Calculation of damping torque of power systems compensated with TCSC

The thyristor‐controlled series capacitor (TCSC) is being developed to improve the transmission capability of power systems. The TCSC is thought to compensate transmission line reactance without causing subsynchronous resonance (SSR). However, in order to evaluate its effect quantitatively, we must calculate the frequency response of the generator damping torque. Simulations need a long computing time, and it is hard to choose the frequency freely. In this paper, we propose a method of analytically calculating the damping torque. First, when a generator rotor oscillates at some frequency, two voltage components appear. We analytically calculate the damping torque from small current variations due to the voltage components. The damping characteristic changes depending on the method of firing thyristors. The best characteristic is obtained when triggering with reference to the fundamental wave of TCSC voltage or current is used. By choosing an appropriate firing angle, we can drastically reduce negative damping by the TCSC. The damping characteristic is closely related to the system impedance. The fact that the TCSC has large resistance in the 0 to 60 Hz range helps significantly in improving the characteristic. Lastly, numerical simulations of SSR are used to examine the validity of our investigation. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 143(1): 39–49, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10068     

相控电容器式可控串补特性分析

揭示了相控电抗器式可控串补与相控电容器式可控串补的对偶特征。用对偶原理阐述了相控电容器式可控串补的性能及相控特点。分析说明了串补电容器、GTO网的电流电压峰值与串补线路电流峰值、串补电容器的工频容抗值之间的关系，这对于理论上确认相控电容器式可控串补的优越性非常重要。阐述了相控电容器式可控串补具有阻尼次同步谐振和抑制低频功率振荡的能力；相控电抗器式可控串补装置的动态性能是一个其时间常数不大于工频0．25周期的一阶惯性环节。     

TCSC阻抗双解现象的机理研究

TCSC是靠调整触发角来获得需要的命令阻抗，因此命令阻抗与触发角的关系尤为重要，以往对TCSC阻抗双解研究局限于讨论电抗器品质因数的影响，该文讨论了考虑晶闸管导通特性和电抗器支路品质因数影响时TCSC的阻抗特性，文中通过相量图分析发现，即使在品质因数不变的情况下，随着晶闸管导通电流的增大，电容电压过零点与线路电流过零点之间的相位差也会逐渐减小，引起晶闸管实际导通幅度和宽度的减小；指出了造成TCSC双解现象的根本原因是晶闸管的导通受阻，其受阻程度由电抗器支路的电流和等效品质因数2个因素决定：线路电流同步方式下晶闸管导通电流的幅度和宽度均受阻；而电容电压同步下，晶闸管导通电流只有幅度受阻，因此阻抗双解现象在线路电流同步方式下更容易出现。数字仿真和动模实验结果分别验证了阻抗双解现象的存在。     

TCSC阻抗双解现象的机理研究

TCSC是靠调整触发角来获得需要的命令阻抗，因此命令阻抗与触发角的关系尤为重要，以往对TCSC阻抗双解研究局限于讨论电抗器品质因数的影响，该文讨论了考虑晶闸管导通特性和电抗器支路品质因数影响时TCSC的阻抗特性，文中通过相量图分析发现，即使在品质因数不变的情况下，随着晶闸管导通电流的增大，电容电压过零点与线路电流过零点之间的相位差也会逐渐减小，引起晶闸管实际导通幅度和宽度的减小；指出了造成TCSC双解现象的根本原因是晶闸管的导通受阻，其受阻程度由电抗器支路的电流和等效品质因数2个因素决定：线路电流同步方式下晶闸管导通电流的幅度和宽度均受阻；而电容电压同步下，晶闸管导通电流只有幅度受阻，因此阻抗双解现象在线路电流同步方式下更容易出现。数字仿真和动模实验结果分别验证了阻抗双解现象的存在。     

特高压输电线路用新型TCSC方案及其控制策略研究

为了在1 000 kV特高压输电线路或有较大额定电流的750 kV输电线路上加装可控串补(thyristor controlledseries compensation,TCSC),解决目前TCSC中所需晶闸管阀通流能力不足的问题,提出了一种基于双阀控电抗器(thyristor controlled reactance,TCR)支路并联的TCSC实现方案,并对其控制策略进行了研究。通过对幅值相等控制策略下双TCR支路TCSC进行数学建模,设计了相应的阻抗控制环节和幅值相等控制环节,实现了相应的控制目标。仿真结果表明,提出的TCSC实现方案及其控制策略可行,适用于工程应用。     

A study of thyristor controlled series capacitor models for power system stability analysis

The thyristor‐controlled series capacitor (TCSC) is promising as a powerful device to increase power transfer capability and transient stability. The basic configuration of the TCSC consists of a series of capacitors connected antiparallel with thyristor‐controlled reactors, so that firing angle control of the thyristors makes the TCSC capable of achieving impedance control in a wide range with quick response. It is important to clarify the relationship between the fundamental reactance of the TCSC and the firing angle of the thyristors, thus leading to practical applications of the TCSC for enhancement of power transfer capability and transient stability in transmission lines. Two relationship equations for the TCSC's fundamental reactance have already been proposed. One is the relationship equation derived from a TCSC circuit whose source is a voltage. The other is the relationship equation derived from a TCSC circuit whose source is a current. For TCSC installed in a transmission line, it is clear which equation is more adequate for analyzing power system stability. In this paper, the authors determine whether either of the equations is valid for analyzing a power system stability.

• 1. In the steady state, the TCSC fundamental reactance is analyzed and compared with the two equations and EMTP. It is clear that the TCSC reactance based on current source is adequate.
• 2. The swing angle of a generator when the firing angle is stepped up is analyzed with EMTP and an analytical model using the TCSC model based on current source. It is shown that the proposed model is effective for power system stability analysis. © 1999 Scripta Technica, Electr Eng Jpn, 129(1): 20–28, 1999

     

Loop current characteristics of a thyristor-controlled series capacitor

This paper presents the results of an investigation on the loop current of a thyristor-controlled series capacitor (TCSC). The knowledge of loop current characteristics is important for understanding analytically the equivalent impedance of TCSC, estimating harmonics produced by TCSC, and determining ratings of the TCSC circuit components. However, little has been written on the loop current of TCSC circuit. Therefore, using a laboratory-scale TCSC installed on a laboratory power system, the TCSC currents and voltages were measured and analyzed to investigate the behavior of loop current. A mathematical model of TCSC was also developed to compare to the experimental results and further clarify the relationship between loop current and steady-state impedance characteristics, including effects of TCSC circuit component size on the characteristics. Capacitor voltage harmonics and their impact on the power system were also investigated. ©1998 Scripta Technica, Electr Eng Jpn, 125(1): 37–46, 1998     

电抗器品质因数对TCSC特性的影响及阻抗特性的双解现象

可控串联电容器(Tcsc)装置的晶闸管控制支路电抗器(TCR)品质因数只能是有限值，该文通过时域数字仿真分析了这一参数对TCSC稳态阻抗特性的影响。仿真分析结果表明在电抗器品质因数有限的情况下，TCSC等效阻抗特性的谐振点相对理想情况会出现偏移；同时，在容性运行区间，对于同样的触发角指令，Q值越小，TCSC的等效基频电抗也越小，而在感性运行区间，情况则刚好相反。这种影响在感性和容性运行区间还因TCSC同步触发控制方式不同而存在较大的差异。当以电容电压过零点为同步触发参考时标时，触发角指令与等效阻抗之间是单值对应关系，而以线路电流为同步触发参考时标时，触发角指令与等效阻抗之间是双值对应关系，即所谓的双解阻抗特性。文章进一步研究了线电流同步方式下TCSC等效基频阻抗呈现双解的现象，指出产生该现象的根本原因是采用了不同的触发参考时标。TCSC等效基频阻抗特性的双解现象实际上是在以线路电流过零点为触发参考时标时TCSC表现出的一种特殊运行特性。它与以电容电压同步触发参考时标的阻抗特性之间具有确定的对应关系。在两种不同的触发时标下，通过详细时域仿真验证了上述结论。     

TCSC暂态过程中晶闸管导通角特性的研究

当晶闸管触发角发生阶跃时,由于TCSC电路固有的电磁暂态特性,使得电容电压过零点发生偏移,因此导通角不会立刻达到预定目标值。章首先给出并证明了触发角阶跃变化与初始导通角之间的定性关系;然后通过分析晶闸管导通期间电容电压的解耦特性,推导出导通角的估算公式,定量地描述了暂态过程中导通角的变化规律。数字仿真验证了上述分析结论并进一步发现：导通角变化趋势与TCSC基频阻抗特性是完全一致的,从而揭示了选择不同同步信号时TCSC会表现出不同暂态响应特性的内在原因。     

Protection of Double-Circuit Line with Thyristor Controlled Series Capacitor Using Principal Component Analysis

In this paper, a fault direction estimation algorithm is proposed for a double-circuit line with thyristor controlled series capacitor (TCSC) using principal component analysis (PCA)-based technique. In case of PCA, an orthogonal transformation is used to convert correlated variables into linearly uncorrelated variables called principal components. Fault in such a compensated line leads to voltage inversion, current inversion, and subsynchronous resonance situations, which affect the performance of the conventional direction estimation process. Transients associated with metal oxide varistor (MOV) operation and control action associated with TCSC, further modulate equivalent impedance of TCSC and MOV combination. In the proposed approach, PCA of angles between positive and negative sequence components of voltage current has been carried out to extract the pattern and to declare the fault direction accurately. The double-circuit line with TCSC is simulated using PSCAD/EMTDC software. The performance of the proposed technique is tested for numerous test cases, and it was found to be accurate.     

考虑阻抗双解现象的可控串补模式切换控制方法

可控串联补偿(thyristor controlled series capacitor,TCSC)的模式切换对电力系统的稳定控制具有重要意义。TCSC阻抗双解现象的存在对其模式切换提出了更高的要求,单一改变触发角的方法无法实现模式切换。在考虑阻抗双解现象影响的基础上,提出了一套相应的TCSC模式切换控制方法。通过强制晶闸管支路电流与线路电流同步,实现由容性区到Bypass模式的切换;在由容性区到感性微调模式切换的过程中提出了晶闸管条件触发的方法,即当线路电流和电容电压满足同向条件时晶闸管才触发导通。同时为及时向切换控制提供线路电流同步信号,提出了一种预测电流过零的新方法。数字仿真及动模实验结果表明,提出的切换方法能使切换过程平稳迅速,且动态特性良好。     

伊冯可控串补主要器件基本工作条件及总体工作能力探讨

本文介绍伊冯可控串补主要器件在稳态和准稳态下的工作条件，其中包括正常运行状态，Ｎ－１运行状态和暂态稳定调节状态下电容器，旁路电抗、晶闸管和ＭＯＶ的工作条件。     

伊敏-冯屯可控串补控制策略的RTDS实验研究

采用RTDS实时仿真工具验证了我国东北电网伊敏－冯屯500 kV交流输电架空线路可控串联补偿控制器的各项控制性能,检验了可控串联补偿装置的稳态运行特性,研究了可控串联补偿装置的阻抗阶跃特性和运行模式转换特性,最后通过三相故障的工况验证了可控串联补偿装置提高系统暂态稳定性尤其是阻尼低频功率振荡的作用。     

电网可靠性对可控串联补偿部件参数的灵敏度分解算法

可控串联补偿器(TCSC)是一种常见的柔性输电设备,多用于改善输电能力。现有TCSC对其电容器组、电抗器等部件的可靠性建模较为粗略,因此无法直接描述部件可靠性对电网可靠性的影响。考虑部件故障模式,提出TCSC可靠性分层等值算法,建立含TCSC线路可靠性状态空间模型。基于改进频率和持续时间(FD)算法,求解串联补偿线路状态概率和转移率,及其对部件可靠性参数的灵敏度。联立电网可靠性对串联补偿线路可靠性、串联补偿线路可靠性对TCSC部件灵敏度,提出电网可靠性对TCSC部件参数的灵敏度分解算法。算例分析验证了算法的可行性和正确性,有助于从电网角度发现和改善柔性交流输电设备的薄弱环节。     

TCSC对抑制次同步谐振的机理分析

对具有可控串联电容补偿的电力系统,提出了一种直接计算可控串补对次同步频率 分量所反映出的等值阻抗的算法。基于该计算原理,对可控串补具有正等值电阻这一特性给 出了详细的机理解释。     

可控串补次同步频率等效阻抗特性的机理分析

利用小信号分析法,在可控串补(thyristor controlled series compensation,TCSC)的工频电流源上叠加一个微小次同步频率分量的电流源,采用数值分析方法获得次同步频率电容电压的时域仿真曲线;在此基础上分析次同步频率电容电压在晶闸管导通前后的变化规律,推导TCSC次同步频率等效阻抗的解析表达式。结果表明通过解析法求得的次同步频率等效电抗与数值方法获得的特性曲线变化趋势基本吻合;根据对解析表达式的分析,研究晶闸管导通对次同步频率电压的调制作用随导通角增大的变化过程,从周期调制作用角度解释TCSC次同步频率等效阻抗特性形成的机理。     

中压配电网串联TCSC调压的应用研究

利用TCSC可以平滑地调节阻抗,实现对不同线路参数或不同负荷的线路进行电压调节,稳定负荷侧电压。对线路电压调节时考虑线路横向压降的影响,从而得到串联补偿容抗计算公式;由于晶闸管的导通压降会影响TCSC的等效基波容抗,因而采用串接受控电压源来消除影响;最后通过TCSC对辐射线路电压调节的仿真分析,说明仿真时通过串接受控电压源可以消除晶闸管导通压降对调压的影响,而在实际应用中只需对查表进行修正,则同样可实现对电压进行精确调节。     

Hybrid‐type immittance converter

The immittance converter has an input impedance that is proportional to the admittance of a load connected across output terminals. Therefore, in this converter, the output current is proportional to the input voltage and the input current is proportional to the output voltage. Consequently, it converts a constant‐voltage source into a constant‐current source and a constant‐current source into a constant‐voltage source. It is well know that the quarter‐wavelength transmission line shows immittance conversion characteristics. However, it has a very long line length for the switching frequency of converters and is not suitable for power electronics application. Thus, we proposed five types of immittance converters that consist of lumped elements L and C and showed improved immittance conversion characteristics at a resonant frequency. The output characteristics and efficiency characteristics of an immittance converter are the most important parameter when it is used in practical applications in a high‐frequency link. In this paper, we show voltage–current transformation characteristics, current–voltage transformation characteristics, and efficiency characteristics of a hybrid‐type immittance converter which consist of L and C elements with losses. The excellent characteristics were confirmed analytically and experimentally. © 2001 Scripta Technica, Electr Eng Jpn, 138(3): 80–86, 2002     

可控串补等值阻抗的计算方法研究

利用小信号分析法 ,对可控串补的频率响应特性进行了研究。对可控串补输入小信号电流 ,求取可控串补中各电压电流 ,并利用傅里叶分析方法求得各信号的相应频率分量 ,进而求得可控串补的频率响应特性。该研究对可控串补系统的次同步谐振以及其他相关的谐波研究有重要意义 ,分析方法对其他FACTS元件的研究有借鉴作用。EMTP仿真验证了本文方法的有效性。     

A thyristor controlled series compensator model for the power flowsolution of practical power networks

A new and comprehensive load flow model for the thyristor controlled series compensator (TCSC) is presented in this paper. In this model the state variable is the TCSC's firing angle, which is combined with the nodal voltage magnitudes and angles of the entire network in a single frame-of-reference for a unified iterative solution through a Newton-Raphson method. Unlike TCSC models available in the open literature, this model takes account of the loop current that exists in the TCSC under both partial and full conduction operating modes. Also, the model takes proper care of the resonant points exhibited by the TCSC fundamental frequency impedance. The Newton-Raphson algorithm exhibits quadratic or near-quadratic convergence characteristics, regardless of the size of the network and the number of TCSC devices