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英文原文
Impact of Wind Power on the Angular Stability of a Power System
Abstract
Wind energy conversion systems are very different in nature from conventional generators. Therefore dynamic studies must be addressed in order to integrate wind power into the power system. Angular stability assessment of wind power generator is one of main issues in power system security and operation. The angular stability for the wind power generator is determined by its corresponding Critical Clearing Time (CCT). In this paper, the effect of wind power on the transient fault behavior is investigated by replacing the power generated by two main types of wind turbine, increasing gradually a rate of wind power penetration and changing the location of wind resources. The simulation analysis was established on a 14 bus IEEE test system by PSAT/Matlab, which gives access to an extensive library of grid components, and relevant wind turbine model.
Keyword Angular Stability, CCT, Wind Turbine, Wind Penetration, PSAT.
Introduction
A power network is a complex system, which is vulnerable to disturbances. A transient short circuit fault is a very common disturbance in a power system [1]. It upsets the
rotating machines in the vicinity of the fault, causing the speeds of these machines, and the power flows in the network to oscillate. When the short circuit is cleared by disconnecting the faulted line, the generators that have accelerated will decelerate and come back into synchronism with the rest of the system. If they do not, and the system becomes unstable, there is a risk of widespread blackouts and of mechanical damage to generators. So the critical clearing time (CCT) is the maximum time interval by which the fault must be cleared in order to preserve the system stability [2, 3].
There is no doubt that wind power will play a predominant role in adding clean and nonpolluting energy to the country’s grid. However, as more wind turbines are connected to the grid, their impact on the power quality of services populated with wind generation is becoming more evident, so it is important to analyze the transient stability of power system including wind power stations [4].
A three-phase fault is applied to a 14 bus IEEE test system, and cleared by disconnecting the affected line.
In this paper, the focus is limited to determine Critical Clearing Time (CCT) for the several cases by observing the transit behavior simulation of a test system during grid faults using a Matlab power system analyze toolbox (PSAT) [5].
The structure of this paper is as follows. First, the wind model is described briefly; also the wind turbine concepts are described. Then, the test system and the applied models are presented. The oscillation of a group of generators during a fault is analyzed by observing the transient behavior for following cases:
A- Changing a wind source locates.
B- Different generator technologies.
C- Increasing gradually a rate of wind sources penetration.
To conclude, the results are clarified on the basis of existing theories and comparison between different cases in order to choose a best case and avoid a worse one. Wind Model
Wind energy is transformed into mechanical energy by means of a wind turbine whose rotation is transmitted to the generator by means of a mechanical drive train.
The wind-power equation [6, 7] is given by: Pt=1/8ρπd2v3 Cp
where ρ is the air density, r is the turbine radius, ν is the wind speed, and Cp is the turbine power coefficient which represents the power conversion efficiency and it is a function of the ratio of the rotor tip-speed to the wind speed, termed as the tip-speed-ratio (TSR).
Such disturbances are the most common in the grid, the grid disturbances considered in this paper are of short duration, maximum a few hundreds of milliseconds. Since the considered grid disturbances are much faster than wind speed variations, the wind speed can he assumed constant. Therefore, natural wind variations need not be taken into account. The wind speed is set to a constant 15 m/s.
Turbine Models
There are many different types of wind turbines in use around the world, each having its own list of benefits and drawbacks [8]. In this paper two main types of wind turbines are taken into account:
? A constant speed wind turbine (Fig. 1a), which consists of a grid coupled short-circuited induction generator [9]. The wind turbine rotor is connected to the generator through a gearbox. The power extracted from the wind is limited in high wind speeds using the stall effect. No active control systems are used.
? A variable speed wind turbine with wound rotor induction generator (Fig. 1b) – doubly-fed induction generator (DFIG). The rotor winding is supplied using a back-to-back voltage source converter [10]. As in the first case, the wind turbine rotor is coupled to the generator through a gearbox. In high wind speeds the power extracted from the wind is limited by pitching the rotor blades.
Figure 1a. Squirrel cage induction generator
Figure 1b. Doubly-fed induction generator
Test System
The test system for this study is presented in Fig. 2, it is derived from IEEE test system; this network consists of 14 buses, 5 generators, 11 loads and 83 branches. The transformers connecting generators to the grid are adjusted accordingly. Wind turbines are the 2 MW machines described above in section 2.
Note that the generators do not represent a single machine but a group of strongly coupled generators and for this test system the total power is divided as follow:
Table 1. Active power of test system generators
Generator N°
1
2
3
4
5
Power(MW)
615
60
60
25
25
The disturbance investigated is a three-phase short-circuit on Bus number 2. This three-phase fault represents the most severe disturbance for transient stability problems.
It must be noted that all simulations are developed by PSAT (version 2.0.0 β1). Results and Discussions
Impact of Location
In order to assume the impact of the wind power to angular stability of power system, we included a three phase symmetrical fault then we calculate the CCT corresponding to a case without wind source and others cases where a wind source is connected to test system by different Buses.
Figure 2. Base case
Without a Wind Source
The Base Case represents the normal operation of the system without any wind power connected to the system. The critical fault clearing time (CCT) can be determined using transient simulations [3]. For this case, the result is CCT = 196 ms. Fig. 3 shows the speed generators in comparison for a fault clearing time close to the critical clearing time.
In Fig. 3b, the fault introduced has duration of t = 197 ms, so the time is exceeding the stability limit of CCT.
Figure 3a. Rotor speed of all generators at t = 196 ms
Figure 3b. Rotor speed of all generators at t=197 ms
With a Wind Source
After that, one wind turbine generator is connected to system through a transmission line on different buses for evaluating their effect to the angular stability.
Table 2. Results from the simulations for the angular stability on different locations
Bus number
Bus 1
Bus 3
Bus 8
Bus 14
CCT (ms)
186
187
263
220
Compared to the previous case where any wind source was connected, the integration of wind source has increased the transit stability when it was connected at BUS 8 or BUS 14, but on the contrary for cases of BUS 1 and BUS 3, so there is no general statement possible, if wind generation improves transient stability margins or if the impact is rather negative. The answer depends on location of wind resources and the problem has to be analyzed individually for each case.
Effect of Type of Generator Technology
In order to determine the effect of type of generator technology to transit behavior of grid, two types of generators are studied with keeping the same fault and the same location of wind source. Case 1: Fixed Speed
The critical fault clearing time (CCT) can be determined using transient simulations. For this case, where wind source is connected to Bus N°3 the result is CCT = 187 ms. Fig. 4 shows the speed rotor of all generators in comparison for a fault clearing time close to the critical clearing time.
Figure 4a. Rotor speed of all generators at t=187 ms
Case 2: Variable Speed (DFIG Technology)
The fixed speed generator added to Bus 3 is now disconnected and substituted by a doubly-fed induction generator (DFIG) having a same power (2MW). Thus, the change in the technology can be considered and analyzed. The analysis of the CCT results in an increased stability limit compared to Case 1 with only fixed speed generators in service. The time increases to CCT = 216 ms as shown in figure 5 .This means, that the transient network stability is enhanced when DFIG are connected instead of fixed speed generator.
Figure 5a. Rotor speed of all generators at t=216 ms
Figure 5b. Rotor speed of all generators at t=217 ms
Table 3. CCT for two types of turbine technology on several buses
Bus N°
1
3
8
14
CCT for fixed speed(ms)
186
187
263
220
CCT for variable speed(ms)
286
216
300
227
According to results, it is very clearly that the DFIG generator increase the critical clearing time, consequently this type of generator presents best performance than a squirrel cage induction generator concerning the angular stability of grid connected to wind power, it is evident that the Wind power generation with DFIG provides better performance for angular stability after fault clearance owing to its ability to control reactive power.
Effect of wind penetration
In this section, the effect of wind power on the oscillations is investigated by gradually increasing the rate of wind source penetration while observing the transit behavior of system [11].
Table 4. CCT for different rates of wind power penetration
Rate of wind sources penetration (%)
3.18
6.7
14.01
21.65
≥ 22
Installed capacity of Wind sources (MW)
24.96
52.59
109.90
169.95
≥172
CCT (ms)
271
229
151
97
00
From the results, it is concluded that the effect of wind power on power system oscillations depends on the rate of wind power penetration, it has been proven that a high level of wind power penetration such in our case study is must be lower than 22 % of total grid power, otherwise the test system lost its stability.
Conclusion
This paper has mainly focused on the assessment of the angular stability by determinate a critical clearing time (CCT), This was done by observing the behavior of speed generators of the test system included a three phase fault when changing several parameters.
According to previously simulations, the following conclusions are obtained:
? There is no general statement possible, if wind generation improves transient stability margins or if the impact is rather negative. The answer depends on location of wind resources and the problem has to be analyzed individually for each case.
? The effect of type of generator technology in transit stability is very significant and the DFIG generator presents more performance than a squirrel cage induction generator.
? It has been proven that a high level of wind power penetration destabilize the power system when a very large part of the synchronous generation capacity is replaced by wind power. Finally, it very important to note that a calculation of a critical clearing time (CCT) in all previous simulations was done by several times which represent a wasting of effort and time so a numerical method of computation of (CCT) is very required for such transit stability studies.
References
1. Sun T., Chen Z., Blaabjerg F., Voltage recovery of grid-connected wind turbines after a short-circuit fault, Annual Conference of the IEEE Industrial Electronics Society, Virginia, USA, 2003.
2. Saffet Ayasun, Yiqiao Liang, Chika O. Nwankpa, A sensitivity approach for computation of the probability density function of critical clearing time and probability of stability in power system transient stability analysis, Applied Mathematics and Computation, 2006, p. 563.
3. Salman S. K., Teo A. L. I., Investigation into the Estimation of the Critical Clearing Time of a Grid Connected Wind Power Based Embedded Generator, Proceedings of the IEEE/PES transmission and distribution Conference and exhibition 2002, Asia Pacific Pucific, Vol. 11, 2002, p. 975-980.
4. Jauch C., S?rensen P., Norheim I., Rasmussen C. Simulation of the Impact of Wind Power on the Transient Fault Behavior of the Nordic Power System, Electric Power Systems Research, VOL: article in press, available online 24 March, 2006, p. 135-144.
5. Federico Milano, Power System Analysis Toolbox Documentation for PSAT version 2.0.0 β1, July 9, 2006.
6. Soerensen P., Hansen A.D., Pedro Andre Carvalho Rosas, Wind Models for Prediction of Power Fluctuations of Wind Farms, J. Wind Eng. Ind. Aerodyn, 2002, 90, p. 1381-1402.
7. Tang Hong, WuJunling, Zhou Shuangxi, Modeling and Simulation for Small Signal Stability Analysis of Power System Containing Wind Farm, J. Power System Technology, 2004, 28(1), 38-41.
8. Hansen A.D., S?rensen P., Iov F., Blaabjerg F., Initialisation of Grid-Connected Wind Turbine Models in Power-System Simulations, Wind Engineering, 2003, 27(1), p. 21-38.
9. Nandigam K., Chowdhury B. H., Power flow and stability models for induction generators used in wind turbines, IEEE Power Engineering Society General Meeting, 2004, 2, p. 2012-2016.
10. Hansen A. D., Michalke G., Fault ride-through capability of DFIG wind turbines, Renewable Energy, 2007, 32, p. 1594-1610.
11. Ha L. T., Saha T. K., Investigation of Power Loss and Voltage Stability Limits for Large Wind Farm Connections to a Sub-transmission Network, Power Engineering Society General Meeting, 2004, 2, p. 2251-2256.
中文譯文
風(fēng)電對電力系統(tǒng)角穩(wěn)定性的影響
摘要
風(fēng)能轉(zhuǎn)換系統(tǒng)是非常不同的性質(zhì)與傳統(tǒng)發(fā)電機組。因此，動態(tài)研究必須加以解決，以便將風(fēng)力為動力系統(tǒng)。角穩(wěn)定評估風(fēng)力發(fā)電機是一個主要問題在電力系統(tǒng)安全運行。角穩(wěn)定的風(fēng)力發(fā)電機是由其相應(yīng)的臨界清除時間（建）。在本文中，風(fēng)力的作用對故障暫態(tài)行為調(diào)查取代產(chǎn)生2種類型的風(fēng)力發(fā)電機，風(fēng)力逐漸增加的速度滲透和改變位置的風(fēng)力資源。仿真分析是建立在14總線測試系統(tǒng)的軟件/，這使獲得一個廣泛的網(wǎng)格組件，以及相關(guān)的風(fēng)力機模型。
關(guān)鍵詞：角穩(wěn)定性，橫向，風(fēng)機，風(fēng)滲透。
引言
電力網(wǎng)絡(luò)是一個復(fù)雜的系統(tǒng)，這是容易受到干擾。瞬態(tài)短路故障是一個非常常見的干擾功率系統(tǒng)。它會在轉(zhuǎn)子附近產(chǎn)生故障，導(dǎo)致這些機器的轉(zhuǎn)速和功率在網(wǎng)絡(luò)中振蕩。當短路清除斷開故障，發(fā)電機，加速將減速，回到同步與其他系統(tǒng)。如果他們不這樣做，并使系統(tǒng)變得不穩(wěn)定，有可能廣泛停電和造成機械性損壞發(fā)電機。因此，臨界清除時間是最大的時間間隔，故障必須清除，以維護系統(tǒng)的穩(wěn)定性。
毫無疑問的是，風(fēng)力將發(fā)揮主導(dǎo)作用，增加國家電網(wǎng)的清潔無污染能源。然而，隨著越來越多的風(fēng)力發(fā)電機連接到電網(wǎng)，其影響的電能質(zhì)量服務(wù)人類與生產(chǎn)是越來越明顯，所以重要的是分析電力系統(tǒng)的暫態(tài)穩(wěn)定性，包括風(fēng)力發(fā)電站。
三相故障應(yīng)用到14個總線測試系統(tǒng)，通過斷開和清除影響線。
本文的重點是：以確定臨界清除時間（橫向）的若干情況下觀察運輸行為仿真測試系統(tǒng)在電網(wǎng)故障期間使用的電力系統(tǒng)分析工具箱（部分）。
本文的結(jié)構(gòu)如下。首先，風(fēng)模型描述也；風(fēng)機的概念描述。然后，測試系統(tǒng)和應(yīng)用模型的提出。振蕩的一組發(fā)電機故障暫態(tài)行為分析觀察下列情況：
風(fēng)模型：風(fēng)能轉(zhuǎn)化為機械能，通過一個風(fēng)力渦輪的旋轉(zhuǎn)傳遞給發(fā)電機采用機械傳動裝置。
風(fēng)力方程給出：Pt=1/8ρπd2v3 Cp
其中ρ是空氣的密度，d是渦輪半徑，ν是風(fēng)速，Cp是風(fēng)力機將風(fēng)能轉(zhuǎn)換為機械能的效率，稱風(fēng)能利用系數(shù)，它與風(fēng)速，葉片轉(zhuǎn)速，葉片直徑和槳葉節(jié)距角均有關(guān)系，是葉尖速比和槳葉節(jié)距角的函數(shù)。葉尖速比是葉尖速度除以風(fēng)速。
有許多不同類型的風(fēng)力渦輪機在世界各地使用，各有其自己的名單的好處和缺點。本文主要類型的風(fēng)力渦輪機是：
?恒速風(fēng)機（圖1），其中包括一個網(wǎng)格耦合感應(yīng)發(fā)電機短路[9 ]。風(fēng)渦輪轉(zhuǎn)子連接到發(fā)電機通過變速箱。功率提取風(fēng)是有限的，在高風(fēng)速時使用失速效應(yīng)。沒有主動控制系統(tǒng)的使用。
?可變速度風(fēng)力渦輪機與繞線轉(zhuǎn)子異步發(fā)電機（圖1 b）–雙饋感應(yīng)發(fā)電機（雙）。轉(zhuǎn)子繞組供給采用背對背電壓源變換器[ 10]。在第一種情況下，風(fēng)機轉(zhuǎn)子耦合到電機通過變速箱。在高風(fēng)速功率提取風(fēng)是有限的俯仰轉(zhuǎn)子葉片。
圖1a鼠籠型異步發(fā)電機。
圖1b雙饋感應(yīng)發(fā)電機
測試系統(tǒng)
測試系統(tǒng)研究是在圖2，它是從測試系統(tǒng)；該網(wǎng)絡(luò)由14路總線，5臺發(fā)電機，11和83分支。發(fā)電機變壓器連接到網(wǎng)格是相應(yīng)的調(diào)整。風(fēng)力渦輪機的2兆瓦的機器上面介紹的2節(jié)。
請注意，發(fā)電機并不代表一個單一的機器，而是一組強烈耦合發(fā)電機，該測試系統(tǒng)總功率分為：
表1 有源電力的發(fā)電機試驗系統(tǒng)
發(fā)電機N°
1
2
3
4
5
功率（MW）
650
60
60
25
25
干擾調(diào)查是一個三相短路對2號總線。這是最嚴重的干擾三相故障暫態(tài)穩(wěn)定問題。
結(jié)果與討：
以假設(shè)的影響，風(fēng)力角穩(wěn)定的電力系統(tǒng)，包括一三階段對稱故障然后計算橫向?qū)?yīng)一個沒有風(fēng)等情況下，風(fēng)源連接到測試系統(tǒng)的不同總線。
圖2。
圖2 基本線路
沒有風(fēng)的來源
基本情況是正常的操作系統(tǒng)沒有任何風(fēng)電連接到系統(tǒng)。故障臨界清除時間（建）才能確定使用瞬態(tài)模擬[ 3]。對于這種情況，其結(jié)果是橫向=196毫秒。圖3a顯示轉(zhuǎn)速發(fā)電機故障清除時間比較接近臨界清除時間。
圖3b中的故障，介紹了時間=197毫秒，所以時間超過穩(wěn)定極限曲線。
圖3a所有發(fā)電機的轉(zhuǎn)子轉(zhuǎn)速=196毫秒
圖3b所有發(fā)電機的轉(zhuǎn)子轉(zhuǎn)速=197毫秒
在風(fēng)源之后，一個風(fēng)力發(fā)電機是連接到系統(tǒng)通過傳輸線路上評價其效果的角穩(wěn)定。
表2。從模擬結(jié)果為角穩(wěn)定在不同的地點
總線
總線1
總線3
總線8
總線14
CCT（ms）
186
187
283
220
相比以前的情況下，任何風(fēng)源連接，整合風(fēng)源增加了運輸穩(wěn)定時，它是連接在總線8或1總線4，但是相反的情況下1和3總線總線，所以沒有一般的陳述可能，如果風(fēng)力發(fā)電提高暫態(tài)穩(wěn)定的利潤或如果是相當消極的影響。答案取決于風(fēng)能資源和問題進行分析，為每個單獨的情況。
影響類型的發(fā)電機技術(shù)
為了確定影響類型的發(fā)電技術(shù)，運輸行為的網(wǎng)格，2型發(fā)電機的研究與保持相同的故障和同一地點的風(fēng)能。
案例1：固定速度
故障臨界清除時間（建）才能確定使用瞬態(tài)模擬。對于這種情況，那里的風(fēng)源連接到總線°3結(jié)果是橫向=187毫秒。圖4顯示所有發(fā)電機轉(zhuǎn)子故障清除時間比較接近臨界清除時間。
圖4a 所有發(fā)電機的轉(zhuǎn)子轉(zhuǎn)速=187毫秒
圖4b 所有發(fā)電機的轉(zhuǎn)子轉(zhuǎn)速=188毫秒
案例2：變速（雙饋技術(shù)）
固定發(fā)電機添加到總線3現(xiàn)在是斷開和取代的雙饋感應(yīng)發(fā)電機（雙饋）具有相同的功率（兩兆瓦）。因此，變化的技術(shù)可以考慮和分析。分析了橫向的結(jié)果增加穩(wěn)定極限的情況相比，1只固定轉(zhuǎn)速發(fā)電機服務(wù)。時間增加橫向=216毫秒，如圖5所示。這意味著，在暫態(tài)網(wǎng)絡(luò)穩(wěn)定性增強時，雙饋發(fā)電機連接而固定測速發(fā)電機。
圖5a 所有發(fā)電機的轉(zhuǎn)子轉(zhuǎn)速=216毫秒
圖5b 所有發(fā)電機的轉(zhuǎn)子轉(zhuǎn)速=217毫秒
比較
分析這方面的更詳細，表3顯示值為雙饋發(fā)電機技術(shù)（變速）和異步發(fā)電機（固定變量）的不同位置上。
表3 建2種汽輪機技術(shù)的幾個公共總線。
總線N
1
3
8
14
橫向固定速度（ms）
186
187
220
223
橫向變速（ms）
286
216
300
227
根據(jù)研究結(jié)果，這是很清楚的，雙饋發(fā)電機增加臨界清除時間，因此這類發(fā)生器提出了最佳性能比鼠籠式異步發(fā)電機的功角穩(wěn)定的網(wǎng)格連接風(fēng)力，顯而易見的是，風(fēng)力發(fā)電，雙饋式提供了更好的性能穩(wěn)定故障消除后，由于角其有能力控制無功功率。
風(fēng)的影響滲透
在本節(jié)中，風(fēng)力的作用振蕩的研究逐漸增加的速度源風(fēng)滲透同時觀察運輸系統(tǒng)行為[ 11]。
表4 橫向速度不同的風(fēng)電穿透
風(fēng)資源穿透率（%）
3.18
6.7
14.01
21.65
≥ 22
風(fēng)電總裝機功率（MW）
24.96
52.59
109.90
169.95
≥172
CCT（ms）
271
229
151
97
0
從結(jié)果，它的結(jié)論是，影響風(fēng)電對電力系統(tǒng)振蕩取決于速度的風(fēng)電穿透，它已被證明，高一級的風(fēng)力滲透在我們的案例研究是必須低于22%的總電網(wǎng)，否則測試系統(tǒng)失穩(wěn)。
結(jié)論
本文主要集中在評估的角穩(wěn)定的確定一個臨界清除時間（建），這是觀察的行為，發(fā)電機的測試系統(tǒng)包括一三個階段的變化時，幾個參數(shù)故障。
根據(jù)先前的模擬，得出以下結(jié)論：
?一般是沒有聲明，如果風(fēng)力發(fā)電提高暫態(tài)穩(wěn)定的利潤或是相當消極的影響。答案取決于風(fēng)能資源和問題進行分析，為每個單獨的情況。
?影響類型的發(fā)電技術(shù)在運輸?shù)姆€(wěn)定性是非常重要的和雙饋發(fā)電機提供了更多的表現(xiàn)比鼠籠式異步發(fā)電機。
?已經(jīng)證明，高一級的風(fēng)電穿透破壞電力系統(tǒng)時，很大一部分的同步發(fā)電能力，取而代之的是風(fēng)力。
最后，很重要的一個計算一個臨界清除時間（建）在所有以前的模擬進行了幾次這是浪費時間和精力，數(shù)值計算方法（橫向）是非常需要這種運輸?shù)姆€(wěn)定性研究。
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