外文翻译---大型风电场的瞬时稳定和模拟

Modelling and transient stability of large wind farms

1.Introduction

Denmark has currently about 2300 MW wind power capacity in on-land and few offshore settings, which corresponds to more than 20% of power consumption(in average). Further, construction of two large-scale offshore wind farms of 150 MW power capacity each has been announced. The first large offshore wind farm in Denmark will be constructed at Homs Rev by the year 2002 in the area of the system operator ELTRA .This will be followed by the first in the area of the Eastern Danish system operator ,ELKRAFT System ,large offshore wind farm at Rodsand by the year 2003.

The installed capacity in on-land settings and in combined heat-power units(UHP)will increase as well, whilst the power production and control ability of the conventional power plants with respect to voltage and frequency are reduced . In the years to come ,the power production pattern in the Danish power system will change from the power supply from conventional power plants―as it is known today―to a power supply mix, where about 30-40%of power consumption(in average) is covered by wind power. In other words, the power technology will undergo changes from a well-known technology built-up about conventional power plants to a p artly unknown technology―wind power.

In the year to come it will be focusing on maintaining power system stability and voltage stability, for example at a short circuit fault, ensuring power supply safety and other important tasks as amount of wind power is drastically increasing. This situation makes it necessary to find solutions with respect to maintaining dynamic stability of the power system with large amount of wind power and its reliable operation. These solutions are based on a number of requirements that are formulated with respect to operation of the large offshore wind farms and the external power system in case of failure events in the external system.

The paper contains separate subjects dealing with design of windmills for large offshore applications and their control that shall be taken into account with respect to improving the short-term voltage stability.

2.system stability requirements

In terms of short-term voltage stability, the major goal is the voltage re-establishing

after failure events in the power system with large amount of wind power. The transmission system operator is responsible for maintaining power system stability and reliable power supply.

As the situation is today, the majority of the Danish windmills on-land are stall wind turbines equipped with conventional induction generators and ac-connected to the power system. In case of a short circuit fault in the power system, those windmills are easily overspeeded and, then, automatically disconnected from the power system and stopped. Such automatic disconnections will be very fast and ordered by the windmill protection system relay settings. When the on-land windmills are automatically disconnected, there is no dynamic reactive compensation demands related to them, despite their large power capacity. When the voltage is re-established, the on-land windmills will be automatically re-connected to the power system in 10-15 min afterwards and continue their operation, The on-land windmill relay settings are decided by the windmill manufacturers or the windmill owners and these, as usual, cannot be changed by the transmission system operator.

In case of the large offshore wind farms, the power system operator has formulated the Specifications for Connecting Wind Farm to Transmission Network. In accordance with the Specifications, the voltage stability at failure events in the external power system shall be maintained without any sub-sequential disconnection of the large offshore wind farms. Establishing dynamic reactive compensation of the large offshore wind farms can be, therefore, necessary. The amount of dynamic reactive compensation depends, generally, on the windmill technology and in the wind farms and is influenced by the windmill electrical and mechanical parameters.

In other countries, similar specifications may be found as the result of large incorporation of wind power into the local power system.

3.Wind farm model

The windmill technology in offshore settings has to be robust, developed and known practical applications. The wind turbine concept with conventional induction generators has been in operation in on-land settings in Denmark during many years, which is why it may be considered that this technology will be used offshore as well. The wind turbines are equipped with blade angle control system-pitch or active stall that make it possible to

adjust the set-points of the wind turbines by the blade by the blade angle adjustments.

The complete representation of the wind farm is chosen because the commonly asked question concerning large wind farms is whether there can be electromechanical interaction between a large number of the closely placed windmills excited by disturbances in the power system when the windmills are working at different set-points, equipped with relatively soft shafts and even having different mechanical data, and equipped with control systems, for instance pitch.

The model of the offshore wind farm is implemented in the dynamic simulation tool PSS/E and consists of 80 wind turbines of 2MW power capacity each, see Fig.1.

Each wind turbine is simulated by a physical windmill model consisting of :

1.the induction generator model with representation of the stator transients,

2.the windmill shaft system model,

3.the aerodynamic model of the wind turbine,

4.the pitch control system given by the control logic and the blade servo.

For computation of wind turbine aerodynamics there are used airfoil data for a 2 MW pitch windmill equipped with an induction generator.

Each wind turbine is via its 0.7 KV/30KV connected to the wind farm internal network. The internal network is organised in eight rows with 10 wind turbines in each row. Within the rows, the wind turbines are connected through the 30 KV sea cables. The distance between two wind turbines in the same row is 500 m and the distance between two rows is 850 m.

The rows are through the 30 KV sea cables connected to the offshore platform with 30 KV/132 KV transformer and, then, through the 132 KV sea/underground cable to the connection point in the transmission system on-land. There is chosen an ac-connection of the offshore wind farm to the transmission network.

An irregular wind distribution over the wind farm area there is assumed since the wind turbines are shadowing each other for incoming wind. The efficiency of the wind farm is 93%at the given wind distribution and the power production pattern is shown in Fig.1.

Furthermore, the windmill induction generators have a little different short circuit capacities viewed from their terminals into the internal network and this is why the wind turbine initial set-points are different.

The short circuit capacity from the wind farm connection point into the transmission network is 1800 MV A. In all the simulating examples, the failure event is a short circuit fault in the transmission system of 150 ms of duration. When the fault is cleared, the faulted line is tripped and the short circuit capacity is reduced to 1000MV A. Only the line tripping and, then, reducing of the short circuit capacity to 1000MV A does not lead to voltage instability. This ensures that possible voltage instability is only the result of the short circuit fault with the following windmill overspeeding.

4. Dynamic reactive compensation

In this work, the dynamic reactive compensation of the large offshore wind farm is a SVC of the capacity that will be necessary for maintaining the short-term voltage stability. The model of the SVC is as in Ref.

5．When operating as stall windmills

Blade angle control is primarily used for optimization of the wind turbine mechanical power with respect to incoming wind and hence, this control ability is not necessarily available at failure events in external power system with respect maintaining the short-term voltage stability. This implies that the pitch or active stall wind turbines may operate as conventional (passive)stall wind turbines, by the same way as windmills on-land, with the exception that they may not be disconnected.

As the basis case with respect to the offshore wind turbine data, the rotor winding resistance u p R R .020.00=, the generator inertia s H G 5.0=,the mill inertia s H M 5.2=,

and the shaft stiffness rad

/..

,see Appendix A.

K.

3.0

el

u

p

If no dynamic reactive compensation is applied, a short circuit fault and a pose-fault line tripping will result in voltage instability, see Fig.2. The windmills will be, then , tripped by the protective relays and power reserves of approx. 150 MW shall be found immediately.

For voltage re-establishing after the short circuit fault, it will be necessary to use 100 MV Ar of dynamic reactive compensation. The simulated curves for the voltages and speeds are given in Fig.3.

It is noticed that the wind turbine dynamic properties such as the voltage, the generator speed etc, show a fluctuating behaviour in the windmill drive-train system.

Despite the wind turbines have different initial set-points, the windmills show a coherent response at the failure event in the external network so that the fluctuations are in-phase and at the same frequency. The fluctuation frequency is the torsional mode of the windmill shafts.

When the voltage is re-established, fluctuations in any electrical or mechanical properties are no longer seen. There is no self-excitation of the wind farm with a large number of wind turbines equipped with induction generators because the induction generators are passive systems in that no synchronizing torque and fast control have been applied.

6. Dynamic stability improvements within conventional technology

The movement equation of a windmill in terms of the lumped-mass system is )(2)(G M E M L H H T T dt d +-=ω, (1a)

Where M T and E T are the mechanical torque of the rotating mill and the electric torque, respectively, and L ω is the lumped-mass system speed

,G M G G M M L H H H H ++=

ωωω (1b)

Where M ω and G ω are the mill mechanical speed and the electric speed of the generator, respectively, and M M M w P T ω)(=at the given wind, w.

The dynamic stability limit of the windmill is found from the movement equations (1a) and (1b) as the speed L ωabove the kip-speed where E M T T =. This solution is the critical speed of the windmill, C ω, so that exceeding the critical speed, C L ωω>, leads to protective disconnection of windmills caused by overspeeding (prevention of voltage instability). Theoretical explanation for this definition can be found in Ref. and its graphical illustration is shown in Fig.4. From the definition of the dynamic stability limit, a number of stability improvement methods can be introduced in terms of conventional windmill technology that are given in the following.

6.1. Generator parameters

The shape of the electric torque versus speed curve, )(G E T ω, is influenced by the windmill induction generator parameters in accordance with

)()()

()()(222G T G T G T G G S G E X R R V T ωωωωωω+=

(2)Where S V is the windmill generator terminal voltage as a function of the generator speed, and the machine impedance )()(G T G T jX R ωω+ with

is given by the induction generator electrical parameters such as the stator resistance, S R , the stator reactance, S X , the magnetizing reactance, M X , the rotor resistance, R R ,and the rotor reactance,R X , as given in Ref.

The short-term voltage stability will be always improved when the critical speed of the windmill is expanded. This can be reached when:

1. the values of M S S X X R ,,and R X are reduced,

2. the value of the rotor resistance, R R ,is increased.

Graphically this is illustrated in case of increasing the rotor resistance value, R R ,is increasing the rotor resistance value, R R ,see Fig.4.

Increasing the rotor resistance by the factor of 2, as in the example, leads to significant expanding of the critical windmill speed,C ω, and the dynamic reactive compensation demands are reduced significantly. When the rotor resistance is ..040.020u p R R =, there will only be necessary to use 25MV Ar dynamic reactive compensation The voltage in the wind farm connection point is shown in Fig.5.

The 25MV Ar dynamic reactive compensation shall be compared with the reactive compensation demands in case of the rotor resistance value of 0R R that are in Section 5 found to be 100MV Ar. The dynamic reactive compensation demands are reduced significantly. On the other hand, this solution leads to increasing the power losses in the rotor circuit when the power system is in normal operation as well.

6.2 Enforcing mechanical construction

It is a common opinion that when the inertia of the rotating system is higher, the more

stable operation is expected in the power system in post-fault situations.

In terms of the dynamic stability limit definition, the inertia value does not influence on the windmill critical speed. Two wind turbines with identical generator data and different inertia values 1M H and 2M H , where 21M M H H >, have the same critical speed values 21C C ωω=.

Due to different inertia values, the wind turbines will, however, accelerate differently at the failure event and hence, have the different critical failure times 21C C t t >. Because of this, the heavy wind turbines show more stable behaviour compared with tinny wind turbines, as long as the failure time is not too long.

In practical situations, the failure time is short enough and the heavy wind turbines will be preferred with respect to maintaining the voltage stability.

Windmills are equipped with the shaft systems where the effective shaft stiffness viewed from the generator terminals is relatively low .In normal operation, there will be accumulated an amount of potential energy in the shafts and the lower the shaft stiffness is, the more the potential energy accumulated is .At a short circuit fault, the shafts are relaxing and the potential energy is disengaged into the generator rotor kinetic energy. This results

in the more intensive acceleration of the generator rotor. The contribution to the generator

rotor speed caused by the shaft relaxation is )/(2G M

G KH T ∝?ω.Increasing the shaft stiffness, K, leads, therefore, to the reduction of the windmill overspeeding at failure events, see Fig.6, and hence, to the improvements of short-term voltage stability, in accordance with the dynamic stability limit considerations.

The simulation results dealing with dynamic reactive compensation demands at varying parameters of the windmill mechanical construction,M H and K ,are collected in Table 1.

Enforcement of the windmill mechanical construction has a significant positive effect on improvement of the short-term voltage stability.

Literature origin: International Journal of Electrical Power & Energy Systems

大型风电场的瞬时稳定和模拟

1．介绍

丹麦当前在陆地和极少海外的放置中有大约2300 MW风能，这已经超过了平均能量消费水平的20% 。此外，二个150 MW的大规模海面风电厂的工程已经被宣布。在丹麦的第一个大的海面风电厂 2002 年以前将会在叙利亚被建造，它是系统操作员ELTRA 的区域。这将会在东方丹麦的系统区域中被第一个跟随操作员 ,ELKRAFT 系统在2003 年以前就向海面的风电厂转变。

在陆地放置中的和在结合的热量单元( UHP )中的安装的能力也将增加，在关于电压和频率的能量的生产和传统发电厂的控制能力被减少的时候。在未来的数年内，丹麦的电力制度的电力生产式样将会从来自传统电力补给改变，当现在对大约30-40% 耗电量 (平均的) 被风能覆盖的一个动力补给混合的之时。换句话说，动力技术将会接受被建造的来自一种众所周知的技术的变化，增加有关对部分未知的技术―风动力的传统发电厂。

在这一年来它将着重于保持电力系统稳定和电压稳定, 举例来说在一个短路中, 当风动力的数量大幅增加的时候，确定电力供应安全和其他的重要工作就是必需解决的，就需要用大量的风能和它的可靠操作维持电力系统的动态稳定。

2. 系统稳定需求

根据短期的电压稳定，主要的目标是在发生故障之后以大量的风能恢复电压。传输系统操作员负责维持电力系统稳定和可靠的电力供应。

今天，丹麦陆地上的多数风车是风力机装备着异步发电机并且直接并网。假使一个电力系统的过失短路, 那些风车就容易地被超速, 然后, 自动地从电力系统中分离而且停止。如此自动的切断将会非常快速而且必须被风车保护制度接替者设定。当那在陆地上的风车自动地被分离,没有动态的起反作用的补偿要求涉及到它们。当电压是恢复后, 在陆地上风车将会再自动地然后被连接到电网在 10-15 分钟中的力量制度而且继续它们的运转。

陆地上的风车继电器设定被风车制造业者决定或者风车拥有者和这些, 像往常一样，不能够被传输系统操作员改变。

假使大的海面风场，电力系统操作员已经制定把风场连结到传输网络的规格。符合规格，电压稳定性在外部系统故障时将会被维修在没断开大型海上风场。因此，建立海上风场动力起反作用的补偿是必需的。通常,大的动态反动的补偿靠风车技术上

和在风场中而且被风电和机械参数影响。

在其他国家,可以找到类似的规定,由于大型风力发电将成为当地电力系统. 3.风场模型

在海上设定的风车技术必须是强健的,发展和知名的实际应用。带异步发电机的风轮机观念已经运转在陆地风场的设定在丹麦这些年,是它可能为什么被视为将会被用在海上的技术。风力涡轮机叶片角度控制设有定位或活动档,可以调整结构项的风力涡轮机叶片的调整来完成.

海面风农场的模型在动态的模拟工具 PSS/E 中被实现，而且有 2MW 发电容量的80个用来发电的风车, 见图1。

风力涡轮机是由每一个物理模拟模型风车包括:

（1）适应模式与发电机定子的旅客代表、

（2）风车槽系统的模式

（3）风力涡轮的气动模型,

（4）由于球的控制系统,完成伺服控制逻辑.

风农场的完全表示法被选择，因为共同地被问的问题关于大风农场是否在动力系统可以有干扰激发的很大数量的严密被安置的风车之间的机电互作用，当风车运转在不同的设置点时。装备相对地软的轴和平衡有另外机械数据和装备以控制系统，例如沥青。

为风涡轮空气动力学的计算有老的机翼数据为一台2兆瓦风车装备异步电动机。每个风涡轮是通过它的0.7 KV/30KV连接到风场内部网络。内部网络在八列在每列被组织与10个机。在列之内，风轮机通过30千伏海底电缆连接。二个风涡轮之间的距离在同一列是500 m，并且二列之间的距离是850 m。

该列是通过30千伏海底电缆连接到近海平台用30 KV/132千伏变压器，然后，通过132千伏海地下电缆对连接点在传动陆地系统。海上风场选择了交流连接到传输网络。

一种不规则的风力分布在风场,由于假设是跟踪对方的风力涡轮风来袭. 风场风轮机效率的93%,分布在特定的风力发电方式显示图1。

此外,风车发电机入门有点短路能力从不同的终端进入内部网络,这就是最初的风力涡轮点不同.

短路容量从风场连接点到传输网络里是1800 MVA。在所有模仿的例子，失败事件是短路缺点在期间的有持续150ms的传动系统。当故障清除，故障线路强度大，并

且短路容量减少到1000MVA。仅线路流畅和减少短路容量到1000MVA, 不会导致电压不稳定。这保证可能的电压不稳定仅仅是因风车超速短路而引起的结果。

4. 动态的电抗补偿

这方面的工作,有力反应补偿近海风力大农场是svc的能力,有必要保持短期稳定电压.

SVC模型在Ref中是交流的。

5.风车停转的操作

浆叶角控制为风涡轮机械动力的优化主要使用关于接踵而来的风并且，这控制能力不是必要可利用的在外部电力系统故障中与维护短期电压稳定有关．这意味倾斜或

有效的延迟作为风力机被常规的停运。同样的方式对风车在陆地也一样， 除非他们可能是连接的。

作为案例对境外风力涡轮数据，转子绕组阻抗u p R R .020.00=，发电机惯性s H G 5.0=，米尔惯量s H M 5.2=，和轴的坚硬rad el u p K ./..3.0=。如果没有应用动态电抗性，短路故障和短路线路将导致电压不稳定，见图2。风车将会由保护继电器和后备保护进行加强。150MW 将要立刻上马。

为恢复短路故障以后的电压， 使用100 MVAr 动态电抗补偿将是必要的。图3给出了模拟仿真中电压和速度曲线。

发现风力涡轮动力特性,例如电压、发电机速度等,呈现波动行为在动力传动系统.

虽然风力涡轮机已初步确定不同点,显示了风车一致反应事件未对外的交通运输网络,使处于波动阶段,在同一频率. 波动的频率是极限模式风车槽.

当电压恢复后,任何电气或机械特性波动已不再出现. 没有自励的风场有大量配备异步发电机的风力涡轮发电机因为异步发电机是被动的,并没有同步扭矩迅速控制了应用.

6. 改进传统技术动态稳定性

风车运动的公式计算的质量体系是

)

(2)(G M E M L H H T T dt d +-=ω (1a)

M T 和 E T 分别是机械转矩和电磁转矩，L ω是角速度。

,G

M G G M M L H H H H ++=ωωω (1b) M ω和G ω分别是发电机的机械角速度和电磁角速度，M M M w P T ω)(=是特定的风。

动态稳定范围内发现的动作方程式(1a)和(1b)作为角速度L ω当E M T T =时。解决方案是风车的临界速率C ω，所以过度的临界速率C L ωω>，因为风车超速运行（防止电压不稳定性），导致保护断开。在Ref 中可以发现这个定义的理论解释，它的绘画插图如图4。从动态稳定性极限的定义， 在以下被给的一定数量的稳定改善方法可以被介绍根据常规风车技术。

6.1 发电机参数

电磁转矩对速度曲线的形状，)(G E T ω，由风车异步发电机参数影响依照

)

()()()

()(222G T G T G T G G S G E X R R V T ωωωωωω+= (2) 风车发电机接头电压S V 作为发电机速度的公式，发电机阻抗为)()(G T G T jX R ωω+

为异步电动机电的参数例如定子电阻S R ，定子电抗S X ，磁阻抗M X ，转子电阻R R ，转子电抗R X ，在Ref 中给出。

短期电压稳定，当风车的临界车速被扩展，总将改进。它可以被影响当以下情况：

（1）M S S X X R ,,and R X 的值下降

（2）转子电阻R R 的值上升

转子电阻值的上升在图中表示，R R ，转子电阻值慢慢上升，见图4。

增加电动子抵抗由因素2，像在例子中，导致重大扩展重要风车速度，C ω，显著减少动态电抗性补偿要求。当转子电阻为..040.020u p R R =，只将有必要使用25MV Ar 电压在风场连接点显示在的动态电抗性补偿。见图5。

25MV Ar 动态电抗性补偿与电抗性补偿要求比较，在那的情况下转子电阻值0R R 在第5部分被发现的100MV Ar 。显著减少动态电抗性补偿要求。另一方面， 当动力系统在正常运行时，这种解答在电动子电路导致增加功率损失。

6.2机械工程实施

它是一个共同的观点，当转动的系统的惯性更高时， 更加稳定的操作在动力系统在故障情况下被期望。

根据动态稳定性极限定义， 惯性值对风车临界速率不影响。二个风轮机以相同发电机数据和不同的惯量值1M H 和2M H ，当1M H >2M H 时，有同样的临界速率值21C C ωω=。

由于不同的惯量值，风轮机将会不同地加速在故障时并且有不同的关键失效时间21C C t t >。因此，重的风轮机显示更好的稳定行为比较锡风涡轮，只要故障时间不是太长的。

在实用情况，故障时间是足够短的，并且重的风轮机将是首选关于维护电压稳定。 风车装备轴系统，从发电接头观看的有效的轴硬度是低的．在正常运行，在轴那里将被积累相当数量势能，并且轴硬度越低，势能积累的越多。在短路故障，轴是松弛的，并且势能被释放到发电机转子动能。这导致发电机转子有更大的加速度。对轴

放松造成的发电机转子速度的贡献是)/(2G M

G KH T ∝?ω。增加轴硬度K ，因此导致在