风力异步电动机_中英文翻译_毕业论文

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外文翻译

2MW风力双馈异步电动机的研究设计

指导老师：盛光忠

学生：安梓铭

（三峡大学 科技学院）

摘要

一个设计为一个2 MW风力发电机的商业,验证了两种连接方式为标准双馈异步机可延长低速下范围到80%滑动没有增加的额定功率电子变换器。这远远超出了正常的30%的下限。较低的速度连接被称作异步发电机模式和机器操作与短路定子绕组和所有的功率流在转子回路。有两个回路逆变器控制系统方案设计和调整为每一个模式。本文的目的是当前仿真结果,说明了该控制器的动态性能均为双馈异步发电机的连接方法为2 MW风力涡轮机。一个简单的分析了双转子电压为连接方法包括作为这个演示的优势的时候,需要考虑设计等先进控制策略。

关键词:双馈电机、异步发电机、风力发电机。

1、介绍

兴趣是持续风力涡轮机,尤其是那些拥有一个额定功率的许多兆瓦这个流行主要由既环保,也可用的化石燃料。立法鼓励减少碳足迹的所谓的地方,所以目前正在感兴趣的可再生能源。风力涡轮机仍然被看作是一种建立完善的技术,已形成从定速风力涡轮机,现在流行的调速技术基于双馈异步发电机(DFIGs)。风力是一DFIG变速与转子变频器控制使转子电压相位和大小调整以保持最佳扭矩和必要的定子功率因数文[1]~[3]。DFIG技术是目前发达,是常用的风力涡轮机。定子的DFIG是直接连接到网格与电力电子转子变换器之间,用以转子绕组的网格。

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这个变量速度范围是成正比的评级的转子等通过变频器调速范围±30%[4、5、6、7]转子转换器只需要的DFIG总量的30%的力量而使全面控制完整的发电机输出功率。这可能导致显著的成本节省了转子转换器[4]。滑动环连接,但必须保持转子绕组,性能安全可靠。电源发电机速度特性,如图1所示为2 MWwind汽轮机。对于一个商业发电机速度随风速,然而这种关系是为某一特定地点。作为风速,并因此机速度快、输出功率下降了的风力发电机减少直至关闭时提取风是比损失的发电机和液力变矩器。操作模式已经提出,风力机制造商宣称延伸速度范围以便在较低的速度力量提取的风是比损失在系统等系统能保持联系。这个建议标准的双(DF)连接在正常使用调速范围所谓DF异步发电机(“模式是用来延长低速运行。先前的工作已经显示了IG模式能够运作的DFIG滑到80%[8]。这一变化在运行时实现定子从电网DF模式,然后短巡回定子使国际组操作。所有的发电机组转子变频器在流经IG模式。免疫球蛋白曲线相同的曲线为±30% DF滑动。估计国际组电力提取的风在低速下所获得的曲线,推断DF模式。参考扭矩由控制器(DF和IG模式),就可以很容易地来源于这样的曲线。扭矩-速度数据可以存储在一个查表所以参考转矩和转速变化自动。

这个能力的现代DF风力涡轮机不同的无功功率吸收或产生[6、第九条、第十条]让风涡轮参与无功功率平衡的格子里。无功功率在电网的连接中描述的工作,由英国,连接条件小节CC.6.3.2[11]从国家电网。无功要求风电场的定义是由图2。

MVAr点——相当于功率因数为0.95领先于额定兆瓦

MVAr B点——相当于功率因数为0.95滞后于额定兆瓦

C - MVAr 5点的额定兆瓦

D点- MVAr 5%额定兆瓦

E - MVAr 12点的额定兆瓦

摘要本文旨在探讨控制器性能和IG模式为DF 2MW 690V,4-pole,DFIG使用机器参数由制造商。这是进一步研究建立在先前的稳态性能进行了两种操作的损耗,以及国际组模式[8]。在[8]探讨了稳态效率为双方关系。工作说明的稳态性能都有好处,这台机器运行一个连接方法相对于其他。摘要本文检视(即瞬态性能)的2千瓦风力涡轮。结果全部动态控制器(电流调节、解耦控制方程和矢量控制

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方式,在DF)的方式显示指定。配置程序做了详细的分析,形成了转子的电压在整个操作范围内DFIG模式,给出了这种能够主宰成分浮出水面。这是特别重要的先进控制方案设计时充分概论的工作范围内,能被确认。仿真模型,它已经被证实对

7.5kW实验室钻机[12],是应用于现实的2千瓦风力使结论是关于拟议中的使用IG模式在真实的风力涡轮。

2、连接方法

双馈异步电机通常连接如图3。GSI网格侧逆变器(保持)是一个固定的直流环节电压与给定的功率因数的网格(在我们的情况下,团结)。转子侧逆变器(劳损)的控制,从而使最大能量提取的动能的风而使定子功率因数控制范围内统一要求,尽管网格的功率因数往往是可取的。另一种连接方式为双馈电机如图4,这叫了异步发电机(指定)连接。定子是脱离电网和短路。转子回路图3。从不变。GSI一样的控制方式。DF)目的是为了控制劳损定子磁链在吸收最大功率的动能,风能。

3、控制器性能

闭环控制方式都和IG模式DF讨论的前期准备工作[12]但只有一个7.5亿千

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瓦实验室试验平台。2千瓦动力学系统会有所不同,本文讨论了。动态控制器的性能和IG模式为DF中显示的是这段2 MW风力涡轮机。

3.1DFIG模式(T和Q控制)

参考价值的扭矩模式控制器DF(见图1)和定子无功使网格代码要求达到

[11],图2。摘要研究了两种速度,使部分的控制性能表现出两上方和下方的标称功率的20%限制电网的规范要求。一个命名可以达到3亿千瓦,约1150转(小于标称功率的20%)

一个额定功率是达到125千瓦1550转(超过20%的额定功率)。参考和实际的扭矩、网球、定子无功功率,Qs,都显示,两者的速度在图5。

参考扭矩,越富有,因为这两者都是具体的名义转矩速度对于一个给定的速度计算出图1; 2672海里为1150转速和 7701海里的1550转速。200海里的速度在双方的动态响应,说明了一步,改变扭矩。参考定子无功功率,Qs *,螺杆转速变化之间的1150年所指定的范围栅格规程的要求;最初 5%的生成与更进了一步,在t = + 5%的3.5s产生电力。在1550转定子动力因素、pfs *,最初0.95并逐步改变在t = 3s团结pfs和最后一步,在t = 0.95滞后4s pfs)。矢量控制回路的调整为一个时间常数的0.9s 0.1秒,为特和Qs循环。矢量控制的设计是为了有一个较慢的带宽比当前的规定。

实际转子电流直接、irds、正交、irqs、部件对应figure6图5中显示。这个步骤的影响是明显的变化对Te * irqs(上标s指出变量是指在定子)。这个irqs *元件包含小瞬态响应1550 rpm在t =三分球和t = 4s是由于步改变Qs价值。这个步骤改变Qs *,如图5,导致快速变化的irds *,图6,如有初步的误差和实际Qs作为参考一会儿,管理作为回应。现行规定,确保带宽防止控制器对这样的流动而不断地获得适当的反应速度这个方程为基础的调谐用来控制器的设计出相似的比例和积分所得的值为现行规定直接和正交循环的Holdsworth魏厚[10]。

3.2 IG模式(T和流量控制)

参考价值的IG模式控制器是定子磁链和转矩。摘要研究了两种条件下2千瓦发电在IG模式中,启动和扭矩步反应,以400转(最低IG模式速度[12])和1420转(所产生的力量以这样的速度与转子上游的额定功率转换器,600亿千瓦)。参考和实际的扭矩、网球、定子磁链,λsr(上标' r”表明变量是指两个方面对转

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子)的速度如图7。

稳态Te标称值处理的速度、 320海里为400转速和 4081海里,源自公元1420年转图1。一个启动顺序必须建立在额定λsr机器,对于一个给定的速度,通过一段斜坡,图7,机器可以产生电力。

一旦该控制器参考λsr已建立了机械,特*增加通过控制的名义价值斜坡给定的速度,然后一阶跃响应50海里在400转速与200海里时转速适用。公元1420年,该控制器控制机器来跟踪Te *果然,参看图7。

矢量控制回路的确定值的参考转子电流如图8。最初的成分迅速上升到建立λsr,大约三倍公称稳态值对于一个给定的负荷点。当前在额定的限制。最初的解码器能够显著降低,如果一个较慢的反应λsr实现。

这个硬中断请求优先级别组成,是由扭矩环使渴望权力产生。最初有轻微的误差影响高解码器的交叉耦合正交循环系统的条款。一旦名义λsr于机器直接和正交环路的解耦。又一特步引起短暂飙升的硬中断请求优先级别*虽然被调谐到这个变化是慢于参考价值。

4、转子的电压元件

双方的性能和IG模式DF已经在上一节。两者都是基于内部控制电流环和外部控制回路为转矩和定子无功功率损耗的案例和转矩和定子磁链的IG。再加上解耦方程的PI控制器的影响,降低产量之间的交叉耦合循环。最后一部分工作的研究做出贡献的稳态组件的转子电压,全部在方程式(1和2),2千瓦机器来评估的重要性,在不同的速度方程式解耦。转子电压、工具、转子电流、国税局,居于

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万物的工具和组件由方程式(1和2)进行了DF转速范围内(1000年到1950年转矩确定)的正常从图表1),和定子动力因素、pfs、范围的0.9落后领先到0.9%。只有pfs被视为GSI可能保持团结酚醛风轮变频器连接到网格的独立的劳损。

图9所示的是变化的速度和vrdqs定子无功功率范围的调查。vrds组件的主导的稳态的ωsfσirqs 的压降和λsq后被忽略的是零组件选择参考帧。这可以比较图9和数字。在一个2千瓦的vrqs机床主导下的ωsf(Lm / Ls)λsd期限为低的总泄漏,降低电感、σirds交叉耦合效应的术语和λs取向的λsq构件框架设置为零。在vrqs变化在恒定的速度(并因此转矩)是由于从irds交叉耦合的定子无功功率调节,Qs,因此pfs这个工具vrqs统治级的组件和对称1500rpm;thesynchronous速度4-pole机。这是经公园等[13]。

在稳态变化直接,irds、正交、irqs、转子电流部件对速度和Qs如图10。irds元件的功率因数、调节定子无,通过控制Qs和太少

s组件调节。irds确定的价值的比例提供发电机无功功率的定子和转子回路。irds增加越来越积极的比例从转子回路Q同时减少了问从出口到Q的静定。越来越消极irds增加问从,减少了定子电路的转子的一面,直到Q是由转子出口。Qs随维持理想Te,因此irds组件无会持续pfs在更高的速度。大致上是恒定的irqs元件恒速恒转矩的力量,积极为产生的定位框架和直接和正交轴排成一线国税局的大小是为所有的额定内部条件图10。

其余的这部分说明了转子的电压,vrdqs、稳态部件从方程式(1和2)。这个Rrsirds术语及术语vrds Rrsirqs vrqs仅仅是irdqs,如图10,攀登通过后,所以不显示。

jσωsfirdqs的交叉耦合条件vrdqs如图11所示， jσωsfirdqs有助于vrds和σωsfirds从 vrqs。Σωsfirds由组成随既速度和定子无功功率为定子无功成正比,与转矩对于一个给定的定子动力因素。σωsfirds随着年龄的增长而增长速度的组件负载力矩增加如图1。σωsfirqs组件是主导学期在vrds组成eqn(1),在不同步性的速度。在极性的结果ωsf定义和大小的扭矩。irdqs

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大小是由频率升高而升高，ωsf与总漏电感。图12表明vrdqs由j(Lm/Ls)和ωsf和λsdq组成，(Lm/Ls)ωsfλsq有助于vrds，这个学期大致上是零因定位框架。 (Lm/Ls)ωsfλsd抑制 vrqs 的组成，(Lm/Ls)ωsfλsd的形状组成完全由ωsf.决定。

5、讨论

分析vrds和vrqs组成的可行性是由占统治地位的条款。λs定位框架的结果λsq和vrds前馈术语被忽略所以稳态vrds组件的结果是Rrsirds σωsfirqs。三种截然不同的区域,然后可以识别sub-synchronous速度，关于同步速度，和超同步速度。vrds的瞬态响应的对于一个步骤irds*主导下的pσirds. p(Lm/Ls)λsd作为一个微不足道的效果了λsd 术语是恒定的,假设一个僵硬的网格。irds*的脉冲一步稳态值影响的vrqs在vrds的稳态条款，vrqs稳定的状态是由主导下的λsd 期限，Vrqs的瞬态响应由irqs*来的是由pσirqs周期正如步骤irqs最初是高的。p(Lm/Ls)λsq有一个最大的作用时λsq约等于零，在vrqs的vrds周期和步骤周期所有的经验值变化的irqs *。

6、结论

摘要首先分析了控制器的响应和IG模式DF连接DFIG MW风力涡轮机。2这台机器参数为2千瓦机,为商用WRIM用于风力涡轮机,由制造商。2千瓦机参数用于这项工作并不仅仅是一种线性比例的前期准备工作在7.5万千瓦的特性与不相同的两个人之间的机器。

两个方面进行了调查分析,对2千瓦DFIG。已经存在的仿真模型用于评估可控性和稳态和瞬态行为DFIG 2千瓦的IG模式和DF)。

结果表明,IG模式是一种可控的运作模式,这将扩大低速运行电压降低转子速度降低(电压),所以IGBTs限制会被尊为将当前的和权限的机器和液力变矩器。电压的组成进行了转子损耗模式DFIG 2千瓦。这显示了重要的解耦方程中的表现DFIG随速度。

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外文原文

Design Study of Doubly-Fed Induction Generators

for a 2MW Wind Turbine

ABSTRACT

A design study for a 2 MW commercial wind turbine is presented to illustrate two connection methods for a standard doubly-fed induction machine which can extend the low speed range down to 80% slip without an increase in the rating of the power electronic converter. This far exceeds the normal 30% lower limit. The low speed connection is known as induction generator mode and the machine is operated with a short circuited stator winding with all power flow being through the rotor circuit. A two loop cascaded PI control scheme has been designed and tuned for each mode. The

purpose of this paper is to present simulation results which illustrate the dynamic performance of the controller for both doubly-fed induction generator connection methods for a 2 MW wind turbine. A simple analysis of the rotor voltage for the doubly-fed connection method is included as this demonstrates the dominant components that need to be considered when designing such advanced control strategies.

Keywords: Doubly-fed, Induction generator, Wind turbine

1. INTRODUCTION

There is continuing interest in wind turbines, especially those with a rated power of many megawatts.This

popularity is largely driven by both environmental concerns and also the availability of fossil fuels. Legislation to encourage the reduction of the so called carbon footprint is currently in place and so interest in renewables is

currently high. Wind turbines are still viewed as a well established technology that has developed from fixed speed wind turbines to the now popular variable speed technology based on doubly-fed induction generators (DFIGs). A DFIG wind turbine is variable speed with the rotor converter being controlled so that the rotor voltage phase and magnitude is adjusted to maintain the optimum torque and the necessary stator power factor [1, 2, 3]. DFIG technology is currently well developed and is commonly used in wind turbines. The stator of a DFIG is directly connected to the grid with a power electronic rotor converter utilised between the rotor winding and the grid. The variable speed range is proportional to the rating of the rotor converter and so by limiting the speed range to ±30%

[4, 5, 6, 7] the rotor converter need only be rated for 30% of the total DFIG power whilst enabling full control over the full generator output power. This can result in significant cost savings for the rotor converter [4]. The slip ring connection to the rotor winding however must be maintained for reliable performance.

The power – generator speed characteristic shown in figure 1 is fora commercial 2 MWwind turbine. The generator speed varies with wind speed however this relation is set for a specific location. As wind speed, and therefore machine speed, falls the power output of the generator reduces until the wind turbine is switched off when the power extracted from the wind is less than the losses of the generator and converter. An operating mode has been proposed by a wind turbine manufacturer that is claimed to extend the speed range so that at lower speed the power extracted from the wind is greater than the losses in the system and so the system can remain connected. This proposed that the standard doubly-fed (DF) connection is used over the normal DF speed range and the

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so-called induction generator (IG) mode is used to extend the low speed operation. Previous work has illustrated that IG mode enables the DFIG to operate down to 80% slip [8]. This change in operation is achieved by

disconnecting the stator from the grid in DF mode and then short circuiting the stator to enable IG operation. All of the generator power flows through the rotor converter in IG mode. The IG curve is identical to the DF curve for ±30% slip. The estimated IG power extracted from the wind at low speeds is obtained by extrapolating the curve for the DF mode.

The reference torque required by both controllers (DF and IG mode) can easily be derived from this curve. The torque – speed data can then be stored in a look-up table so the reference torque is automatically varied with speed. The capability of modern DF wind turbines to vary the reactive power absorbed or generated [6, 9, 10] allows a wind turbine to participate in the reactive power balance of the grid. The reactive power at the grid connection considered in this work is described, for the UK, by the Connection Conditions Section CC.6.3.2 [11] available from the National Grid. The reactive power requirement for a wind farm is defined by figure 2.

Point A - MVAr equivalent for 0.95 leading power factor at rated MW

Point B - MVAr equivalent for 0.95 lagging power factor at rated MW

Point C - MVAr -5 % of rated MW

Point D - MVAr 5 % of rated MW

Point E - MVAr -12 % of rated MW

The objective of this paper is to investigate the controller performance of DF and IG mode for a 2MW, 690V, 4-pole DFIG using machine parameters provided by the manufacturer. This is further research building on a

previous paper which demonstrated the steady-state performance of the two modes of operation, DF and IG mode

[8]. In [8] the authors discussed the steady-state efficiency for both connections. The steady-state performance work illustrated that there were benefits to operating the machine in one connection method as opposed to the other.

This paper examines the controllability (i.e. transient performance) of the 2 MW wind turbine. Results of the full dynamic controller (current regulation, decoupling equations and vector control) in both DF mode and IG mode are shown. A detailed analysis of thecomponents that form the rotor voltage over the full operating range in DFIG mode is presented as this enables the dominant control components to be identified. This is particularly important when designing advanced control schemes as an overview over the full operating range can be identified.

Simulation models, which have been validated against a 7.5kW laboratory rig [12], are applied to a realistic 2 MW wind turbine to enable conclusions to be made regarding the proposed use of IG mode in a real wind turbine

2. CONNECTION METHODS

Doubly-fed induction machines are commonly connected as shown in figure 3. The grid side inverter (GSI) is controlled to maintain a fixed dc link voltage with a given power factor at the grid (in our case unity). The rotor side inverter (RSI) is controlled so the maximum energy is extracted from the kinetic energy of the wind whilst enabling the stator power factor to be controlled within the limits of the grid requirements though unity power factor is often desirable.

An alternative connection method for a doubly-fed machine is shown in figure 4, here called the induction generator (IG) connection. The stator is disconnected from the grid and is short-circuited. The rotor circuit is unchanged from figure 3. The GSI is controlled as in DF mode. The objective of the RSI is to control the stator flux linkage while extracting the maximum power from the kinetic wind energy.

3. CONTROLLER PERFORMANCE

A closed loop controller for both DF mode and IG mode has been discussed in prior work [12] but only for a 7.5

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kW laboratory test rig. The dynamics of a 2 MW system are somewhat different and are investigated in this paper. The performance of the dynamic controller for both DF and IG mode are shown in this section for a 2 MW wind turbine.

3.1. DFIG Mode (T and Q Control)

The reference values for the controller in DF mode are torque (see figure 1) and stator reactive power to enable the grid code requirement [11] to be achieved, figure 2. Two speeds are investigated in this section to enable the

performance of the controller to be shown both above and below the 20% of rated power limit from the grid code requirements. A nominal generated power of 320 kW is achieved at 1150 rpm (less than 20% of rated power) and a nominal power of 1.25 MW is achieved at 1550 rpm (greater than 20% of the rated power). The reference and actual torque, Te, and stator reactive power, Qs, are shown for both speeds

in figure 5.

The value of reference torque, Te*, for both speeds is the specific nominal torque for a given speed calculated from figure 1; 2672 Nm for 1150 rpm and 7701 Nm for 1550 rpm. A step of 200 Nm is applied at both speeds to illustrate the dynamic response to a step change in torque. The value of reference stator reactive power, Qs*, at 1150 rpm is varied between the limits specified by the grid code requirements; initially 5% of the generated power with a step at t=3.5s to +5% of the generated power. At 1550 rpm the stator power factor, pfs*, is initially 0.95 leading with a step change at t=3s to unity pfs and a final step at t=4s to a 0.95 lagging pfs. The vector control loops are tuned for a time constant of 0.1s and 0.9s for the Te and the Qs loops respectively. The vector control is designed to have a slower bandwidth than the current regulation.

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The actual rotor current direct, irds, and quadrature, irqs, components corresponding to figure 5 are shown in figure6. The effect of the step change in Te* is apparent on the irqs (the superscript s indicates that the variable is referred to the stator) as expected. The irqs* component at 1550 rpm contains small transient responses at t=3s and t=4s that are due to the step changes in the Qs value. The step change in Qs*, shown in figure 5, causes a fast change in irds*, figure 6, as there is initially an error between the reference and actual Qs as the control takes a short while to respond. The current regulation is tuned to ensure that the bandwidth prevents the controller responding to such transients while still achieving a suitable speed of response.The equation based tuning used to design the controller gives similar values of proportional and integral gains for the current regulation direct and quadrature loops to those used by Holdsworth et al [10].

3.2. IG Mode (T and Flux Control)

The reference values for the controller in IG mode are stator flux linkage and torque. Two conditions are

investigated for the 2 MW generator in IG mode, start-up and torque step responses, at 400 rpm (minimum IG mode speed [12]) and 1420 rpm (generated power at this speed corresponds to the upper power rating of rotor converter, 600 kW). The reference and actual torque, Te, and stator flux linkage, λsr (the superscript r indicates that the variable is referred to the rotor), for both speeds are shown in figure 7.

The steady-state Te is the nominal value for the speed of operation, 320 Nm for 400 rpm and 4081 Nm for 1420 rpm derived from figure 1. A start-up sequence is required to establish the rated λsr in the machine, for a given speed, by means of a ramp, figure 7, before the machine can generate power.

Once the controller reference λsr has been established in the machine, the Te* is increased by means of a controlled ramp to the nominal value for a given speed and then a step response of 50 Nm step at 400 rpm and 200 Nm at 1420 rpm is applied. The controller regulates the machine to track Te* as expected, see figure 7.

The vector control loops determine the reference rotor current values that are shown in figure 8. The ird component initially increases rapidly to establish the λsr and is approximately 3 times the nominal steady-state value for a given load point. The current is within the rated limit at all times. The initial ird can be significantly reduced if a slower response of λsr is implemented.

The irq component is regulated by the torque loop to enable the desired power to be generated. Initially there is a slight error due to the high ird which affects the quadrature loop by the cross coupling terms. Once nominal λsr is established in the machine the direct and quadrature loops are decoupled. Again a Te step causes a transient spike in irq* though the control is tuned to be slower than this change in reference value.

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4. CONTRIBUTION OF ROTOR VOLTAGE COMPONENTS

The performance of both DF and IG mode has been illustrated in the previous section. Both controllers are based on an inner current loop and an outer control loop for torque and stator reactive power in the DF case and torque and stator flux linkage in the IG case. Decoupling equations were then added to the PI controller outputs to reduce the effect of cross coupling between the loops. The final part of this work studies the contribution of the steady state components of rotor voltage, given in full in eqns (1 and 2), for a 2 MW machine to assess the importance of decoupling equations at various speeds. The rotor voltage, vrs, rotor current,irs, and the non-differential components of vrs given by eqns (1 and 2) are investigated for the full DF speed range (1000 to 1950 rpm) with the nominal torque determined from figure 1, and a stator power factor, pfs, range of 0.9 lagging to 0.9 leading. Only the pfs is considered as the GSI is assumed to maintain unity pf at the rotor converter connection to the grid independent of the RSI.

Figure 9 shows the variation of vrdqs for the speed and stator reactive power range investigated. The vrds component is dominated in the steady-state by the ωsfσirqs term as the voltage drop across Rrs is negligible and the λsq

component is zero due to the choice of reference frame. This can be confirmed by comparing figure 9 with figures

11. The vrqs in a 2 MW machine is dominated by the ωsf(Lm/Ls)λsd term as the low total leakage inductance, σ, reduces the effect of the irds cross coupling term and the λs orientation frame sets the λsq component to zero. The variation in vrqs at constant speed (and therefore torque) is due to the cross coupling from the irds which is regulating the stator reactive power, Qs, and therefore pfs.The vrs magnitude is dominated by the vrqs component and is symmetrical 1500rpm; thesynchronous speed for a 4-pole machine. This is confirmed by Park et al [13]. The steady-state variation in the direct, irds, and quadrature, irqs, rotor current components with respect to speed and Qs is shown in figure 10. The irds component regulates the stator power factor, pfs, by controlling Qs and the ird s component regulates Te. The value of irds determines the proportion of the generator reactive power supplied by the stator and rotor circuits. An increasingly positive irds increases the proportion of Q from the rotor circuit while decreasing the Q from the stator until Q is exported by the stator. An increasingly negative irds increases the Q from the stator circuit, reducing the Q from the rotor side until Q is exported by the rotor. Qs increases with Te to maintain the desired pfs and so the irds component will be higher for constant pfs at higher speeds. The irqs

component is approximately constant at constant speed due to the constant torque and is positive for generated power due to the orientation frame and the direct and quadrature axis alignment.The irs magnitude is within the rated value for all conditions considered in figure 10.

The remainder of this section illustrates the rotor voltage, vrdqs, steady-state components from eqns (1 and 2). The Rrsirds term in vrds and the Rrsirqs term in vrqs are simply irdqs, figure 10,scaled by Rrs and so are not shown.

The jσωsfirdqs cross coupling terms of vrdqs are shown in figure 11. The jσωsfirqs term contributes to vrds and σωsfirds forms part of vrqs. The σωsfirds component varies with both speed and stator reactive power as stator reactive power is proportional to torque for a given stator power factor. The σωsfirds component increases with speed as the load torque increases,figure 1. The σωsfirqs component is the dominant term in the vrds component, eqn (1), at non-synchronous speeds; the polarity is a result of ωsf and the magnitude is defined by the torque. The magnitude is irdqs scaled by slip frequency, ωsf, and the total leakage inductance, σ.Figure 12 shows the j(Lm/Ls)ωsfλsdq

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component of vrdqs. The (Lm/Ls)ωsfλsq term contributes to vrds; the term is approximately zero due to the orientation frame. The (Lm/Ls)ωsfλsd term dominates the vrqs component. The shape of the (Lm/Ls)ωsfλsd component is clearly influenced by ωsf.

5. DISCUSSION

This analysis enables the vrds and vrqs components to be characterised by the dominant terms. The λs orientation frame results in the λsq feed forward term in vrds being negligible and so the steady state vrds component is a result of Rrsirds σωsfirqs. Three distinct regions can then be identified, sub-synchronous speed (low irqs due to low load so vrds is approximately Rrsirds), about synchronous speed (ωsf is around 0 so vrds is approximately Rrsirds) and supersynchronous speed (irds and irqs are comparable due to higher load torque and high stator power factor so vrds is approximately Rrsirds σωsfirqs). The transient response of vrds for a step in irds* is dominated by the pσirds. The p(Lm/Ls)λsd term has a negligible effect as the λsd term is constant assuming a stiff grid. An irds* step affects both the steady state value of vrqs and the steady state terms in vrds.

The steady state vrqs component is dominated by the λsd term, confirmed by Hopfensperger et al [9] (with the exception of synchronous speed when the steady state vrqs is dependent on the Rrsirqs term). The transient response of vrqs to an irqs* step is dominated by the pσirqs term as the differential of the step change in irqs is initially high.The p(Lm/Ls)λsq term has a negligible effect as λsq is approximately zero. The vrds term and the steady-state terms in vrqs all experience a change in value due to the irqs* step.

6. CONCLUSIONS

This paper has investigated the controller response for the DF and IG mode connections for a 2 MW DFIG wind turbine. The machine parameters for the 2 MW machine were provided, for a commercially available WRIM used in wind turbines, by the manufacturer. The 2 MW machine parameters used in this work are not simply a linear scaling of prior work on a 7.5 kW machine and so the characteristics are not identical between the two machines. Two areas of analysis have been investigated with respect to the 2 MW DFIG. Existing simulation models have been used to evaluate the controllability and steady-state and transient behaviour of a 2 MW DFIG in DF and IG mode. The outcome shows that IG mode is a controllable mode of operation which will extend the low speed operation as rotor voltage decreases (as speed reduces) and so the voltage limit of the IGBTs will be respected as will the current and power limits of the machine and converter. The composition of the rotor voltage was

investigated in DF mode for the 2 MW DFIG. This showed how the importance of the decoupling equations on the performance of the DFIG varied with speed.

ACKNOWLEDGEMENTS

The authors are grateful to FKI Industrial Drives and the EPSRC for their support.

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