WTG) in the above-rated region characterized by high turbulence intensities demands a trade-off between two performance metrics: maximization of energy harvested from the wind and minimization of damage caused by mechanical fatigue. This paper presents a learning adaptive controller for output power leveling and decrementing cyclic loads on the drive train. The proposed controller incorporates a linear quadratic Gaussian (LQG) augmented by a neurocontroller (NC) and regulates rotational speed by specifying the demanded generator torque. Pitch control ensures rated power output. A second-order model and a stochastic wind field model are used in the analysis. The LQG is used as a basis upon which the performance of the proposed paradigm in the trade-off studies is assessed. Simulation results indicate the proposed control scheme effectively harmonizes the relation between rotor speed and the highly turbulent wind speed thereby regulating shaft moments and maintaining rated power.     

可变叶片安装角立轴风力机的转动力矩计算

为提高市轴风力机的效率,对可变叶片安装角的立轴风力机进行了分析,根据机翼升力与阻力的理论,在固定来流风速和旋转速度下计算了叶片在每个方位角上产生力矩最大的最佳安装角的变化规律,为了更好的运行,对最佳安装角的变化规律进行了一定修改.计算比较了固定安装角度的叶片与可变安装角度的叶片旋转一周产生的力矩,结果表明叶片在最佳安装角下运行时,每一转的正力矩都有明显增大,平均力矩町提高14倍.多个叶片在最佳安装角下运行时的力矩变化较平稳.可变叶片安装角立轴风力机是一种有发展前途的动力设备.     

Measurements and modelling of the power performance of a model floating wind turbine under controlled conditions

This paper describes power performance measurements undertaken on a model floating wind turbine installed on a tension‐leg platform (TLP) in a wind/wave generator facility. Initially, the surge of the platform was measured under different rotor and wave conditions. The surge behaviour depended considerably on the rotor tip speed ratio and the wave frequency and amplitude. High‐frequency data sampling techniques were then used to derive the instantaneous power coefficient and tip speed ratio directly from the measurements, together with the surge velocity of the floating system. The power measurements were compared with those predicted by three independent numerical models, two of which are based on the blade element momentum approach and the third involving a lifting‐line free‐wake vortex model. The fluctuations of the power coefficient with time predicted by the three models were in close agreement; however, these were all significantly larger than those derived from the rotor shaft torque measurements. This was found to be due to the limitations of the torque measurement technique. Although being accurate in measuring the time‐averaged torque, the sensor was incapable of measuring the high‐frequency low‐amplitude fluctuations in the rotor shaft torque induced by the TLP surge. This was confirmed using an alternative experimental technique involving hot‐wire near‐wake measurements. The study also investigated the influence of the platform surge motion on the time‐averaged power coefficients. Both the measurements and the free‐wake vortex model revealed marginal deviations in the time‐averaged power coefficients when compared with those obtained for a fixed, non‐surging rotor. Copyright © 2014 John Wiley & Sons, Ltd.