Optimized linearization of chord and twist angle profiles for fixed-pitch fixed-speed wind turbine blades

The chord and twist angle radial profiles of a fixed-pitch fixed-speed (FPFS) horizontal-axis wind turbine blade are based on a particular design wind speed and design tip speed ratio. Because the tip speed ratio varies with wind speed, the originally optimized chord and twist angle radial profiles for a preliminary blade design through optimum rotor theory do not necessarily provide the highest annual energy production (AEP) for the wind turbine on a specific site with known wind resources. This paper aims to demonstrate a novel optimal blade design method for an FPFS wind turbine through adopting linear radial profiles of the blade chord and twist angle and optimizing the slope of these two lines. The radial profiles of the blade chord and twist angle are linearized on a heuristic basis with fixed values at the blade tip and floating values at the blade root based on the preliminary blade design, and the best solution is determined using the highest AEP for a particular wind speed Weibull distribution as the optimization criteria with constraints of the top limit power output of the wind turbine. The outcomes demonstrate clearly that the proposed blade design optimization method offers a good opportunity for FPFS wind turbine blade design to achieve a better power performance and low manufacturing cost. This approach can be used for any practice of FPFS wind turbine blade design and refurbishment.     

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。     

Design,analysis and test of a model turbine blade for a wave basin test of floating wind turbines

Froude scaling is a generally reliable way to design models of floating wind turbines for wave basin testing. However, the resulting rotor thrust of the model is far lower than the Froude-scaled value of a full-size turbine, because the reduction in Reynolds number decreases the lift coefficients and increases the drag coefficients (the Reynolds number scaling effect). A 1/50th scale model wind turbine based on a NREL-5MW reference turbine is examined here. To mitigate the Reynolds number scaling effect in the model, the original aerofoils of the reference turbine (DU series and NACA 64-618) were replaced by an aerofoil at a low Reynolds number (NACA 4412). Such a model with aerofoil-adjusted blades was used in the mathematical optimization of rotor thrust. The design objective was to guarantee that while the rotor thrust of the model equalled the Froude-scaled rotor thrust of the reference, the smallest chord lengths were achieved, considering the weight control in building the model blade. The distribution of chord lengths fitted a fourth-order polynomial curve, and the distribution of twist angles along the blade fitted a second-order polynomial curve. The eight coefficients of the two curves were chosen as optimization variables, and pattern search method was used to solve the optimization model. The model blade was designed at zero pitch angle and further tested in FAST, a fully coupled simulation tool. A model test was conducted using the optimized blade geometry in the State Key Laboratory of Ocean Engineering in Shanghai, China, and the thrusts were compared with the predicted values.     

实度对低风速风电机组风轮气动性能影响研究

为提高低风速地区的风能利用率,研究风轮实度对低风速风电机组气动性能的影响。考虑影响风轮实度因素（叶片数量、弦长及安装角）,设计2组不同弦长叶片与可调安装角轮毂。安装角改变时不仅会引起实度变化,还会使叶尖速比发生改变。通过车载试验验证安装角不同时对风轮气动性能的影响主要与叶尖速比相关。根据不同风轮表面压力分布数值模拟结果得出：相同风速下,弦长由叶根到叶尖逐渐增大的叶片更易启动。相同条件下,试验机组输出功率与数值模拟机组输出功率最大相差5.37%,说明数值模拟结果可信。随着风轮实度的增加,风速5 m/s时,其风能利用系数呈增大趋势,风速8 m/s时,其风能利用系数呈减小趋势,两趋势相交时实度为25.38%,得出该实度下风轮气动性能较优,即可得到适合低风速地区的风轮实度。     

Experimental investigation of wake effects on wind turbine performance

The wake interference effect on the performance of a downstream wind turbine was investigated experimentally. Two similar model turbines with the same rotor diameter were used. The effects on the performance of the downstream turbine of the distance of separation between the turbines and the amount of power extracted from the upstream turbine were studied. The effects of these parameters on the total power output from the turbines were also estimated. The reduction in the maximum power coefficient of the downstream turbine is strongly dependent on the distance between the turbines and the operating condition of the upstream turbine. Depending on the distance of separation and blade pitch angle, the loss in power from the downstream turbine varies from about 20 to 46% compared to the power output from an unobstructed single turbine operating at its designed conditions. By operating the upstream turbine slightly outside this optimum setting or yawing the upstream turbine, the power output from the downstream turbine was significantly improved. This study shows that the total power output could be increased by installing an upstream turbine which extracts less power than the following turbines. By operating the upstream turbine in yawed condition, the gain in total power output from the two turbines could be increased by about 12%.     

基于偏航尾流模型的风电场功率协同优化研究

为减小风电场尾流效应的影响,提升风电场整体发电量,提出一种基于偏航尾流模型的风电场功率协同优化方法。首先建立风电场偏航尾流模型,该模型包括用于计算单机组尾流速度分布的Jensen-Gaussian尾流模型、尾流偏转模型及多机组尾流叠加模型,对各机组风轮前来流风速进行求解;再根据来流风速计算风电场输出功率,并以风电场整体输出功率最大为优化目标,利用拟牛顿算法协同优化各机组轴向诱导因子和偏航角度。以4行4列方形布置的16台NREL-5 MW风电机组为对象进行仿真研究。结果表明,所提出的基于偏航尾流模型的风电场功率协同优化方法能显著提升风电场整体输出功率。     

Evaluation of the effects of turbulence model enhancements on wind turbine wake predictions

The modelling of wind turbine wakes is investigated in this paper using a Navier–Stokes solver employing the k–ω turbulence model appropriately modified for atmospheric flows. It is common knowledge that even single‐wind turbine wake predictions with computational fluid dynamic methods underestimate the near wake deficit, directly contributing to the overestimation of the power of the downstream turbines. For a single‐wind turbine, alternative modelling enhancements under neutral and stable atmospheric conditions are tested in this paper to account for and eventually correct the turbulence overestimation that is responsible for the faster flow recovery that appears in the numerical predictions. Their effect on the power predictions is evaluated with comparison with existing wake measurements. A second issue addressed in this paper concerns multi‐wake predictions in wind farms, where the estimation of the reference wind speed that is required for the thrust calculation of a turbine located in the wake(s) of other turbines is not obvious. This is overcome by utilizing an induction factor‐based concept: According to it, the definition of the induction factor and its relationship with the thrust coefficient are employed to provide an average wind speed value across the rotor disk for the estimation of the axial force. Application is made on the case of five wind turbines in a row. Copyright © 2010 John Wiley & Sons, Ltd.     

海上风电场功率提升和疲劳平衡综合优化控制

针对海上风电场,综合功率提升和疲劳平衡分配的优化目标,提出一种以天为优化周期的优化策略。在电网高负荷时段,基于Jensen尾流模型,以轴向诱导因子为优化变量,风电场整场功率最大为目标,运用随机粒子群算法进行风功率利用提升优化控制;在电网低负荷时段,基于风电机组综合疲劳系数计算方法,以机组轴向诱导因子为优化变量,应用尾流计算模型调整轴向诱导因子来满足电网限功率指令,以机组疲劳系数标准差最小为目标,采用粒子群算法寻优进行疲劳平衡优化。以某海上风电场进行算例分析,结果表明该优化策略在一天的优化周期内可较好地实现风电场功率提升和疲劳平衡的综合优化。     

Maximization of the annual energy production of wind power plants by optimization of layout and yaw‐based wake control

This paper presents a wind plant modeling and optimization tool that enables the maximization of wind plant annual energy production (AEP) using yaw‐based wake steering control and layout changes. The tool is an extension of a wake engineering model describing the steady‐state effects of yaw on wake velocity profiles and power productions of wind turbines in a wind plant. To make predictions of a wind plant's AEP, necessary extensions of the original wake model include coupling it with a detailed rotor model and a control policy for turbine blade pitch and rotor speed. This enables the prediction of power production with wake effects throughout a range of wind speeds. We use the tool to perform an example optimization study on a wind plant based on the Princess Amalia Wind Park. In this case study, combined optimization of layout and wake steering control increases AEP by 5%. The power gains from wake steering control are highest for region 1.5 inflow wind speeds, and they continue to be present to some extent for the above‐rated inflow wind speeds. The results show that layout optimization and wake steering are complementary because significant AEP improvements can be achieved with wake steering in a wind plant layout that is already optimized to reduce wake losses. Copyright © 2016 John Wiley & Sons, Ltd.     

Multidisciplinary design optimization of offshore wind turbines for minimum levelized cost of energy

This paper presents a method for multidisciplinary design optimization of offshore wind turbines at system level. The formulation and implementation that enable the integrated aerodynamic and structural design of the rotor and tower simultaneously are detailed. The objective function to be minimized is the levelized cost of energy. The model includes various design constraints: stresses, deflections, modal frequencies and fatigue limits along different stations of the blade and tower. The rotor design variables are: chord and twist distribution, blade length, rated rotational speed and structural thicknesses along the span. The tower design variables are: tower thickness and diameter distribution, as well as the tower height. For the other wind turbine components, a representative mass model is used to include their dynamic interactions in the system. To calculate the system costs, representative cost models of a wind turbine located in an offshore wind farm are used. To show the potential of the method and to verify its usefulness, the 5 MW NREL wind turbine is used as a case study. The result of the design optimization process shows 2.3% decrease in the levelized cost of energy for a representative Dutch site, while satisfying all the design constraints.     

Wake impacts on downstream wind turbine performance and yaw alignment

Aerodynamic wake interaction between commercial scale wind turbines can be a significant source of power losses and increased fatigue loads across a wind farm. Significant research has been dedicated to the study of wind turbine wakes and wake model development. This paper profiles influential wake regions for an onshore wind farm using 6 months of recorded SCADA (supervisory control and data acquisition) data. An average wind velocity deficit of over 30% was observed corresponding to power coefficient losses of 0.2 in the wake region. Wind speed fluctuations are also quantified for an array of turbines, inferring an increase in turbulence within the wake region. A study of yaw data within the array showed turbine nacelle misalignment under a range of downstream wake angles, indicating a characteristic of wind turbine behaviour not generally considered in wake studies. The turbines yaw independently in order to capture the increased wind speeds present due to the lateral influx of turbulent wind, contrary to many experimental and simulation methods found in the literature. Improvements are suggested for wind farm control strategies that may improve farm‐wide power output. Additionally, possible causes for wind farm wake model overestimation of wake losses are proposed.Copyright © 2012 John Wiley & Sons, Ltd.     

Tidal farm analysis using an analytical model for the flow velocity prediction in the wake of a tidal turbine with small diameter to depth ratio

A tidal turbine is a device converting hydrodynamic power into electrical power. Lately, more and more projects have been developed in order to optimize the productivity of this kind of energy. In such research with industrial interest, under the impact of the wake effect on the output power, the analysis of a tidal farm layout is regarded as the first priority. Simple approaches such as those developed for wind farms could be used in tidal turbine arrangement optimization. These methodologies can be improved by taking into account the turbulence in tidal farms and tidal turbines' mechanical characteristics. The goal of this work is to propose a predictive analytical model to estimate the tidal speed in the far wake of tidal turbines with small diameter to depth ratio (20% here). It is a first step prior to integrate the wake model in a tidal farm layout optimization algorithm. The wake model development is achieved reanalyzing the far wake's equations used in wind farm applications. A turbine represented by an Actuator Disc (AD) in conjunction with a Computational Fluid Dynamics (CFD) numerical model is used as a reference for this purpose. The CFD-AD model has been validated with experimental results from literature. The novelty of the present work consists in expressing the far wake's radius expansion as a function of the ambient turbulence and the thrust coefficient. The proposed equation is used in conjunction with the Jensen's model in a manner that the velocities downstream a tidal turbine can be estimated. The velocity distribution in the far wake of a single turbine obtained by the proposed model is in good agreement with the CFD numerical model. As a matter of fact, the model provides satisfactory accuracy in the cases of two parks: one with five aligned turbines and one with ten staggered turbines.     

Application of a LES technique to characterize the wake deflection of a wind turbine in yaw

When a wind turbine works in yaw, the wake intensity and the power production of the turbine become slightly smaller and a deflection of the wake is induced. Therefore, a good understanding of this effect would allow an active control of the yaw angle of upstream turbines to steer the wake away from downstream machines, reducing its effect on them. In wind farms where interaction between turbines is significant, it is of interest to maximize the power output from the wind farm as a whole and to reduce fatigue loads on downstream turbines due to the increase of turbulence intensity in wakes. A large eddy simulation model with particular wind boundary conditions has been used recently to simulate and characterize the turbulence generated by the presence of a wind turbine and its evolution downstream the machine. The simplified turbine is placed within an environment in which relevant flow properties like wind speed profile, turbulence intensity and the anisotropy of turbulence are found to be similar to the ones of the neutral atmosphere. In this work, the model is used to characterize the wake deflection for a range of yaw angles and thrust coefficients of the turbine. The results are compared with experimental data obtained by other authors with a particle image velocimetry technique from wind tunnel experiments. Also, a comparison with simple analytical correlations is carried out. Copyright © 2009 John Wiley & Sons, Ltd.     

Wind plant power optimization through yaw control using a parametric model for wake effects—a CFD simulation study

This article presents a wind plant control strategy that optimizes the yaw settings of wind turbines for improved energy production of the whole wind plant by taking into account wake effects. The optimization controller is based on a novel internal parametric model for wake effects called the FLOw Redirection and Induction in Steady‐state (FLORIS) model. The FLORIS model predicts the steady‐state wake locations and the effective flow velocities at each turbine, and the resulting turbine electrical energy production levels, as a function of the axial induction and the yaw angle of the different rotors. The FLORIS model has a limited number of parameters that are estimated based on turbine electrical power production data. In high‐fidelity computational fluid dynamics simulations of a small wind plant, we demonstrate that the optimization control based on the FLORIS model increases the energy production of the wind plant, with a reduction of loads on the turbines as an additional effect. Copyright © 2014 John Wiley & Sons, Ltd.     

Real-time rotor effective wind speed estimation based on actuator disc theory: Design and full-scale experimental validation

The use of state estimation techniques offers a means of inferring rotor effective wind speed from standard measurements of wind turbines. Typical wind speed estimators rely upon a pre-computed quasi-steady aerodynamic mapping, which describes the relationship between pitch angle and tip-speed ratio and the power coefficient. In practice, the static mapping does not capture the influence of turbine structural dynamics and atmospheric turbulence, inevitably resulting in poor performance of the wind speed estimation. In addition, the turbine aerodynamic properties might not be easily accessible. Thus, this paper presents a rotor effective wind speed estimation method that obviates the requirement for prior knowledge of turbine power coefficients. Specifically, the proposed method exploits a simple actuator disc model, where the aerodynamic power and thrust coefficients can be characterized in terms of axial induction factors. Based on this insight and standard turbine measurements, real-time estimation of rotor effective wind speed and axial induction factors can then be achieved using a simplified turbine drive-train model and an extended Kalman filter. In addition, the actuator disc model can be updated easily over time by calibrating solely two correction factors. Thus, the proposed algorithm presents an alternative for estimating the rotor effective wind speed, which is valuable for numerous applications, for example, LiDAR-assisted control and coherence studies.     

Experimental study of the effect of turbulence on horizontal axis wind turbine aerodynamics

Incident flows on wind turbines are often highly turbulent, because these devices operate in the atmospheric boundary layer and often in the wake of other wind turbines. This article presents experimental investigations of the effects of a high turbulence level on wind turbine aerodynamics. Power and thrust are measured on a horizontal axis wind turbine model in the ‘Lucien Malavard’ wind tunnel. A grid is used to generate three turbulence levels (4·4%, 9% and 12%) with integral length scale of the order of magnitude of the chord length. Experiments show little effect of turbulence on the wind turbine model power and thrust. This can be justified by analysis of the aerodynamic loads along the blade. Copyright © 2005 John Wiley & Sons, Ltd.     

考虑尾流效应的风电机组启停优化研究

以某典型风电场为例,采用尾流模型模拟研究风电机组启停优化对风电机组尾流干涉和发电量的影响。在速度恢复系数小于0.06时,典型机位的停机可增加风电场全场发电量。以中国北方某实际风电场为例进行现场试验,在主风向下,通过调度上游风电机组的启停,实现区域内风电机组发电量提升,验证方法的有效性。     

A pragmatic approach to wind farm simulations using the dynamic wake meandering model

This paper presents a computationally efficient method for using the dynamic wake meandering model to conduct simulations of wind farm power production. The method is based on creating a database, which contains the time and rotor‐averaged wake effect at any point downstream of a wake‐emitting turbine operating in arbitrary ambient conditions and at an arbitrary degree of wake influence. This database is later used as a look‐up table at runtime to estimate the operating conditions at all turbines in the wind farm, thus eliminating the need to run the dynamic wake meandering model at runtime. By using the proposed method, the time required to conduct wind farm simulations is reduced by three orders of magnitude compared with running the standalone dynamic wake meandering model at runtime. As a result, the wind farm production dynamics for a farm of 100 turbines at 10,000 different sets of ambient conditions run on a normal laptop in 1 h. The method is validated against full scale measurements from the Smøla and OWEZ wind farms, and fair agreement is achieved. Copyright © 2014 John Wiley & Sons, Ltd.     

新型双风轮风力机气动特性的三维流场数值模拟

基于Simplic算法,采用SST κ-ω湍流模型,利用Fluent6．3数值模拟软件对新型的小型双风轮风力机的气动特性进行了三维流场研究,并与同规格单风轮风力机的三维流场进行了比较．结果表明：与单风轮风力机相比,随着后风轮叶片数目的增加,新型双风轮风力机的湍流强度变大,风力机运行的稳定性在一定程度上有所降低;当后风轮的叶片数目合理时,后风轮对前风轮的影响较小,且可以有效地捕捉到前风轮的漏风,使得新型双风轮风力机的风轮在获得较大迎风面积的同时可以保持较高的转速,进而能够高效地实现风能的两级利用,明显提高发电功率和增大风能利用系数．     

Power optimization of wind turbines with data mining and evolutionary computation

A data-driven approach for maximization of the power produced by wind turbines is presented. The power optimization objective is accomplished by computing optimal control settings of wind turbines using data mining and evolutionary strategy algorithms. Data mining algorithms identify a functional mapping between the power output and controllable and non-controllable variables of a wind turbine. An evolutionary strategy algorithm is applied to determine control settings maximizing the power output of a turbine based on the identified model. Computational studies have demonstrated meaningful opportunities to improve the turbine power output by optimizing blade pitch and yaw angle. It is shown that the pitch angle is an important variable in maximizing energy captured from the wind. Power output can be increased by optimization of the pitch angle. The concepts proposed in this paper are illustrated with industrial wind farm data.