Theoretical and Empirical Limits: Reexamining Betz’s Upper Limit towards a Practical Power Coefficients in Wind Turbines*

The aspiration of all wind turbine designers is to attain Betz’s upper limit, which represents the highest efficiency in wind energy extraction. Majority of working turbines operate slightly below this limit with an exception of a few operating in wind tunnels. This study proposes for a comprehensive reevaluation of Betz’s derivation, aiming to establish the gap between a theoretical power limit and a practical limit for realization. There are two common expressions for power coefficient giving the same optimal value of 59%, but they generate different power-coefficient curves when plotted against velocity ratios. This paper presents a new method being referred as “Direct Multiplication Fractional Change” (DMFC) for deriving power-coefficient curves in wind energy, and compares its generated curve with established models. Discrepancies in power-coefficient expressions are identified and harmonized. Three approaches, namely EVAM, LVM, and DMFCM, were used for the numerical derivation of cp in the study, with their evaluation summarized in a table. The study collaborates its findings with a formulated velocity-distance curve, commonly presented as a hypothetical velocity profile in some publications. The results from DMFCM indicate two distinct maxima for the power coefficient. On the front side of the disc, a maximum of 0.5 is achievable in practice, although it is not the highest theoretically. On the rear side, a theoretical maximum of 0.59 is observed, but this value is not attainable in practice. These maxima are separated by their positions along the line of flow relative to the disc. However, this approximation is limited to a streamlined flow model of the rotor disc.

Application of 2D Numerical Model to Unsteady Performance Evaluation of Vertical-Axis Tidal Current Turbine

Abstract Tidal current energy is renewable and sustainable, which is a promising altemative energy resource for the future elec- tricity supply. The straight-bladed vertical-axis turbine is regarded as a useful tool to capture the tidal current energy especially under low-speed conditions. A 2D unsteady numerical model based on Ansys-Fluent 12.0 is established to conduct the numerical simulation, which is validated by the corresponding experimental data. For the unsteady calculations, the SST model, 2x 105 and 0.01 s are se- lected as the proper turbulence model, mesh number, and time step, respectively. Detailed contours of the velocity distributions around the rotor blade foils have been provided for a flow field analysis. The tip speed ratio （TSR） determines the azimuth angle of the appearance of the torque peak, which occurs once for a blade in a single revolution. It is also found that simply increasing the incident flow velocity could not improve the turbine performance accordingly. The peaks of the averaged power and torque coeffi- cients appear at TSRs of 2.1 and 1.8, respectively. Furthermore, several shapes of the duct augmentation are proposed to improve the turbine performance by contracting the flow path gradually from the open mouth of the duct to the rotor. The duct augmentation can significantly enhance the power and torque output. Furthermore, the elliptic shape enables the best performance of the turbine. The numerical results prove the capability of the present 2D model for the unsteady hydrodynamics and an operating performance analy- sis of the vertical tidal stream turbine.

Effect of additional cylinders on power-extraction performance of a Savonius vertical-axis wind turbine

To improve the power-extraction performance of the Savonius vertical-axis wind turbine(S-VAWT),additional cylinders,which are used to control the fluid flow around the wind turbine blade,were introduced into the blade design.In contrast to the traditional numerical method,a mathematical model in the form of a dynamical system was used in this study.A numerical calculation program that could effectively solve the equations of wind-induced rotation of S-VAWT was developed,and combined with the Taguchi experimental method to investigate the influence of additional cylinders on the power-extraction characteristics of the S-VAWT.The results showed that the additional cylinders have a significant impact on the power-extraction performance of the S-VAWT.At 4-m/s wind speed,the average power coefficient of the S-VAWT with additional cylinders is 15%higher than that of the conventional S-VAWT.After construction of the wind turbine prototype and power-extraction tests,the results showed that compared with a conventional S-VAWT,the output power was 29%higher for the S-VAWT with additional cylinders under the same particular conditions.

Numerical investigation on the flow and power of small-sized multi-bladed straight Darrieus wind turbine

Straight Darrieus wind turbine has attractive characteristics such as the ability to accept wind from random direction and easy installation and maintenance. But its aerodynamic performance is very complicated,especially for the existence of dynamic stall. How to get better aerodynamic performance arouses lots of interests in the design procedure of a straight Darrieus wind turbine. In this paper,mainly the effects of number of blades and tip speed ratio are discussed. Based on the numerical investigation,an assumed asymmetric straight Darrieus wind turbine is proposed to improve the averaged power coefficient. As to the numerical method,the flow around the turbine is simulated by solving the 2D unsteady Navier-Stokes equation combined with continuous equation. The time marching method on a body-fitted coordinate system based on MAC (Marker-and-Cell) method is used. O-type grid is generated for the whole calculation domain. The characteristics of tangential and normal force are discussed related with dynamic stall of the blade. Averaged power coefficient per period of rotating is calculated to evaluate the eligibility of the turbine.

考虑功率匹配的风储联合一次调频控制策略

风储联合参与电网一次调频能够较好地利用风电和储能的优势进行调频控制,逐渐成为一种新的趋势。然而,风储在协调过程中存在储能利用不充分、风储功率不匹配的问题。针对上述问题提出一种改进风储联合一次调频控制策略。通过频率分离、设计六种工况切换规则、设置风电和储能自适应下垂系数,优化了储能电池的充放电功能,改善了电池的荷电状态,解决了工况切换过程中的功率不匹配问题,避免了由此导致的功率缺额过度补偿。最后通过仿真与风储实验平台对比了所提控制策略与现有控制策略的风能利用率和调频效果,验证了所提控制策略的有效性和优越性。

Experimental Investigation of Performance of the Wind Turbine with the Flanged-Diffuser Shroud in Sinusoidally Oscillating and Fluctuating Velocity Flows

The wind turbine with a flanged-diffuser shroud—so called “wind-lens turbine”—is developed as one of high performance wind turbines by Ohya et al. In this paper, the wind turbine performance is investigated for both steady and unsteady winds. The compact-type wind lens turbine shows higher efficiency than the only rotor wind turbine. Also, the flow structure around the compact-type wind turbine is made clear by CFD and PIV in steady wind. Furthermore, the performances of the only rotor and the compact-type wind-lens turbines for unsteady wind are experimentally and numerically investigated. Experimental and numerical results are presented to demonstrate the dependence of frequency of the harmonic oscillating velocity wind on power coefficient. Consequently, the compact-type wind-lens turbine show better performance than the only rotor one in sinusoidally oscillating velocity wind. Furthermore, the numerical estimation can predict the power coefficient in the oscillating flows to an accuracy of 94% to 102%. In addition, the dependence of the turbine performance on turbulent intensity and vortex scale of natural fluctuating wind is presented.

Effect of blade pitch angle on aerodynamic performance of straight-bladed vertical axis wind turbine

Wind energy is one of the most promising renewable energy sources, straight-bladed vertical axis wind turbine(S-VAWT) appears to be particularly promising for the shortage of fossil fuel reserves owing to its distinct advantages, but suffers from poor self-starting and low power coefficient. Variable-pitch method was recognized as an attractive solution to performance improvement, thus majority efforts had been devoted into blade pitch angle effect on aerodynamic performance. Taken into account the local flow field of S-VAWT, mathematical model was built to analyze the relationship between power outputs and pitch angle. Numerical simulations on static and dynamic performances of blade were carried out and optimized pitch angle along the rotor were presented. Comparative analyses of fixed pitch and variable-pitch S-VAWT were conducted, and a considerable improvement of the performance was obtained by the optimized blade pitch angle, in particular, a relative increase of the power coefficient by more than 19.3%. It is further demonstrated that the self-starting is greatly improved with the optimized blade pitch angle.

Criterion of aerodynamic performance of large-scale offshore horizontal axis wind turbines

With the background of offshore wind energy projects, this paper studies aerodynamic performance and geometric characteristics of large capacity wind turbine rotors （1 to 10 MW）, and the main characteristic parameters such as the rated wind speed, blade tip speed, and rotor solidity. We show that the essential criterion of a high- performance wind turbine is a highest possible annual usable energy pattern factor and a smallest possible dimension, capturing the maximum wind energy and producing the maximum annual power. The influence of the above-mentioned three parameters on the pattern factor and rotor geometry of wind turbine operated in China＇s offshore meteoro- logical environment is investigated. The variation patterns of aerodynamic and geometric parameters are obtained, analyzed, and compared with each other. The present method for aerodynamic analysis and its results can form a basis for evaluating aerodynamic performance of large-scale offshore wind turbine rotors.

A Summary Study of Wind Turbine with Related Control

One specific issue associated with the wind turbine is how to manage and adjust the rotor speed and pitch angle in the turbine with the wind increasing to achieve the maximum power extraction from the wind. The aim of this paper is to provide a summary study of the impact of related controls and operating strategies on the wind turbine which mean how parameters affect the wind turbine operation. The software of “GH bladed” produced by GL Garrad Hassan will be used to model wind turbine and to perform the analysis. Following two strategies, control of rotor speed and control of blade pitch angle, are applied to the model of the wind turbine to see how output power are adjusted and optimized. The final part proposes the operating strategy of the wind turbine to understand the running procedure of wind turbine inside.

CFD-Based Performance Analysis and Experimental Investigation of Design Factors of Vertical Axis Wind Turbines under Low Wind Speed Conditions in Thailand

This paper presents effects of design factors on mechanical performance of Vertical Axis Wind Turbines (VAWTs), and an experimental investigation of optimal VAWT performance under low wind speed conditions in Thailand. Design factors include types of wind turbines, number of blades, types of materials, height-to-radius ratios, and design modifications. Potential VAWT models with different design factors are numerically analyzed within a virtual wind tunnel at various wind speeds by utilizing XflowTM?Computational Fluid Dynamics (CFD) software. The performance curves of each VAWT are obtained as plots of power coefficients against tip speed ratios. It is found that the type of wind turbine, number of blades, and height-to-radius ratio have significant effects on mechanical performance whereas types of materials result in shifts of operating speeds of VAWTs. Accordingly, an optimal VAWT prototype is developed to operate under actual low speed wind conditions. The performance curve from experimental results agrees with the CFD results. The proposed methodology can be used in the computer design of VAWTs to improve mechanical performance before physical fabrication.

Aerodynamic Performance and Vibration Analyses of Small Scale Horizontal Axis Wind Turbine with Various Number of Blades

The need to generate power from renewable sources to reduce demand for fossil fuels and the damage of their resulting carbon dioxide emissions is now well understood. Wind is among the most popular and fastest growing sources of alternative energy in the world. It is an inexhaustible, indigenous resource, pollution-free, and available almost any time of the day, especially in coastal regions. As a sustainable energy resource, electrical power generation from the wind is increasingly important in national and international energy policy in response to climate change. Experts predict that, with proper development, wind energy can meet up to 20% of US needs. Horizontal Axis Wind Turbines (HAWTs) are the most popular because of their higher efficiency. The aerodynamic characteristics and vibration of small scale HAWT with various numbers of blade designs have been investigated in this numerical study in order to improve its performance. SolidWorks was used for designing Computer Aided Design (CAD) models, and ANSYS software was used to study the dynamic flow around the turbine. Two, three, and five bladed HAWTs of 87 cm rotor diameter were designed. A HAWT tower of 100 cm long and 6 cm diameter was considered during this study while a shaft of 10.02 cm diameter was chosen. A good choice of airfoils and angle of attack is a key in the designing of a blade of rough surface and maintaining the maximum lift to drag ratio. The S818, S825 and S826 airfoils were used from the root to the tip and 4° critical angle of attack was considered. In this paper, a more appropriate numerical models and an improved method have been adopted in comparable with other models and methods in the literature. The wind flow around the whole wind turbine and static behavior of the HAWT rotor was solved using Moving Reference Frame (MRF) solver. The HAWT rotor results were used to initialize the Sliding Mesh Models (SMM) solver and study the dynamic behavior of HAWT rotor. The pressure and velocity contours on different blades surfaces were analyzed and presented in this work. The pressure and velocity contours around the entire turbine models were also analyzed. The power coefficient was calculated using the Tip Speed Ratio (TSR) and the moment coefficient and the results were compared to the theoretical and other research. The results show that the increase of number of blades from two to three increases the efficiency;however, the power coefficient remains relatively the same or sometimes decreases for five bladed turbine models. HAWT rotors and shaft vibrations were analyzed for two different materials using an applied pressure load imported from ANSYS fluent environment. It has proven that a good choice of material is crucial during the design process.

基于虚拟同步机的风-光-储并网系统自适应功频控制策略

风-光-储系统通过虚拟同步发电机(virtual synchronous generator,VSG)并网时,其运行工况变化将引起系统功频波动。针对这一问题,提出一种VSG自适应惯量阻尼功频控制策略。首先,建立VSG的数学模型及功率小信号模型,分析虚拟参数变化对系统稳定性的影响;然后,依据系统受扰时的功角曲线分析惯量阻尼的动态特性,设计了一种分段线性调整函数,并给出参数选取原则;最后,在Matlab/simulink平台中搭建仿真模型验证。结果表明,在工况变化情况下,采用VSG自适应控制的风光储并网系统功频响应得到了改善,相比传统VSG控制具有更好的动态调节性能。

倾覆力耦合的大兆瓦风机主轴-齿轮箱法兰结构疲劳寿命研究

大兆瓦风机主轴-齿轮箱法兰连接受倾覆力及其他交变载荷的作用,极易产生疲劳破坏。文中建立了考虑倾覆力耦合作用的法兰连接有限元数值模型,分析了特定工况下法兰连接各部件应力场分布规律;通过GH-Bladed获得主轴实际转矩变化数据,根据雨流计数法计算得到了主轴和螺栓多种工况下载荷-时间历程曲线,基于Brown-Miller准则并结合材料的S-N曲线,使用FE-SAFE给出了不同预紧力条件下主轴和螺栓的疲劳寿命,疲劳分析结果表明:随着预紧力的减小,主轴的疲劳寿命大于螺栓的,螺栓在风机运行过程中更容易发生疲劳破坏。基于VDI2230规范,结合法兰界面涂层增摩工艺,得到了法兰界面摩擦因数、螺栓预紧力与法兰结构疲劳寿命的理论模型。该研究对于大兆瓦风机主轴-齿轮箱法兰连接结构设计和疲劳寿命提升具有一定的指导意义。

基于VC-综合赋权法的海上风电APF配置优化方法研究

大容量海上风电机组的接入改变了传统电力系统结构,给电网带来了谐波等问题,影响了电能质量。为抑制海上风电机组产生的低次谐波,文章首先建立了海上风电机组并网电流的低次谐波理论模型;然后,在仿真软件ETAP上搭建海上风电机组仿真模型,验证不同出力情况下风电场的输出谐波特性;最后,基于风电场输出谐波特性,提出变异系数(Variation Coefficient,VC)综合赋权法对风电场有源滤波器(APF)进行优化配置,提升了风电场谐波的治理效果。基于实际算例验证了所提方法的有效性。

周期性脉动源对风力机功率的影响

针对WindPACT1.5 MW机组,通过大涡模拟探究风轮5°仰角时周期性脉动源(仰角、塔影效应、偏航、风剪切)对风力机总功率的影响,并结合逆叶素动量理论,进一步分析功率与升力系数之间的联系。结果表明,仰角、塔影效应加仰角与偏航加仰角均使得风力机总功率产生“3P”的波动规律,而风剪切加仰角使得总功率产生“锯齿状”的高频率波动规律,其中偏航是总功率损失的主要因素,塔影效应是功率波动的主要因素,且发现升力系数波动规律与功率单周期内的波动规律相似。

改善惯性响应与一次调频的风电全直流系统协调控制策略

针对风电全直流系统并网给交流电网带来的系统惯量降低、调频能力不足等问题,提出一种改善惯性响应与一次调频的变系数风电全直流系统协调控制策略。在惯量响应方面,网侧换流站采用惯性同步控制,直流升压站采用恒变比控制,实现直流电容对电网的惯量支撑及直流低压侧的直流电压对交流系统频率的感知,在此基础上对直流风电机组(direct current wind turbine,DCWT)附加变虚拟惯性系数的虚拟惯量控制,使风电全直流系统在不同频率响应阶段具备不同的等效惯量。在一次调频方面,DCWT采用超速与变桨相结合的减载运行方式,通过变下垂控制来改变其有功出力,充分利用不同风速下的备用容量,使风电全直流系统更有效地参与一次调频。仿真算例表明,文中所提策略改善了风电全直流系统接入后电力系统的惯性响应及一次调频。

经柔性高压直流输电并网的海上风电送出线路拟功率和、差波形比较式纵联保护

经柔性高压直流输电并网的海上风电送出线路在故障情况下呈现出的两端电流存在较大相角差等故障特性导致传统纵联保护面临不能正确动作的风险。根据电路中的拟功率定理,分别利用线路两端故障前后电压、电流瞬时值列写拟功率表达式,并对两表达式进行求和与作差运算,得到拟功率和与拟功率差。分析表明,发生区内故障时,两者波形相似性高,波形接近完全重合;发生区外故障时,两者含有成分不同,相似性较差,据此形成拟功率和、差波形比较式纵联保护的保护判据。利用EMTP-RV软件搭建经柔性高压直流输电并网的海上风电场模型,对不同故障类型、过渡电阻、噪声、数据窗长、控制方式、同步误差进行仿真验证,理论分析与仿真结果表明所提保护方法具有较强的适应性。

高风电渗透率下考虑系统风电备用容量的储能配置

风电的高比例渗透削弱了电力系统的惯性与调频容量,储能凭借响应迅速、出力稳定等特点被广泛应用于电网的惯量支撑及频率调节工作。首先以双馈风机额定转速与有功出力为约束条件,基于转子超速控制设置最适功率预留系数,划分风机参与系统调频的风速范围。在此基础上,考虑系统频率支撑能力,提出一种风电机组与储能协调配合的调频方法。通过对储能有功出力与系统稳态恢复过程的分析,刻画了虚拟同步机控制策略下储能系统的动态频率调节特性,由此实现储能在应对系统不同工况与不同支撑需求下控制参数的最优配置。仿真结果表明,所提方法能够在保证系统调频需求的同时充分利用风电自身的调频容量,优化储能系统参数的配置结果,实现储能出力的平滑输出,提高系统的频率支撑能力。

垂直轴风力机变桨规律及气动性能优化研究

以H型Darrieus垂直轴风力机为研究对象,基于最大切向力原则和Fourier函数,提出了一种适用于不同叶尖速比的变桨策略,即基于最大切向力原则确定最优攻角,进而生成理论变桨规律曲线;同时为保证变桨规律的周期性和便于实施,将理论变桨规律曲线离散成控制点,采用Fourier函数进行二次优化拟合,进而以数值模拟的方式,从垂直轴风力机的静态启动性能及动态输出性能方面研究变桨规律对其气动性能的影响。结果表明,变桨后垂直轴风力机各叶尖速比的功率系数显著提升,且提升效果在叶尖速比较低时尤为显著,最优叶尖速比为1.25,其功率系数峰值提升了13.5%;同时垂直轴风力机各相位角的静态启动性能大幅提升,静态力矩系数最大处较变桨前提升了261.1%。研究结果可为垂直轴风力机的气动性能优化提供参考依据。

防风网对大跨度煤棚风荷载特性的影响

为了研究防风网对大跨煤棚风荷载的影响,通过风洞刚性模型测压试验,对3种透孔率的防风网下煤棚表面风荷载进行研究,分析了风向角、有无防风网和防风网透孔率对典型测点和分区的体型系数以及测点的脉动风荷载的功率谱特性的影响。结果表明:不同风向角下,结构体型系数极值出现的位置和范围差别较大;防风网对减小煤棚风荷载有较好效果,放置防风网后煤棚表面呈现为绝对值较小的负压;大部分风向角下,20%的透孔率防风网对减小风荷载效果更好;不同位置测点受来流脉动影响情况不同,煤棚迎风侧角部测点脉动风荷载无量纲功率谱数值较大,且功率谱成分复杂,放置防风网后其峰值明显减小。