电气工程及其自动化毕业设计外文翻译

1、原文:A SPECIAL PROTECTION SCHEME FOR VOLTAGESTABILITY PREVENTIONTara Alzahawi Student Member, IEEE Mohindar S. Sachdev Life Fellow, IEEEG. Ramakrishna Member, IEEEPower System Research Group University of Saskatchewan Saskatoon, SK S7N5A9, CanadaAbstractVoltage instability is closely related to the ma

2、ximum load-ability of a transmission network. The energy flows on the transmission system depend on the network topology, generation and loads, and on the availability of sources that can generate reactive power. One of the methods used for this purpose is the Voltage Instability Predictor (VIP). Th

3、is relay measures voltages at a substation bus and currents in the circuit connected to the bus. From these measurements, it estimates the Thvenins equivalent of the network feeding the substation and the impedance of the load being supplied from the substation. This paper describes an extension to

4、the VIP technique in which measurements from adjoining system buses and anticipated change of load are taken into consideration as well.Keywords: Maximum load ability; Voltage instability; VIP algorithm.1. IntroductionDeregulation has forced electric utilities to make better use of the available tra

5、nsmission facilities of their power system. This has resulted in increased power transfers, reduced transmission margins and diminished voltage security margins.To operate a power system with an adequate security margin, it is essential to estimate the maximum permissible loading of the system using

6、 information about the current operation point. The maximum loading of a system is not a fixed quantity but depends on various factors, such as network topology, availability of reactive power reserves and their location etc. Determining the maximum permissible loading, within the voltage stability

7、limit, has become a very important issue in power system operation and planning studies. The conventional P-V or V- Q curves are usually used as a tool for assessing voltage stability and hence for finding the maximum loading at the verge of voltage collapse 1. These curves are generated by running

8、a large number of load flow cases using, conventional methods. While such procedures can be automated, they are time-consuming and do not readily provide information useful in gaining insight into the cause of stability problems 2.1To overcome the above disadvantages several techniques have been pro

9、posed in the literature, such as bifurication theory 3, energy method 4, eigen value method 5, multiple load flow solutions method 6 etc.Reference 7 proposed a simple method, which does not require off-line simulation and training. The Voltage Indicator Predictor (VIP) method in 7 is based on local

10、measurements (voltage and current) and produces an estimate of the strength / weakness of the transmission system connected to the bus, and compares it with the local demand. The closer the local demand is to the estimated transmission capacity, the more imminent is the voltage instability. The main

11、 disadvantage of this method is in the estimation of the Thvenins equivalent, which is obtained from two measurements at different times. For a more exact estimation, one requires two different load measurements.This paper proposes an algorithm to improve the robustness of the VIP algorithm by inclu

12、ding additional measurements from surrounding load buses and also taking into consideration local load changes at neighboring buses.2. Proposed MethodologyThe VIP algorithm proposed in this paper uses voltage and current measurements on the load buses and assumes that the impedance of interconnectin

13、g lines (Z12,Z13) are known, as shown in (Figure 1). The current flowing from the generator bus to the load bus is used to estimate Thvenins equivalent for the system in that direction. Similarly the current flowing from other load bus (Figure 2) is used to estimate Thvenins equivalent from other di

14、rection. This results in following equations (Figure 3). Note that the current coming from the second load bus over the transmission line was kept out of estimation in original (VIP) algorithm.V1(ZL1+Zth1)-V2(Z12)=Eth1(Zth1)-1-1-1-1-1-1-1-1 1 2 V2(ZL2+Zth2)-V1(Z12)=Eth2(Zth2)Eth1(Zth1)-V1(Zth1)=IE1-

15、1-1-1-1 34 Eth2(Zth2)-V2(Zth2)=IE2Where IE1 and IE2 are currents coming from Thvenin buses no.1 and 2. Equation (1)-(4) can be combined into a matrix form:-1-1ZL1-1+Z12-1+Zth1-1V-Z12-Zth101-1-1-1-1-1-Z12ZL2+Z12+Zth20-Zth2V2= *-1-1-Zth10Zth10Eth1-1-1E0-Zth20Zth2th2005 IE1IE22Using the first 2 rows in

16、 the system Equations (1)-(4), the voltage on buses number 1 and 2 can be found as shown in Equation (6) below. From Equation (6) we can see that the voltage is a function of impedances. Note that the method assumes that all Thvenins parameters are constant at the time of estimation.-1-1-1-1Eth1Zth1

17、-1-Z12V1ZL1+Zth1+Z12 6 =*-1-1-1-1-1V-Z12ZL2+Zth2+Z122Eth2Zth2-1Where, y1=ZL1 y12=Z12 and y2=ZL2The system equivalent seen from bus no.1 is shown in Figure 3. Figure 4(a) shows the relationship between load admittances (y1 and y2) and voltage at bus no.1. Power delivered to bus no.1 is (S1) and it is

18、 a function of (ZL1,ZL2).S1=V1*yL1 7Equation 7 is plotted in figure 4 (b) as a landscape and the maximum loading point depends on where the system trajectory goes over the hill.2-1-1-1Fig. 1. 3-Bus system connections Fig. 2. 1-Bus modelFig. 3. System equivalent as seen by the proposed VIP relay on b

19、us #1 (2-bus model) 3(a)Voltage Profile (b) Power ProfileFig. 4. Voltage and power profiles for bus #12.1. On-Line Tracking of Thvenins ParametersThvenins parameters are the main factors that decide the maximum loading of the load bus and hence we can detect the voltage collapse. In Figure3, Eth can

20、 be expressed by the following equation:Eth=Vload+ZthI 8V and I are directly available from measurements at the local bus. Equation (8) can be expressed in the matrix form as shown below.VrEth(r)10-IrIi.0E(i)0000 9 =thViRth01-Ii.Ir0X0000thB= A X 10 The unknown parameters can be estimated from the fo

21、llowing equation:TT AAX=AB 11 Note that all of the above quantities are functions of time and are calculated on a sliding window of discrete data samples of finite, preferably short length. There are additional requirements to make the estimation feasible: There must be a significant change in load

22、impedance in the data window of at least two set of Measurements. For small changes in Thvenins parameters within a particular data window, the algorithm can estimate properly but if a sudden large change occurs then the process of estimation is postponed until the next data window comes in. The mon

23、itoring device based on the above principle can be used to impose a limit on the loading at each bus, and sheds load when the limit is exceeded. It can also be used to enhance existing voltage controllers. Coordinated control can4also be obtained if communication is available.Once we have the time s

24、equence of voltage and current we can estimate unknowns by using parameter estimation algorithms, such as Ka lm an Filtering approach described 6.stability margin (VSM) due to impedances can be expressed as (VSMZ); where subscript z denotes the impedance.Therefore we have: VSMZ=ZLoad-Zthev 12 ZLoadT

25、he above equation assumes that both load impedances (Z1, Z2) are decreasingat a steady rate, so the power delivered to bus 1 will increase according to Equation(7). However once it reaches the point of collapse power starts to decrease again.Now assume that both loads are functions of time. The maxi

26、mum critical loading point is then given by Equation(13): dsCritical=1=0 13 S1dtExpressing voltage stability margin due to load apparent power as ( VSMS), we have: SCritical-SLoad VSMS= 14 CriticalSNote that both VSMZ and VSMS are normalized quantities and their values decrease as the load increases

27、.At the voltage collapse point, both the margins reduce to zero and thecorresponding load is considered as the maximum permissible loading.Fig. 5. VIP algorithm2.2. Voltage Stability Margins and the Maximum Permissible LoadingSystem reaches the maximum load point when the condition: Zload=Zthevis sa

28、tisfied (Figure5).Therefore the voltage stability boundary can be defined by a circle 5with a radius of the Thvenins impedance. For normal operation the Zthevis smaller than Zload (i.e. it is outside the circle) and the system operates on the upper part (or the stable region) of a conventional P-V c

29、urve 2. However, when ZthevexceedsZloadthe system operates on the lower part (or unstable region) of the P-V curve, indicating that voltage collapse has already occurred. At the maximum power point, the load impedance becomes same as the Thvenins (ZL Zthev). Therefore, for a given load impedance (Zl

30、oad), the difference between Zthevand Zloadcan be considered as a safety margin. Hence the voltage as given in an IEEE survey, which described (111) schemes from (17) different countries 8.Fig. 6. Load actions to prevent from voltage instability2.3. Advantages of the proposed VIP algorithmBy incorpo

31、rating the measurements from other load buses (Figure 3), the proposed VIP algorithm achieves a more accurate value of Zload . The on-line tracking of Zthev is used to track system changes.The proposed improvements in the VIP algorithm will result in better control action for power system voltage st

32、ability enhancement. The control measures are normally shunt reactor disconnection, shunt capacitor connection, shunt VARcompensation by means of SVCs and synchrouns condensers, starting of gas turbines, low priority load disconnection, and shedding of low-priority load 8. Figure 6 shows the most co

33、mmonly used remedial actions .3. Conclusions6An improved Voltage Instability Predictor (VIP) algorithm for improving the voltage stability is proposed in this paper. The previous VIP method 7 usedmeasurements only from the bus where the relay is connected. The new method uses measurements from other

34、 load buses as well. The voltage instability margin not only depends on the present state of the system but also on future changes.Therefore, the proposed algorithm uses an on-line tracking Thvenins equivalent for tracking the system trajectory. The algorithm is simple and easy to implement in a num

35、erical relay. The information obtained by the relay can be used for load shedding activation at the bus or VAR compensation. In addition, the signal may be transmitted to the control centre,where coordinated system-wide control action can be undertaken. The algorithm is currently being investigated

36、on an IEEE 30 bus system and results using the improved VIP algorithm will be reported in a future publication. References1 M.H.Haque, “On line monitoring of maximum permissible loading of a power system within voltage stability limits”, IEE proc. Gener. Transms. Distrib.,Vol. 150, No. 1, PP. 107-11

37、2, January, 20032 V. Balamourougan, T.S. Sidhu and M.S. Sachdev, “Technique for online prediction of voltage collapse”, IEE Proc.Gener.Transm. Distrib., Vol.151, No. 4, PP. 453-460, July, 20043 C.A. Anizares, “On bifurcations voltage collapse and load modeling “IEEE Trans. Power System, Vol. 10, No.

38、 1, PP. 512-522, February, 19954 T.J Overbye and S.J Demarco, “Improved Technique for Power System voltage stability assessment using energy methods“, IEEE Trans. Power Syst., Vol. 6, No. 4, PP. 1446-1452, November, 19915 P.A Smed Loof. T. Andersson, G. Hill and D.J,”Fast calculation of voltage stab

39、ility index”, IEEE Trans. Power Syst. Vol. 7, No. 1, PP. 54-64, February, 19926 K. Ohtsuka ,” An equivalent of multi- machine power system and its identification for on-line application to decentralized stabilizers”, IEEE Trans. Power Syst., Vol. 4 No. 2, PP. 687-693, May, 19897 Khoi Vu, Miroslav M

40、Begovic, Damir Novosel, Murari Mohan Saha, “ Use of localMeasurements to estimate voltage stability margin “ IEEE Trans. Power syst. Vol. 14, No. 3, PP. 1029-1035, August, 19998 G.Verbic and F. Gubina “Fast voltage-collapse line protection algorithm based on local phasors”, IEE Proc.Gener.Transm. Di

41、strib., Vol. 150, No. 4, PP. 482-486, July, 2003译文：7一种特殊的预防电压波动的保护方案塔拉阿里扎哈维 学生会员,IEEE 摩亨达瑞S.萨凯戴维 院士,IEEE G.罗摩克里希纳 会员,IEEE （IEEE:美国电气和电子工程师协会）萨斯喀彻温省萨斯卡通大学的电力系统研究小组,SK S7N 5A9,加拿大摘要电压的波动与输电线路的最大负载能力密切相关。输电系统中电能的传输依赖于输电线路的拓扑结构,发电和负载,以及无功电源的出处。一种用于分析电压波动的方法是电压波动的预测(VIP)。由继电器测量变电所连接到线路上的电路的电流和电压。根据测量结果,借

42、助戴维南定理估算出输送到变电所线路和从变电所提供的负载的阻抗。本文描述了一个测量相邻系统母线并考虑到的负荷预期变化的扩展的VIP技术。关键词:最大负载能力;电压波动;VIP算法。1.简介宽松的政策迫使发电企业要更好地利用电力系统中的输电。这导致了输电量的增加,降低了输电利润和减小了电压安全裕度。操作一个有足够安全裕度的电力系统,在系统的使用信息中估算当前操作点的最大允许负载是必要的。一个电力系统的最大负载不是一个固定的值而是取决于各种各样的因素,比如输电线路的拓扑、无功电源的出处和他们的位置等等。决定最大允许负载,在电压稳定极限内,在电力系统运行和规划研究中已成为一个非常重要的问题。常见的P-

43、V或V-Q曲线通常当作一个评估电压稳定的依据,进而为在电力系统电压崩溃端寻找最大负载提供依据1。这些曲线常规的方法是在大量负载流运行使用的情况下产生的。虽然这样的过程已经可以自动化,但它们是耗时的,在发现稳定性问题的起因时不易提供一些有用的信息2。为了克服上述缺点的多个方法已经在文献上提到,比如分叉理论3,能量法4、本征值法5,多个负载流解法6等。参考7提出了一个简单的方法,它不需要离线的模拟和训练。电压指标预测方法(VIP)7是在本地测量值(电压和电流)的基础上,产生一个连接到母线上估算优点和缺点的输电系统,并将它与当地的需求对比。估算出最接近本地需求的 8输电量,更为紧迫的是电压波动。该方

44、法的主要缺点是在戴维南定理的估算,它在不同时刻获得两个测量值。对于一个更精确的估值,一般需要两个不同的负荷测量值。本文提出了一种提高稳定性算法的算法,包括周围负载母线的额外的测量值外也考虑到相邻总线之间局部的负载变化。2.提出的方法VIP算法在本文中提到在负载母线和互连线(Z12 ,Z13)的假设阻抗在已知的情况下使用电压和电流测量 ,如下所示(图1)。发电机负载母线的电流被用来估计戴维南等效的输电方向。类似于用从其他负载母线(图2)的电流来估计戴维南等效的其他方向。这个结果在以下方程式(图3)。注意在输电线路上来自第二负载母线的电流被排除在最初的估算(VIP)算法。V1(ZL1+Zth1)-

45、V2(Z12)=Eth1(Zth1) 1 V2(ZL2+Zth2)-V1(Z12)=Eth2(Zth2) 2 Eth1(Zth1)-V1(Zth1)=IE1 3 Eth2(Zth2)-V2(Zth2)=IE2 4由戴维南定理得来自第一和第二母线的电流IE1和IE2。方程(1)-(4)可以组合为一个矩阵形式:-1-1ZL1-1+Z12-1+Zth1-1V-Z12-Zth101-1-1-1-1-1-Z12ZL2+Z12+Zth20-Zth2V2= *-1-1-Zth10Zth10Eth1-1-1E0-Zth20Zth2th2-1-1-1-1-1-1-1-1-1-1-1-1005 IE1IE2使用第

46、一行系统方程(1)-(4)中的2,在母线1和2上的电压可以发现如以下方程式(6)所示。从方程式(6)中我们可以看到,电压是一个阻抗的函数。请注意这个方法是假定所有戴维南的参数是常数时的估算。-1-1-1-1Eth1Zth1-1-Z12V1ZL1+Zth1+Z12 6 * =-1-1-1-1-1V-Z12ZL2+Zth2+Z122Eth2Zth2-1在 y1=ZL1 y12=Z12 和 y2=ZL2 中9 -1-1-1系统等效理解为母线1如图3所示。图4(a)显示了负载通道(y1和y2) 和母线1电压之间的关系。电力输送到母线1是(S1),它是一个(ZL1,ZL2).S1 V12*yL1的函数。

47、 7方程式7如图4(b)“形象化”绘制并且最大负载点取决于系统轨迹”超过顶点”。图1.3母线系统连接 图2.1母线模型图3.系统等效为被提议的VIP转接到母线#1(母线#2模型)10(a)电压分布图 (b)功率分布图图4.母线# 1的电压和功率分布图2.1. 即时跟踪戴维南的参数戴维南的参数是决定负载母线最大负载的的主要因素,因此我们可以检测输电系统电压崩溃。在图3，Eth可以用以下的方程式表示: Eth=Vload+ZthI 8 电压和电流可以从测量本地母线直接得到。方程式(8)可以用矩阵形式表达,如下所示。VrEth(r)0E(i)=thViRth0Xth10000-IrIi.000 9

48、1-Ii.Ir000B= A X 10 未知参数可以从以下方程式的估算:ATAX=ATB 11注意,上述所有数量的计算是函数的时间和在滑动窗口的有限的离散数据样本之内计算,最好长度是短的。在额外的需求下做出可行的估算:必须有一个显著的变化，负载阻抗数据窗口至少两组测量值。对于戴维南参数在一个特殊的数据窗口小的变化,该算法可以正确地估算除一个突然大的变化以外，估算的过程推迟到下一个数据窗口的到来。这种监视装置基于上述原理可以用来强加限制装载在每个母线,和流负载超过限制时。它也可以用来加强现有的电压控制器。协调控制同样可以得到在交流是否空闲的情况下。11一旦我们有了时间序列的电压和电流，我们可以通

49、过使用参数估算算法估算未知参数,如卡尔曼滤波方法描述6。稳定裕度(VSM) 由于阻抗可以表示为（VSMZ）;在下标z表示阻抗。因此我们有: VSMZ=ZLoad-Zthev 12 ZLoad上述方程式假设两个负载阻抗(Z1, Z2)是在一个稳定的速度下减少,所以电力送到母线1将根据方程(7)增加。然而一旦它达到饱和点的时候电力再一次开始减少。现在,假设两个负载是时间的函数。最大的临界负载点方程式(13)给出: S1Critical=ds1=0 13 dt电压稳定裕度表示由于负载视在功率为( VSMS),我们有: SCritical-SLoad VSMS= 14 CriticalS注意,VSMZ和VSMS两个都是标准化的定量和随着负载的增加它们的价值减少。在电力系统电压崩溃点,同时两个裕度