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风力发电控制系统研究综述(1),风力,发电,控制系统,研究,综述
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风力发电控制系统研究综述摘要：在现行的风力发电系统中，控制系统需要解决的基本矛盾是如何在风速变化的情况下,获得较稳定的电压输出,以及如何解决无风时的用电问题。控制系统的设计必须结合风能的特点及用户的需要。本文将从能量控制方式、应用范围、经济性以及未来技术导向这几个方面对风力发电控制系统进行综述。一、风力发电系统风能作为一种清洁的能源，已经成为除水能以外，技术最成熟、最具有规模化开发条件和商业发展 前景的能源之一。在近20年来，风能在风力发电领域的应用技术飞速发展。常规的风力发电机组主要由风轮、发电机、电能变换单元控制系统组成。能量转换结构如下1：风能通过风力机械转换为机械能并驱动发电机工作，从而转换为电能向负载或电网输出，或者经由储能设备存储。整个从风能转换为电能的过程则由风电控制系统控制。风电控制系统是综合性控制系统,除了要对电网、风况和机组运行参数进行监视,以确保运行过程的安全性和可靠性,还要根据风速、风向的变化,对机组进行优化控制,以提高机组的运行效率和发电量。二、风电控制系统上世纪八九十年代，现代风力发电产业开始崛起。20世纪80年代初,风力发电机组电气控制系统得以实现,但仍局限于采用模拟电子器件2。到了80年代中后期,随着计算机技术的发展及其在控制领域的应用,出现了基于微处理器的风力发电机组电气控制系统2。步入90年代,随着微处理器在电力电子、数据采集、信号处理、工业控制等领域的广泛应用,风力发电机组的电气控制系统往往采用基于单板机、单片机或可编程控制器的微机控制2。风力发电控制系统的基本目标分为3个层次:保证可靠运行、获取最大能量、提供良好的电力质量1。为了达到这一控制目标,风力发电系统的控制技术从定桨距发展到变桨距又发展到近年来采用的变速控制技术1。20世纪80年代中期开始进入风力发电市场的定浆距风力发电机组,主要解决了风力发电机组的并网问题和运行的安全性与可靠性问题,采用了软并网技术、空气动力刹车技术等并网运行的风力发电机组需要解决的最基本问题1。20世纪90年代以后,风力发电机组的可靠性已不是问题,变距风力发电机组开始进入风力发电市场1。此种机组起动时可对转速进行控制,并网后可对功率进行控制,使风力机的起动性能和功率输出特性都有显著改善。由于变距风力发电机组在额定风速以下运行时的效果仍不理想,到了20世纪90年代中期,基于变距技术的各种变速风力发电机组开始进入风电市场。 现行的风电控制系统主要为变速风力发电机组控制系统。其基本控制方式是把风速信号作为控制系统的输入变量来进行转速和功率控制的。变速风力发电机组的主要特点是:低于额定风速时,能跟踪最佳功率曲线,使风力发电机组具有最高的风能转换效率;高于额定风速时,增加了传动系统的柔性,使功率输出更加稳定,特别是解决了高次谐波与功率因素等问题后,达到了高效率、高质量地向电网提供电力的目的3。风力发电机组控制系统的作用是对整个风力发电机组实施正常操作、调节和保护。除了常规的启动控制、并/脱网控制、偏航与解缆、限速及刹车等控制功能外，还具有以下功能:根据功率以及风速自动进行转速和功率控制;根据功率因数自动投入(或切出)相应的补偿电容;机组运行过程中,对电网、风况和机组运行状况进行检测和记录,对出现的异常情况能够自行判断并采取相应的保护措施,而且还能根据记录的数据生成各种图表,以反映风力发电机组的各项性能指标;对在风电场中运行的风力发电机组还应具备远程通信功能4。目前绝大多数风力发电机组的控制系统都选用集散型或分布式(DCS)工业控制计算机。风力发电机组DCS控制系统的结构如下图所示3：三、风电系统的环保特性风能是风力发电的主要载体，风能资源具有可再生、洁净、规模大的优势，目前，国际倡导的正是清洁能源。其具有良好的发展前景和其它能源无可比拟的优越性。大体可归纳为以下几点。风力发电是一种干净无污染的可再生自然资源，取之不尽，用之不竭，没有常规能源( 煤电、油电、核电) 会造成环境污染的问题。风电技术装备在风电领域里扮演着重要的角色，是风电产业发展赖以生存的基础，国际上已风电作为一种温室气体零排放的替代能源技术5，被广泛认为有可能在未来取代传统燃料，成为新增发电量的主力军。随着能源短缺和全球经济的强劲增长导致环境问题激增，公众环保意识增强，风电在世界能源电力市场中发展最为迅速，其所拥有的技术含量高、易开发、能量大等特点使其一举成为了最具发展潜力的一大洁净能源。发展风能、光伏发电等新能源是缓解全球资源瓶颈、确保能源供给的流畅性以及安全性、可靠性的不二之选；是保护环境生态、 改善人类居住环境的有效方式；是实现可持续发展，构建和谐社会的最佳选择。四、风电系统的经济特性风电系统的成本主要由容量系数，风机价格，风机使用寿命，风资源状况以及电量损失决定6。容量系数是风力发电成本的影响因素之一，在风电成本的计算中，容量系数是一个重要的参考值。一般是容量系数越大，风力发电的成本越高，在其他因素一定的条件下，容量系数是影响风力发电成本的决定性因素。风机是风力发电中的主要设备，对于风电的开发和利用有重要的作用。风机的价格、使用寿命也与风力发电的成本息息相关，价格较高的风机不仅使用寿命长而且能够节约风能，减少消耗。但同时也增加了风电系统建设的前期投资成本。风资源状况对于风力发电成本也有一定的影响，如果风力不足或者风速不够大的话，就会使得发电的速度降低，效率降低，达不到预期的成果。在发电的过程中由于种种原因会造成电量损失，电量的流失造成发电量不足，就必须花费更多的时间和成本继续发电，不仅延长了发电的周期还造成了发电成本的增加。现如今，风电技术已日趋成熟，产品质量可靠，能源可用率达 95% 以上，风力发电的经济性日益提高6。如果计及煤电的环境保护及交通运输等投资，风电成本也低于煤电。风力风电场建设工期短，单台机组安装方便; 投资规模灵活易操作。总体而言发电成本较低，低于油电和核电。五、风电控制系统技术趋势从目前风电系统的应用来看，主要存在以下几个问题：一、不同风电机组厂商的风电机组难以通过一套统一的集控系统对风电组进行监控。造成重复投资。二、风电场环境复杂。单纯依靠人工分析数据、排除故障已经不能满足风电场对风电机组的全面维护，这些都导致了风电场运维困难。三、国家电网出台了风电并网技术规范，要求风电场对发电生产进行计划上报，并能对风电场进行电能调度。风电场集控系统迫切需求增加该功能，并且改造风电机组主控及变流器具备有功无功调节功能。四、没有对其他风电机组运行历史数据进行存储与分析，造成了风电机组设计与风电场选型是个开环的过程，不能进行改进与评估。风电系统未来的技术发展将聚焦于解决上述几个问题，将通过改进控制系统有效地对风电场内各风电机组进行管理以及运行状态监控, 使整个风电场风电机组运行安全、可靠、经济;并解决风电场电网接入问题，满足电网调度;以及通过风电机组运行数据的分析，持续对风电机组性能进行优化，对风电场选址进行评估。参考文献：1曾婧婧,杨平,徐春梅,蒋式勤. 风力发电控制系统研究J. 自动化仪表,2006,S1:32-35. 2张相考. 基于PLC的风电机组控制系统设计D.沈阳工业大学,2015. 3JB.Freeman and M.J Balas Direct Model Reference Adaptive Control of Variable Speed Horizontal Axis Wind Turbines J. Wind Energy 1999 22 (5).4姚秀萍,常喜强,张慧玲,孙立成,李静坤. 风电智能有功控制系统研究与实现J. 四川电力技术,2012,05:4-7. 5李雪明,行舟,陈振寰,陈永华,王福军,罗剑波. 大型集群风电有功智能控制系统设计J. 电力系统自动化,2010,17:59-63. 6刘华伟,黄慧杰. 我国风力发电成本研究J. 科技展望,2015,03:70.(c)l999 American Institute of Aeronautics & Astronautics AIAA-99-0028 AN INVESTIGATION OF VARIABLE SPEED HORIZONTAL-AXIS WIND TURBINES USING DIRECT MODEL-REFERENCE ADAPTIVE CONTROL J. B. Freeman, M. J. BaIas Aerospace Engineering Dept. University of Colorado Boulder, Colorado Abstract Pitch-controlled variable-speed horizontal-axis wind turbines (HAWTs) are increasingly being investigated for use in electrical power production. The governing equations of HAWTs are expensive to calculate and test, change substantially over time, and are extremely non-linear. Therefore, adaptive methods are a suitable approach for control of HAWTs. Direct model-reference adaptive control is shown to perform well as a pitch- regulated control scheme. The adaptive controller shows performance comparable to previous work in steady speed operation (Region 3), and shows model-tracking with errors of less than 1% during varying speed operation (Region 2). Simulations of the transition from Region 2 to Region 3 indicate an average overshoot of six percent. The controller is tested using MATLAEYSIMULINK simulations based on a computer generated and experimentally verified non-linear plant model of a Grumman Windstream- HAWT. An appropriate reference model that operates in Region 2 without knowledge of windspeed and plant parameters has yet to be found. Introduction Variable speed horizontal-axis wind turbines (HAWTs) are increasingly being researched for use in utility-scale applications. The term “variable speed” came about in comparison to traditional constant speed wind turbines that use varying generator torque to hold the turbine at a constant rotational speed. With increased winds and hence increased aerodynamic torque, the power electronics of constant speed turbines increase the generator torque to match it, thereby resulting in zero net torque on the rotor Copyright 0 1999 by the American Institute of Aeronautics and Astronautics, Inc. and American Society of Mechanical Engineers All rights reserved. 66 and a zero change in rotor speed. One drawback to this approach occurs in the condition of high winds. The opposing aerodynamic and generator torques rise to such magnitudes that the stress on the rotor blades, shaft, and gearbox becomes unacceptable. This either impacts the life expectancy of the turbine or causes one to lose valuable energy by shutting down the turbine during such conditions. Variable speed turbines do not use generator torque speed control Variable speed turbines allow increased power production in low wind by allowing the turbine to operate at speeds that more optimally capture wind energy. They also are able to capture more wind power in high winds by their ability to operate in higher wind conditions with less damage to the HAWT. The wind turbines that are examined and simulated in this work are pitch-controlled variable speed HAWTs. The primary method of control of these turbines is changing the pitch of Downloaded by TONGJI UNIVERSITY on March 14, 2016 | | DOI: 10.2514/6.1999-28 (c)l999 American Institute of Aeronautics & Astronautics the rotor blades, thereby changing the aerodynamic torque received from the turbine blades. Variable speed turbines operate in three operating states or regions characterized by rotor speed. The first, Region 1, represents the startup of a turbine. It includes the rotational speeds starting from no rotation to the turbine operating at a speed at which it can begin to harness power. Control within this region of operation is not approached in this work. Region 3 is the state of operation where the turbine is operating at full speed producing full power. In this scenario, the turbine speed is controlled to a designated speed by pitch control Pitch control prevents the rotor from reaching dangerously high speeds that could cause failure or undue fatigue. Pitch control also improves the use of a turbine as part of a grid of many turbines operating together in a region. The steady speed and generator torques allow easier integration of power into the grid by generating constar& predictable power. A primary goal of any control scheme is to have the HAWT operating in Region 3 for as much of the time as possible. Region 2 describes the variable speed region between Regions 1 and 3 where the turbine can harness useful energy but is not operating at the full Region 3 speed. This variability makes Region 2 difficult to manage with control algorithms. This work examines the applicability of model- reference adaptive control in Regions 2 and 3 of pitch-controlled HAWTs. MATLAB/Simulink models of the Grumman Windstream- 3 turbine are used to test the performance of the adaptive control scheme and are compared with other methods including Disturbance Accommodating Control and PID control. It also examines the transition from Region 2 to Region 3, where the difference in control objectives between the regions dictates a substantial change in the operation of the controller. Dvnamic modeling of plant A rigid, non-linear plant model of the Grumman Windstream- HAWT was developed for use in controller design4. A Windstream- was mod&d for variable-pitch use in testing at the National Renewable Energy Laboratory (NREL) National Wind Technology Center (NWTC) and is hoped to be used for validation of the simulated results. The original HAWT drive train consisted of a high-speed shaft, gearbox, low-speed shaft and generator. It was replaced by a direct-drive generator, reducing the drive- train compliance to a single, stiff shaft. The drive-train compliance is therefore ignored in the plant model. The fundamental dynamics of the turbine are represented in the following plant model: (1) JT moment of inertia of the rotor 2 rotational speed of the turbine aerodynamic torque generated by interaction of wind and rotor blades Qs electrical torque imposed on the rotor by the generator The modeled generator torque, a, is set proportional to rotor speed. This would be implemented by the power electronics of the generator. The inertia of the generator is orders of magnitude less than that of the rotor and will therefore be ignored in this model. The aerodynamic torque, C&, is calculated by: i air density swept area of the rotor R radius of the rotor c, torque coefficient ?L tip-speed ratio, %R / W P blade-pitch angle W prevailing wind speed The first three values are modeled as constants at values of p = 1.225, A = 78.5m2, R = 5m. The modeled spatially uniform wind speed is taken from actual data measured at the NWTC. The data was measured at a rate of 1Hz and is implemented at the same rate in simulation. The torque coefficient (Cs) is a highly non- linear function of tip-speed ratio and blade-pitch angle. It is referenced in the plant model from a 67 Downloaded by TONGJI UNIVERSITY on March 14, 2016 | | DOI: 10.2514/6.1999-28 (c)l999 American Institute of Aeronautics & Astronautics look-up table that was created by the PROPPC aerodynamic simulation computer program and verified experimentally at the NWTC. The tip- speed ratio (A) is the ratio of the linear speed of the tip of the rotor blade to the prevailing wind speed. The most important parameter in Region 2 is the electrical power created by the generator. It is used as the primary measure of performance in that region. The generator power is calculated as: P=&o* (3) The pitch controller for the modeled HAWT is an electrical motor. It is a pitch-rate-controlled motor that accepts a desired pitch, compares it with the current value and delivers current proportional to the error. This current is limited to a maximum absolute value by electrical constraints. The motor controller also ignores very small inputs in order to eliminate high frequency oscillations that could reduce the life span of the motor. Direct Model Reference Adaptive Control Of Hawts Model reference adaptive control is presented in depth by Narendra md Armaswamy. The direct model-reference control method used in this work was developed by Balas . It hinges on the fact that one can develop a reference model of the plant output that represents a desirable, attainable output. The control system adapts the gains of the system so that the output of the plant will closely match that of the reference model. Thus, the criteria for using model reference adaptive control are that the controller can adapt to the plant and that there exists an appropriate reference model that represents “good” performance of the plant. This work focuses on the adaptation of the controller such that the plant follows the given reference model. The primary advantages in using adaptive control are that one does not need to know the exact parameters of the plant being controlled and that the controller can adapt to changes in the plant. This is especially beneficial when working with HAWTS. The parameters of turbines are often difficult to specifically obtain due to the complexities of the aerodynamic properties and are diflicuh to control due to the extreme non-linearities of the system. The aerodynamic properties are also subject to significant change during operation due to residue and, in some cases, ice and moisture build-up on the rotor blades. The most important state variable of a HAWT is the rotational speed, or, which is the controlled output variable of the plant. The reference model therefore produces a desired rotational speed Q,. The inputs to the adaptive controller are the error of the plant compared to the reference model, the state vector of the reference model, and the external input to the system. These values are multiplied by their respective adaptive gains and the sum of the products is set as the control variable, blade-pitch. The equation for the controller pitch determination is: p=G,+G,x, (4) e, output error y-ym Jkl state of the model The equations for adaptation of the gains are: Gy = -K,e,et G, = -K,e,xi (5) (6) Where KY, K, and Ku are constants that control the rate of adaptation. The output of the plant Q is oT. The output of the model elm) is OT, The lone state variable of the reference model is its rotational speed (or,3 which iS used as X, . After much experimentation, “good” adaptation rate constants were determined to be K,=lOO, K,=O.l, ad K,=O.l. A block diagram of the system is shown in Figure 1. Retion 2 - varying soeed ooeration Creating a reference model for Region 2 operation presents a di8icult problem. Unlike Region 3, which has a well defined, constant target speed, finding the best reference model for power harnessing in Region 2 is diflicult without a well-known windspeed and plant 68 Downloaded by TONGJI UNIVERSITY on March 14, 2016 | | DOI: 10.2514/6.1999-28 (c)l999 American Institute of Aeronautics & Astronautics model. Without knowledge of the windspeed, either by measuring it or estimating it from operation of the turbine, the potential speed of the turbine is unknown. Because an appropriate reference model for Region 2 that does not use windspeed and plant parameters remains elusive, this paper fomses on the ability of the controller to follow given reference models. Often, when little is known about the plant parameters or no suitable control law is available, researchers use a constant pitch in Region 2. This pitch is determined either heuristically or by some simple analysis of the HAWT. Some have even dubbed it as the “magic beta,” due to its sometimes mysterious origins. Constant pitch simulations will be used for power output comparisons with the adaptive controller. An open loop control strategy that sets the pitch to maximize aerodynamic torque was developed by Fingersh and Carlin. It uses a PROPPC computer-generated and experimentally verified torque coefficient (CJ surface. The C, surface contains torque coefficient values as a function of tip-speed ratio and pitch angle. In Fingersh and Carlins method, the maximum C, value for each tip-speed ratio is determined from the C, surface, and the corresponding pitch is recorded in a table. During operation, the measured windspeed and rotational speed are used to calculate the tip-speed ratio and the pitch is set from the table to correspond with the maximum torque coefficient. This produces the maximum instantaneous torque available from the wind and is used as a benchmark reference model for the adaptive controller. While the primary strength of adaptive control is its ability to operate without exact knowledge of the plant and inputs, Fingersh and Carlins strategy allows one to test the model-following performance of the controller for an optimal reference model. The optimal reference model is produced in simulation by implementing the control strategy on a simulated plant and using its output as the reference model output &,). The adaptive controller becomes unstable when attempting to track the optimal model, so a scaled version is tested. The output speed of the reference model is scaled by a factor of less than one that simulates a sub-optimal performance that extracts much of the power. The cormoIler is able to follow as much as ninety percent of the optimal reference model speed, producing eighty-one percent of the optimal power with a model output error of less than one percent. The inability of the controller to follow the optimal reference model can be understood by examining the C, curve. Figures 2 and 3 show graphs of the C, curve with the instantaneous simulated operating values of C, superimposed. Figure 2 shows that the sub-optimal reference model of the HAWT operates with C, values along the relatively linear, sloping region away from the ridge of the curve. The optimal plant model operates with C, values on the ridge of the curve where it is much more nonlinear as seen in Figure 3. When the controller attempts to track the optimal model, the gains are unable to adapt quickly enough in the non-linear area along the ridge of the surface, causing the controller to become unstable. Figure 4 shows a comparison of the power output of the adaptive controller following an eighty-five percent of optimal reference model with the power outputs of simulations using different values of constant pitch over the same windspeed profiles. The optimal reference model does not have the highest power output of the four simulations, but it does show good performance. The best pitch angle for this wind profile was seven degrees, but other wind profiles have different constant pitches that produce the most power. Figure 5 displays the average power output of the adaptive controller compared with the average power produced by setting the pitch constant at three, six, and nine degrees. The simulations are of five, ten-minute wind proliles ranging in average windspeed from 8.3 m/s to 11.2 m/s. The adaptive model performs better than the nine-degree constant pitch for all but one data point, but only bests the six-degree constant pitch for one data point. The low power output of the three degree constant pitch, which was chosen by the NWTC as their “magic beta”, is explained by the starting simulated rotational speed of three r&/s. At three rad/s and with a pitch of 3 degrees the windspeed must remain below 5mJs in order to produce positive torque. 69 Downloaded by TONGJI UNIVERSITY on March 14, 2016 | | DOI: 10.2514/6.1999-28 (c)l999 American Institute of Aeronautics & Astronautics Region 3 - constant-speed optimal operation Constant speed operation of pitch-controlled HAWTs is a well-studied topic with a history of good performance. The intention of this work is not to describe and test a methodology that breaks new ground in this area, but to show comparable performance to previous work. Some examples of such work are Disturbance Accommodating Control (DAC)4, gain- scheduled control, and classic PID control. The obvious adaptive control reference model for Region 3 is a constant value of ar,m As seen in Figure 6, model-reference adaptive control displays excellent performance for much of the wind profile. Drastic changes in windspeed create oscillations, however. The windspeed is not drawn to scale, but is included in the graph to relate trends. Table 1 shows the average errors for each of the controllers over several wind profiles. Figure 7 shows that the adaptive controller performs comparably to the DAC and PID controllers in both RMS error and maximum error. The simulations are of ten-minute wind profiles. The low average windspeed simulations have very high errors due to the fact that the winds were not consistently strong enough to maintain the simulated HAWT in Region 3. Transition between regions 2 and 3 An important advantage of model-reference adaptive control for HAWTs is that it does not need to change controllers when switching between distinct regions of operation. It therefore avoids questions of when to switch from one controller to another and instabilities arising from the switching. Another option is to use a controller that has one set of gains for both regions. This leads to degradation in performance in both regions and is therefore less desirable. The adaptive control scheme presented in this work changes the tracking model instead of the controller. The primary state variable of the model is the rotational speed. This value is upper bounded by the desired Region 3 speed. Thus, if there is sufficient wind to operate the turbine at or above the Region 3 speed it remains at that speed until the wind decreases enough to force the model to fall to a lower speed (Region 2). A simulation of the controller operating with a windspeed profile that dictates transition between Regions 2 and 3 is shown in Figure 8. It begins at a value of six radlsec, which is the midrange of Region 2. It then moves quickly to Region 3 where it oscillates for about ten seconds before falling into Region 2 for thirty seconds. It then returns to Region 3, drops into Region 2 after twenty-five seconds and finally returns to Region 3. This behavior of following the model with oscillations when switching into Region 3 is typical of operation in wind profiles which dictate transition between regions. Results of compiling the twenty-five simulations, which included region to region transition, are shown in Table 2. The plant oscillates when the reference model changes from one region to another with an average overshoot of six percent. It settles to an error of less than one percent in an average of 11 seconds. Model-reference adaptive control shows promise for use with HAWTs. Its primary applicability is to situations where the turbine is not well modeled. The performance in Region 3 is exceptional considering it requires no prior knowledge of the plant dynamics. In Region 2 adaptive control shows promise in sub-optimal model following capability, but has diBIculty following an optimal model. The problem of &ding an acceptable reference model that does not require knowledge of the plant and windspeed remains unresolved. The use of a single controller for both areas of operation eases the diEiculty of transitioning between the regions, which is of substantial benefit. Recommendations for future work The primary intent of future work should focus on applicable reference models for Region 2. The strength of the adaptive control lies in its ability to perform without exact knowledge of the turbine and windspeed. Developing an adapting reference model is therefore 70 Downloaded by TONGJI UNIVERSITY on March 14, 2016 | | DOI: 10.2514/6.1999-28 (c)l999 American Institute of Aeronautics & Astronautics recommended. A second direction for further research to take is to develop and test a wind estimator based on turbine dynamics. A HAWT whose dynamic parameters have been rigorously studied and that is typical of a class of turbines could be used to develop a Region 2 reference model based on the one described in this work. A windspeed estimator would provide the required windspeed data necessary to implement such a reference model. The reference model developed with the well-known turbine could then be used by turbines with similar characteristics, thus avoiding the need to individually tune controllers for each turbine. J. : Prentice Hall. Bibliographv 1 BaJas, M. J. 1995. Finite-dimensional direct adaptive control for discrete-time inlinite- dimensional linear systems. Journal of Mathematical Analysis and Applications, Vol. 196, No. 1. pp. 153 2 Fingersh, L. J., Carlin, P. W. 1998. Results from the NREL variable-speed test bed. Proceedings of the Wind Energy Symposium, Reno, NV. 3 Hand, M. M., BaJas, M. J. 1998. Systematic approach for PID controller design for pitch- regulated, variable-speed wind turbines. Proceedings of the Wind Energy Symposium, Reno, NV. 4 Kendall, L., Balas, M. J., Lee, Y. J., Fingersh, L. J. 1997. Application of proportional-integraJ and disturbance accommodating control to variable speed variable pitch horizontal axis wind turbines. Wind Engineering, Vol. 21, No. 1, pp. 21-38. 5 Leith, D. J. Leithead W. E. 1996. Appropriate realization of gain-scheduled controllers with application to wind turbine regulation. International Journal of Conkol, Vol. 65, No. 2. pp. 223-248. 6 Leith, D. J. Leithead W. E. 1997. Implementation of wind turbine controllers. International Journal of Control. Vol. 66, No. 3. pp. 349-380. 7 Narendra, K. S. Annaswamy, A. M. 1989. Stable adaptive sysfems. Englewood Cliffs, N. 71 Downloaded by TONGJI UNIVERSITY on
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