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1、原文: A SPECIAL PROTECTION SCHEME FOR VOLTAGE STABILITY PREVENTION Tara Alzahawi Student Member, IEEE Mohindar S. Sachdev Life Fellow, IEEE G. Ramakrishna Member, IEEE Power System Research Group University of Saskatchewan Saskatoon, SK S7N 5A9, Canada Abstract Voltage instability is

2、 closely related to the maximum 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 Insta

3、bility Predictor (VIP). This relay measures voltages at a substation bus and currents in the circuit connected to the bus. From these measurements, it estimates the Thvenin’s equivalent of the network feeding the substation and the impedance of the load being supplied from the substation. This paper

4、 describes an extension to 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. Introduction Deregulation has forced electric utilities to

5、make better use of the available transmission 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

6、permissible loading of the system using 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

7、 loading, within the voltage stability 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

8、]. These curves are generated by running 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]. To overcome the above

9、disadvantages several techniques have been proposed 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 Volta

10、ge Indicator Predictor (VIP) method in [7] is based on local 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 cap

11、acity, the more imminent is the voltage instability. The main disadvantage of this method is in the estimation of the Thvenin’s 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

12、algorithm to improve the robustness of the VIP algorithm by including additional measurements from surrounding load buses and also taking into consideration local load changes at neighboring buses. 2. Proposed Methodology The VIP algorithm proposed in this paper uses voltage and current measur

13、ements on the load buses and assumes that the impedance of interconnecting lines (,) are known, as shown in (Figure 1). The current flowing from the generator bus to the load bus is used to estimate Thvenin’s equivalent for the system in that direction. Similarly the current flowing from other load

14、bus (Figure 2) is used to estimate Thvenin’s equivalent from other direction. 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.

15、 [1] [2] [3] [4] Where and are currents coming from Thvenin buses no.1 and 2. Equation (1)-(4) can be combined into a matrix form: *[5] Using the first 2 ro

16、ws in 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 Thvenin’s parameters are constant at the time of estimation.

17、 [6] Where, and The system equivalent seen from bus no.1 is shown in Figure 3. Figure 4(a) shows the relationship between load admittances ( and ) and voltage at bus no.1. Power delivered to bus no.1 is () and it is a function of (,).

18、 [7] Equation 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’. Fig. 1. 3-Bus system connections Fig. 2. 1-Bus model Fig. 3. System equivalent as seen by the propose

19、d VIP relay on bus #1 (2-bus model) (a)Voltage Profile (b) Power Profile Fig. 4. Voltage and power profiles for bus #1 2.1. On-Line Tracking of Thvenin’s Parameters Thvenin’s parameters are the main factors that decide the maximum loading of the load b

20、us and hence we can detect the voltage collapse. In Figure3, can be expressed by the following equation: [8] V and I are directly available from measurements at the local bus. Equation (8) can be expressed in the matrix form as shown below.

21、 [9] B= A X [10] The unknown parameters can be estimated from the following equation: [11] Note th

22、at 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 impedance in the data w

23、indow of at least two set of Measurements. ? For small changes in Thvenin’s 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

24、 monitoring 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 can also be obtained if communication is available. Once we have the

25、 time sequence 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 (); where subscript z denotes the impedance.Therefore we have:

26、 [12] The above equation assumes that both load impedances (, ) are decreasing at 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

27、both loads are functions of time. The maximum critical loading point is then given by Equation(13): [13] Expressing voltage stability margin due to load apparent power as ( ), we have: [14] Not

28、e that both and are normalized quantities and their values decrease as the load increases. At the voltage collapse point, both the margins reduce to zero and the corresponding load is considered as the maximum permissible loading. Fig. 5. VIP algorithm 2.2. Voltage Stability Margins and t

29、he Maximum Permissible Loading System reaches the maximum load point when the condition: is satisfied (Figure5).Therefore the voltage stability boundary can be defined by a circle with a radius of the Thvenin’s impedance. For normal operation the is smaller than (i.e. it is outside the circle)

30、and the system operates on the upper part (or the stable region) of a conventional P-V curve [2]. However, when exceedsthe 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

31、becomes same as the Thvenin’s (). Therefore, for a given load impedance (), the difference between and can 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 volta

32、ge instability 2.3. Advantages of the proposed VIP algorithm By incorporating the measurements from other load buses (Figure 3), the proposed VIP algorithm achieves a more accurate value of . The on-line tracking of is used to track system changes. The proposed improvements in the VIP algori

33、thm will result in better control action for power system voltage stability enhancement. The control measures are normally shunt reactor disconnection, shunt capacitor connection, shunt VAR compensation by means of SVC’s and synchrouns condensers, starting of gas turbines, low priority load disconne

34、ction, and shedding of low-priority load [8]. Figure 6 shows the most commonly used remedial actions . 3. Conclusions An improved Voltage Instability Predictor (VIP) algorithm for improving the voltage stability is proposed in this paper. The previous VIP method [7] used measurements only from th

35、e bus where the relay is connected. The new method uses measurements from other 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 Thvenin’s equivalent for tra

36、cking the system trajectory. The algorithm is simple and easy to implement in a numerical 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-wi

37、de control action can be undertaken. The algorithm is currently being investigated on an IEEE 30 bus system and results using the improved VIP algorithm will be reported in a future publication. References [1] M.H.Haque, “On line monitoring of maximum permissible loading of a power system within

38、 voltage stability limits”, IEE proc. Gener. Transms. Distrib.,Vol. 150, No. 1, PP. 107-112, January, 2003 [2] 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, 2004 [3] C.A. A

39、nizares, “On bifurcations voltage collapse and load modeling “IEEE Trans. Power System, Vol. 10, No. 1, PP. 512-522, February, 1995 [4] 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.

40、1446-1452, November, 1991 [5] P.A Smed Loof. T. Andersson, G. Hill and D.J,”Fast calculation of voltage stability index”, IEEE Trans. Power Syst. Vol. 7, No. 1, PP. 54-64, February, 1992 [6] K. Ohtsuka ,” An equivalent of multi- machine power system and its identification for on-line application

41、 to decentralized stabilizers”, IEEE Trans. Power Syst., Vol. 4 No. 2, PP. 687-693, May, 1989 [7] Khoi Vu, Miroslav M Begovic, Damir Novosel, Murari Mohan Saha, “ Use of local Measurements to estimate voltage – stability margin “ IEEE Trans. Power syst. Vol. 14, No. 3, PP. 1029-1035, August, 1999

42、 [8] G.Verbic and F. Gubina “Fast voltage-collapse line protection algorithm based on local phasors”, IEE Proc.Gener.Transm. Distrib., Vol. 150, No. 4, PP. 482-486, July, 2003 譯文： 一種特殊的預(yù)防電壓波動(dòng)的保護(hù)方案 塔拉阿里扎哈維 學(xué)生會(huì)員,IEEE 摩亨達(dá)瑞S.薩凱戴維 院士,IEEE G.羅摩克里希納 會(huì)員,IEEE （IEEE:美國(guó)電氣和電子工程師協(xié)會(huì)） 薩斯喀徹溫省薩斯卡

43、通大學(xué)的電力系統(tǒng)研究小組,SK S7N 5A9,加拿大 摘要 電壓的波動(dòng)與輸電線路的最大負(fù)載能力密切相關(guān)。輸電系統(tǒng)中電能的傳輸依賴于輸電線路的拓?fù)浣Y(jié)構(gòu),發(fā)電和負(fù)載,以及無(wú)功電源的出處。一種用于分析電壓波動(dòng)的方法是電壓波動(dòng)的預(yù)測(cè)(VIP)。由繼電器測(cè)量變電所連接到線路上的電路的電流和電壓。根據(jù)測(cè)量結(jié)果,借助戴維南定理估算出輸送到變電所線路和從變電所提供的負(fù)載的阻抗。本文描述了一個(gè)測(cè)量相鄰系統(tǒng)母線并考慮到的負(fù)荷預(yù)期變化的擴(kuò)展的VIP技術(shù)。 關(guān)鍵詞:最大負(fù)載能力;電壓波動(dòng);VIP算法。 1.簡(jiǎn)介 寬松的政策迫使發(fā)電企業(yè)要更好地利用電力系統(tǒng)中的輸電。這導(dǎo)致了輸電量的增加,降低了輸電利潤(rùn)和

44、減小了電壓安全裕度。 操作一個(gè)有足夠安全裕度的電力系統(tǒng),在系統(tǒng)的使用信息中估算當(dāng)前操作點(diǎn)的最大允許負(fù)載是必要的。一個(gè)電力系統(tǒng)的最大負(fù)載不是一個(gè)固定的值而是取決于各種各樣的因素,比如輸電線路的拓?fù)?、無(wú)功電源的出處和他們的位置等等。決定最大允許負(fù)載,在電壓穩(wěn)定極限內(nèi),在電力系統(tǒng)運(yùn)行和規(guī)劃研究中已成為一個(gè)非常重要的問(wèn)題。常見(jiàn)的P-V或V-Q曲線通常當(dāng)作一個(gè)評(píng)估電壓穩(wěn)定的依據(jù),進(jìn)而為在電力系統(tǒng)電壓崩潰端尋找最大負(fù)載提供依據(jù)[1]。這些曲線常規(guī)的方法是在大量負(fù)載流運(yùn)行使用的情況下產(chǎn)生的。雖然這樣的過(guò)程已經(jīng)可以自動(dòng)化,但它們是耗時(shí)的,在發(fā)現(xiàn)穩(wěn)定性問(wèn)題的起因時(shí)不易提供一些有用的信息[2]。 為了克服上述

45、缺點(diǎn)的多個(gè)方法已經(jīng)在文獻(xiàn)上提到,比如分叉理論[3],能量法[4]、本征值法[5],多個(gè)負(fù)載流解法[6]等。 參考[7]提出了一個(gè)簡(jiǎn)單的方法,它不需要離線的模擬和訓(xùn)練。電壓指標(biāo)預(yù)測(cè)方法(VIP)[7]是在本地測(cè)量值(電壓和電流)的基礎(chǔ)上,產(chǎn)生一個(gè)連接到母線上估算優(yōu)點(diǎn)和缺點(diǎn)的輸電系統(tǒng),并將它與當(dāng)?shù)氐男枨髮?duì)比。估算出最接近本地需求的輸電量,更為緊迫的是電壓波動(dòng)。該方法的主要缺點(diǎn)是在戴維南定理的估算, 它在不同時(shí)刻獲得兩個(gè)測(cè)量值。對(duì)于一個(gè)更精確的估值,一般需要兩個(gè)不同的負(fù)荷測(cè)量值。 本文提出了一種提高穩(wěn)定性算法的算法,包括周圍負(fù)載母線的額外的測(cè)量值外也考慮到相鄰總線之間局部的負(fù)載變化。 2.提

46、出的方法 VIP算法在本文中提到在負(fù)載母線和互連線( ,)的假設(shè)阻抗在已知的情況下使用電壓和電流測(cè)量 ,如下所示(圖1)。發(fā)電機(jī)負(fù)載母線的電流被用來(lái)估計(jì)戴維南等效的輸電方向。類似于用從其他負(fù)載母線(圖2)的電流來(lái)估計(jì)戴維南等效的其他方向。這個(gè)結(jié)果在以下方程式(圖3)。注意在輸電線路上來(lái)自第二負(fù)載母線的電流被排除在最初的估算(VIP)算法。 [1] [2] [3]

47、 [4] 由戴維南定理得來(lái)自第一和第二母線的電流和。方程(1)-(4)可以組合為一個(gè)矩陣形式: *[5] 使用第一行系統(tǒng)方程(1)-(4)中的2,在母線1和2上的電壓可以發(fā)現(xiàn)如以下方程式(6)所示。從方程式(6)中我們可以看到,電壓是一個(gè)阻抗的函數(shù)。請(qǐng)注意這個(gè)方法是假定所有戴維南的參數(shù)是常數(shù)時(shí)的估算。 [6] 在 和 中 系統(tǒng)等效理解為母線1如圖3所示。圖4(a)顯示了負(fù)載通道(y1和y2) 和母線1電壓之間的關(guān)系。電力輸送到母線1是(),它是一個(gè)(,).的函數(shù)。

48、 [7] 方程式7如圖4(b)“形象化”繪制并且最大負(fù)載點(diǎn)取決于系統(tǒng)軌跡”超過(guò)頂點(diǎn)”。 圖1.3母線系統(tǒng)連接 圖2.1母線模型 圖3.系統(tǒng)等效為被提議的VIP轉(zhuǎn)接到母線#1(母線#2模型) (a)電壓分布圖 (b)功率分布圖 圖4.母線# 1的電壓和功率分布圖 2.1. 即時(shí)跟蹤戴維南的參數(shù) 戴維

49、南的參數(shù)是決定負(fù)載母線最大負(fù)載的的主要因素,因此我們可以檢測(cè)輸電系統(tǒng)電壓崩潰。在圖3，可以用以下的方程式表示: [8] 電壓和電流可以從測(cè)量本地母線直接得到。方程式(8)可以用矩陣形式表達(dá),如下所示。 [9] B= A X

50、 [10] 未知參數(shù)可以從以下方程式的估算: [11] 注意,上述所有數(shù)量的計(jì)算是函數(shù)的時(shí)間和在滑動(dòng)窗口的有限的離散數(shù)據(jù)樣本之內(nèi)計(jì)算,最好長(zhǎng)度是短的。在額外的需求下做出可行的估算: ?必須有一個(gè)顯著的變化，負(fù)載阻抗數(shù)據(jù)窗口至少兩組測(cè)量值。 ?對(duì)于戴維南參數(shù)在一個(gè)特殊的數(shù)據(jù)窗口小的變化,該算法可以正確地估算除一個(gè)突然大的變化以外，估算的過(guò)程推遲到下一個(gè)數(shù)據(jù)窗口的到來(lái)。 ?這種監(jiān)視裝置基于上述原理可以用來(lái)強(qiáng)加限制裝載在每個(gè)母線,和流負(fù)載超過(guò)限制時(shí)。它也可以用來(lái)加強(qiáng)

51、現(xiàn)有的電壓控制器。協(xié)調(diào)控制同樣可以得到在交流是否空閑的情況下。 一旦我們有了時(shí)間序列的電壓和電流，我們可以通過(guò)使用參數(shù)估算算法估算未知參數(shù),如卡爾曼濾波方法描述[6]。 穩(wěn)定裕度() 由于阻抗可以表示為（）;在下標(biāo)z表示阻抗。因此我們有: [12] 上述方程式假設(shè)兩個(gè)負(fù)載阻抗(, )是在一個(gè)穩(wěn)定的速度下減少,所以電力送到母線1將根據(jù)方程(7)增加。然而一旦它達(dá)到飽和點(diǎn)的時(shí)候電力再一次開(kāi)始減少。 現(xiàn)在,假設(shè)兩個(gè)負(fù)載是時(shí)間的函數(shù)。最大的臨界負(fù)載點(diǎn)方程式(13)給出:

52、 [13] 電壓穩(wěn)定裕度表示由于負(fù)載視在功率為( ),我們有: [14] 注意,和兩個(gè)都是標(biāo)準(zhǔn)化的定量和隨著負(fù)載的增加它們的價(jià)值減少。 在電力系統(tǒng)電壓崩潰點(diǎn),同時(shí)兩個(gè)裕度減少到零和相應(yīng)的負(fù)載被視為最大允許負(fù)載。 圖5.VIP算法 2.2. 電壓穩(wěn)定裕度和最大允許加載 系統(tǒng)達(dá)到最大負(fù)載點(diǎn)當(dāng)滿足條件: (圖5)。所以,電壓穩(wěn)定裕度可以定義為一個(gè)戴維南阻抗為半徑的圓。正常操作的是小于 (即它是圓外面)和系統(tǒng)對(duì)上部(或穩(wěn)定的地區(qū)

53、)的一個(gè)常見(jiàn)的P-V曲線起作用[2]。 然而,當(dāng)超過(guò)系統(tǒng)運(yùn)行在較低的部分(或波動(dòng)的地區(qū))的P-V曲線,表明電力系統(tǒng)電壓崩潰已經(jīng)發(fā)生。在最大功率點(diǎn),負(fù)載阻抗等同于戴維南()。因此,對(duì)于一個(gè)給定的負(fù)載阻抗 ()，和之間的差異可以被視為一種安全裕度。因此,給IEEE一份描述(111)計(jì)劃從(17)不同的國(guó)家[8] 的電壓調(diào)查。 圖6.負(fù)載的行為阻止電壓不穩(wěn)定 2.3. 提議的VIP算法的優(yōu)點(diǎn) 通過(guò)整合其他負(fù)載母線(圖3)的測(cè)量值,這個(gè)VIP算法達(dá)到更精確的估算。即時(shí)地跟蹤是用來(lái)跟蹤系統(tǒng)的變化。 提議的改進(jìn)的VIP算法對(duì)輸電系統(tǒng)電壓穩(wěn)定性增強(qiáng)有了更好的控制作用?？刂拼胧┩ǔ２⒙?lián)電

54、抗器用來(lái)斷開(kāi),并聯(lián)電容器連接,分流器VAR通過(guò)SVC補(bǔ)償和同步冷凝器,燃?xì)鉁u輪機(jī)的開(kāi)始,低優(yōu)先級(jí)負(fù)載斷開(kāi)和低優(yōu)先級(jí)負(fù)載的脫落[8]。圖6顯示了最常用的補(bǔ)救措施。 3.結(jié)論 本文提出一種為提高電壓穩(wěn)定性而改進(jìn)的電壓波動(dòng)預(yù)測(cè)(VIP)算法。前面的VIP方法[7]只使用繼電器連接的母線的測(cè)量值。新方法很好地使用其他負(fù)載母線的測(cè)量值。電壓波動(dòng)裕度不僅取決于當(dāng)前的輸電系統(tǒng)狀態(tài)還取決于將來(lái)的變化。 因此,該算法對(duì)跟蹤輸電系統(tǒng)的軌跡使用了一個(gè)即時(shí)跟蹤的戴維南等效。該算法簡(jiǎn)易地實(shí)現(xiàn)了一個(gè)數(shù)字繼電器。通過(guò)繼電器得到的信息可以用于在母線減載激活或無(wú)功補(bǔ)償。此外,信號(hào)可能傳輸?shù)娇刂浦行?協(xié)調(diào)整個(gè)輸電系統(tǒng)承擔(dān)的

55、控制作用。該算法是現(xiàn)在正在IEEE母線30輸電系統(tǒng)被研究而且使用改進(jìn)的VIP算法的研究結(jié)果將被刊登在最近的出版物上。 參考文獻(xiàn) [1]M.H.Haque,“一個(gè)電力系統(tǒng)在電壓穩(wěn)定極限下在線監(jiān)測(cè)最大允許負(fù)載”,IEE proc.Gener.Transms.Distrib。,Vol.150, No.1,第112 - 107頁(yè),2003年1月 [2] V. Balamourougan, T.S. Sidhu和 M.S. Sachdev,“在線預(yù)測(cè)電壓崩潰技術(shù)”,IEE Proc.Gener.Transm. Distrib。, Vol.151, No.4,第460 - 453頁(yè),2004年7

56、月 [3]C.A. Anizares,”分支電壓崩潰和負(fù)荷建?！盜EEE反式。輸電系統(tǒng)》雜志,Vol.10, No.1,第522 - 512頁(yè),1995年2月 [4]T.J Overbye和S.J Demarco,“用于輸電系統(tǒng)電壓穩(wěn)定評(píng)估使用能量法的改進(jìn)技術(shù),IEEE 翻譯.輸電系統(tǒng)?！?Vol.6, No.4,第1446 - 1452頁(yè),1991年11月 [5]P.A Smed Loof. T. Andersson, G. Hill and D.J,“電壓穩(wěn)定指標(biāo)的快速估算”,IEEE 翻譯.輸電系統(tǒng)。Vol.7, No.1, 第54-64頁(yè),1992年2月 [6] K. Ohts

57、uka ”,一個(gè)類似于多機(jī)輸電系統(tǒng)及其為聯(lián)機(jī)應(yīng)用識(shí)別來(lái)分散穩(wěn)定,IEEE 翻譯.輸電系統(tǒng)。Vol.4 No.2,第693 - 687頁(yè),1989年5月 [7]Khoi Vu, Miroslav M Begovic, Damir Novosel, Murari Mohan Saha,“使用本地測(cè)量值估算電壓穩(wěn)定裕度“IEEE 翻譯.輸電系統(tǒng)。Vol.14, No.3,第1035 - 1029頁(yè),1999年8月 [8] G.Verbic 和 F. Gubina“基于本地相量的電壓崩潰線路保護(hù)快速算法”, IEE Proc.Gener.Transm. Distrib。Vol.150,No.4,第486 - 482頁(yè),2003年7月 15