Calculation of frequency response of thyristor‐controlled series capacitor

In this paper, we propose a method of analytically calculating an impedance of a thyristor‐controlled series capacitor (TCSC). The TCSC consists of a thyristor‐controlled reactor (TCR) and a capacitor. If a small voltage component of frequency f superimposes the TCSC voltage of frequency f_o, then current components of frequency (nf_o ± f) flow through the TCR, where n takes even numbers. We derive theoretical equations for them. In the derivation, we consider an influence of odd harmonics in the TCSC voltage. We also consider deviations in its zero‐crossing times due to the superimposed voltage. The current components flow through the capacitor and the transmission line, and produce new voltage components of frequency (nf_o ± f). In order to count their influence, we introduce admittance matrices for the TCR, the capacitor, and the transmission line. By solving a network equation consisting of the matrices, we can obtain the distribution of the voltage and current components. We define the impedance of TCSC as a ratio of the voltage component of frequency f to the current one of the same frequency. The impedance analytically obtained corresponds well with that obtained by simulations. Its frequency responses vary with the firing method of thyristors. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 139(3): 35–44, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.1158     

TCSC对发电机组次同步谐振阻尼特性影响研究

采用基于时域仿真实现的复转矩系数法—测试信号法研究了含有可控串补(TCSC)的电力系统中的次同步谐振(SSR)阻尼特性。采用 IEEE SSR第一标准测试系统模型,将其中部分固定串补电容改造为 TCSC。TCSC采用3种闭环控制方式如恒电流、恒功率及阻尼功率振荡控制。通过频率扫描计算出发电机组在次同步频率范围内的电气阻尼特性曲线,分别研究了开环控制和3 种不同闭环控制方式下 TCSC导通角对电气阻尼特性的影响。结果表明,不论在何种控制方式下,相对于固定电容串补,TCSC都能大大减小谐振点附近的电气负阻尼;TCSC的导通角对阻尼特性有很大影响,TCSC运行在较大导通角时可有效减小谐振点附近的电气负阻尼。     

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。     

Subsynchronous resonance analysis using a discrete time model of thyristor controlled series compensator

The characteristic of a thyristor controlled series compensator (TCSC) is nonlinear in nature. Usually the TCSC control systems employs a conventional type controller to obtain the reactance order, which in turn, is converted into the corresponding firing angle of the TCR through a look-up table. The main drawback of this approach is the absence of a closed-loop model through which the stability of the system can be analyzed. To alleviate this problem a linear, discrete-time state space model of a TCSC compensated transmission line in the d–q domain is proposed (Srivastava et al., Model-based control design of a TCSC compensated power system, to appear in Electrical Power and Energy Systems). This model is further utilized in this paper for damping torsional oscillations arising due to subsynchronous resonance (SSR). The model is interfaced with synchronous generator and turbine-shaft models to obtain a closed form homogeneous state space representation that is suitable for eigenvalue analysis. Through eigenvalue analysis it is shown that proper choice of control gains can effectively damp out SSR. The eigenvalue analysis results are subsequently validated through PSCAD/EMTDC simulation studies.     

Clarification of the SSR mitigation mechanism of a TCSC

A thyristor controlled series capacitor (TCSC) is considered to be effective not only for flow control and stabilization of power systems, but also for mitigation of subsynchronous resonance (SSR). This paper clarifies the SSR mitigation mechanism of a TCSC. First, using time simulations, we show that SSR appears and disappears depending on the firing angle of the TCSC. Next, we show that the frequency characteristics vary considerably with the firing angle. Further, we show that SSR occurs in TCSC-compensated systems as well as in conventional series-capacitor-compensated systems when 60 Hz minus the electrical resonance frequency of a transmission system coincides with the torsional oscillation frequency of a generator-turbine shaft. TCSC can avert SSR by changing the firing angle and by shifting the electrical resonance frequency. Next, we propose an equivalent circuit to TCSC which consists of a series capacitor in parallel with a resistor and a reactor. We adjust the parameters so that it shows the same frequency characteristics as TCSC. We apply it to time simulations to see if it is equivalent to TCSC. Finally, we perform an eigenvalue analysis on the equivalent circuit. We obtain results that correspond to the time simulations. © 1997 Scripta Technica, Inc. Electr Eng Jpn, 120(4): 31–39, 1997     

可控串补晶闸管阀触发控制的电容电压增量控制算法

根据TCSC的数学模型,研究了电容电压增量的特点和性质,提出了电容电压计量控制的触发算法。该算法中控制量计算所用参数均取自TCSC装置本身固定参数和运行参数的实测值,与TCSC安装位置和电力系统的运行方式无关。采用该算法的TCSC在实现阻抗控制的同时,可以对次同步分量快速调制,实现抑制SSR作用。     

可控串联电容补偿器的负阻尼特性研究

由于在暂稳控制器的设计中通常将可控串联电容补偿器(TCSC)处理为带限幅器的一阶惯性环节,而忽略了电力系统动态行为对TCSC脉冲触发过程影响以及装置动态响应特性的研究.文中建立了装有TCSC的电力系统的扩展Phillips Heffron模型,通过分析TCSC对系统同步和阻尼转矩的贡献,给出了在开环定触发角控制下TCSC表现为负阻尼特性的解析解.基于NETOMAC的数字仿真结果验证了模型分析的正确性,同时指出通过合适的底层控制策略可以减弱和消除负阻尼,有效地改善 TCSC的动态响应特性.     

抑制次同步谐振的TCSC主动阻尼控制

采用同步电压反转(synchronous voltage reversal,SVR)触发控制的可控串联补偿电容(thristor controlled series compensator,TCSC)本身不会诱发系统的次同步谐振(sub- synchronous resonance SSR),而且因为其在次同步频率范围内固有的感性阻抗特性,一直以来工程中都把TCSC作为一种缓解SSR的有效措施。虽然采用SVR触发的TCSC可缓解系统SSR的压力,但其本身却无法主动抑制SSR,该文提出一种TCSC的附加控制--主动阻尼控制,通过调节TCSC的触发,可使系统在危险振荡模式下向机组提供正值的电气阻尼,从而更好地抑制SSR。时域及频域的仿真也验证了该主动阻尼控制的有效性。     

数模混合式实时仿真装置中含多质量块轴系的发电机模型及其在工程研究中的应用

介绍了数模混合式实时仿真装置中多质量块轴系发电机模型的构成及其在伊冯可控串补工程中的应用。为了抑制或消除次同步谐振 (SSR) ,中国电科院 TCSC课题组提出了一种新的微调控制方法——电压增量控制 ,其基本原理是在SSR条件下保持电容电压增量水平接近稳态波形 ,使大部分SSR电流仅能通过晶闸管控制的电感支路。此时 ,串联电容补偿装置 (TCSC)呈电感特性 ,因此抑制次同步谐振是该方法的固有特性。通过接入 TCSC物理模拟控制器所进行的试验研究 ,验证了该方法在理论上是正确的 ,应用此策略的TCSC控制器可以有效地抑制或消除次同步谐振。     

TCSC对电力系统次同步谐振的影响

以IEEE次同步谐振第1标准模型为研究对象,采用扫频和时域仿真相结合的复转矩系数法,从系统阻尼特性的角度分析了系统发生SSR的危险性,并用时域仿真法验证了该方法的正确性.在系统中加入TCSC,通过对电气阻尼特性的深入研究,发现在一定的条件下,TCSC使系统的电气谐振点发生了偏移,从而破坏系统发生SSR的条件;但是TCSC运行在较小导通角时,可能引起系统负阻尼频带加宽的现象,从而引起系统的次同步振荡,并通过时域仿真验证了该现象的危险性.讨论了TCSC的参数设计原则,使TCSC能够最大限度地提高对SSR的抑制能力.     

含有可控串联补偿电容的电力系统次同步谐振研究

根据采用复数力矩系数法分析同步振荡要求,在分析ＴＣＳＣ的物理特性的基础上,建立了可控串联补偿电容（ＴＣＳＣ）的数字模型,推导出适用于复数力矩系数不地的ＴＣＳＣ的复频域等效端地纳矩阵,在此基础上可方便地利用复频域扫描法分析ＴＣＳＣ对电力系统交仙步谐振的影响。对１个２机５节点系统用所提方法进行了次同步谐振分析,同时进行了全时域数字仿真数字仿真结果验证了所提方法的有效性。     

TCSC次同步谐振阻尼控制器设计

输电线路采用串联电容补偿存在引起电力系统次同步谐振的危险,TCSC常用来解决这一问题。基于提升系统电气阻尼的思想,设计了TCSC附加阻尼控制器,该控制器针对分模态控制方法存在的不足进行了改进。基于IEEE SSR第一标准测试模型的分析表明改进后的控制器能将系统在几乎整个次同步频段内的电气阻尼提高为正,从而消除了该频段内的SSR危险。     

基于傅里叶分析的高压直流输电次同步振荡控制研究

当高压直流输电遭受短时扰动时,电气量变化产生的电磁转矩变化量所包含的电气负阻尼转矩,加剧了汽轮发电机的转速变化,使得输电线路中产生次同步振荡现象。文中通过傅里叶分析方法计算得出电网次同步振荡频率,在汽轮发电机的转子转速控制系统中通过调节励磁系统锁相环的频率合成,减小励磁电流波动,生成一个新的附加电磁转矩量,使最终的电气阻尼转矩分量为正,实现对转子转矩控制。仿真结果表明,在电网出现短时扰动时,汽轮发电机的转速没有出现大波动,实现了对次同步振荡的有效抑制。     

TCSC的次频阻抗特性

在假设可控串联补偿（TCSC）两端电压中工频分量和次频分量能够解耦的条件下,推导出了当在TCSC的基波电压上叠加一个微小的次同步频率分量电压的情况下,TCSC等效次频阻抗表达,式此基础上,分析了TCSC抑制次同步谐振的机理,分析表明,TCSC对次同步频率分量呈现正电阻特性,共抑制SSR的机理在于电阻效应和电感效应等的综合作用。仿真结果证实了 频模型分析结果的正确性。     

串补装置次同步谐振特性分析

通过在PSCAD中建立IEEE First Benchmark进行仿真,分析了FSC和TCSC的SSR特性。针对两者不同的特性,建立TCSC次频阻抗特性分析模型,重点分析TM4不稳模式,详细解释了TCSC抑制SSR的原因。基于TCSC的阻抗特性可以抑制SSR,进行了FSC+ TCSC的仿真实验,发现选择合适的参数可以使FSC+ TCSC的串补装置抑制SSR。     

复转矩系数法的适用性分析及其时域仿真实现

针对广泛应用于电力系统次同步振分析的复转矩系数法,对其成立的基本前提进行了分析,在此基础上,研究了其适用范围。对复转矩系数法与小扰动特征值分析法进行了比较,系统地评述了小扰动特征值分析法的特点,指出了复转矩系数法的到之处。提出了用时域仿真计算复转矩系数的方法,论证了本方法的可行性,并用时域仿真的方法计算了一个具体系统的复转矩系数。     

Damping torsional oscillations of nuclear generators by using firing delay angle modulation of HVDC schemes

The paper presents the results of hybrid simulation studies of HVDC firing delay angle (α) modulation as a countermeasure to subsynchronous resonance (SSR) torsional oscillations occurring in a nuclear generator interfaced to the rectifier terminals of an HVDC transmission scheme. SSR oscillations can be amplified owing to the negative damping introduced by the HVDC scheme. This report illustrates the α modulation scheme and presents hybrid simulator results to ascertain its effectiveness in damping the low frequency SSR oscillation due to HVDC system control interactions.     

Analysis of subsynchronous resonance with generalized unified power flow controller

The Generalized Unified Power Flow Controller (GUPFC) is one of the most versatile flexible ac transmission system (FACTS) controllers which controls the active and reactive power flows in multiple transmission lines originating from a substation while controlling the sending end bus voltage. The sending end bus voltage is regulated by control of shunt reactive current while the active and reactive power flows in the transmission line are regulated by series injected voltages. This paper reports the analysis and study of Subsynchronous Resonance (SSR) characteristics of hybrid compensated system with GUPFC. The various operating mode combinations of series and shunt converters are considered to investigate their effect on SSR characteristics. The methods of analysis of SSR with GUPFC is based on the evaluation of damping torque, eigenvalues of the system and transient simulation. The computation of damping torque considers D–Q model of GUPFC to determine the torsional mode stability. The study is performed on a system adapted from IEEE Second Benchmark Model (SBM). The results demonstrate the effectiveness of series real injected voltage in mitigating the SSR.     

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

     

Investigation of SSR characteristics of unified power flow controller

The unified power flow controller (UPFC) is the most versatile flexible ac transmission system (FACTS) controller which can be used to control active and reactive power flows in a transmission line in addition to the bus voltage. The active series compensation is provided by injecting series reactive voltage. The voltage at the two ports of UPFC are regulated by control of shunt current and series real voltage. It also has several operating control modes such as voltage and power regulation, line impedance compensation, etc. This paper presents the analysis and study of sub-synchronous resonance (SSR) characteristics of UPFC. The various combination of operating modes of shunt and series converters are considered for investigating their effect on SSR characteristics.The analysis of SSR with UPFC is carried out based on frequency domain method, eigenvalue analysis and transient simulation. The frequency domain method considers D-Q model of UPFC for the computation of damping torque for quick check in determining torsional mode stability. The study is performed on IEEE First Benchmark Model (FBM).