电力系统次同步振荡分析方法与抑制技术研究
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摘要
随着电力系统中单机容量不断增大、超大规模的远距离交直流混合输电和灵活交流输电装置的广泛应用,我国电网已进入了大容量、超高压、远距离的交直流混合输电时代。正是这一复杂电网结构和运行方式使次同步振荡(SSO)问题日渐凸现,针对该课题的研究面临诸多新的挑战。结合我国电网实际,对SSO分析方法和抑制技术进行了深入研究,主要内容如下：
(1)从线性系统频率响应的角度,对复转矩系数法的基本公式进行了深入推导和分析,得到了发电机电磁功率与转子角增量之间的复转矩复频域表达式,进而从系统稳定性的角度分析了复转矩系数法的适用性。结果表明,复转矩系数法适用于渐进稳定的多机系统。
在此基础上,以IEEE次同步振荡第二标准模型为研究对象,对复转矩系数法应用中的计算方法、非待研机组的轴系模型和非待研机组等效模型对分析结果的影响进行了分析。结果表明,非待研机组轴系采用单刚体模型与采用多质量块模型相比,在其自然扭振频率点附近的电气阻尼存在一定的差异,其他频率点基本一致；非研究发电机采用固定频率电源模型等效时会带来一定的误差,影响分析的准确性。研究结果进一步完善了复转矩系数法的理论体系。
(2)从发电机组扭振与HVDC相互作用的角度,深入阐述HVDC引起SSO的机理；提出了具有工程实用性的用于抑制SSO的附加次同步阻尼控制器(SSDC)方案,并研发了SSDC参数整定和特性分析的系统,通过对呼辽直流输电工程的抑制效果验证了其有效性。
(3)以国内第一个TCSC与HVDC并列运行的交直流系统-伊冯／呼辽系统为研究对象,采用复转矩系数和时域仿真法,分析了运行方式和补偿方式对SSO特性的影响。结果表明,联网运行增强了与交流系统的联系,增大了系统的电气阻尼,从而比解网运行方式更稳定；TCSC不仅改善了交流线路的稳定性,也增强了HVDC的电气阻尼,从而提高了系统的整体稳定性。
(4)对静止同步串联补偿器(SSSC)主动阻尼SSO的机理进行了分析。基于次同步频率下三相不平衡能够减少发电机电气侧与机械侧的能量交互的原理,提出了采用单相SSSC的抑制SSO的新方法。结果表明,该方案能够快速、有效抑制SSO,对系统三相电压不平衡度的影响在允许范围内。该方案大大降低了SSSC的应用成本,推进了SSSC的工程化进程。
(5)从理论上分析了VSC-HVDC阻尼SSO的机理,并采用复转矩系数法研究了控制方式和运行状态对阻尼特性的影响。提出通过为VSC-HVDC配置混合附加次同步阻尼控制器(H-SSDC)抑制串补引发的SSO的方法,并对其抑制效果进行了验证。研究结果表明,VSC-HVDC无论处于整流还是逆变状态,都能够显著提高相邻发电机的阻尼；配置H-SSDC后,VSC-HVDC能有效抑制其相邻机组因串补引发的SSO。
With the unit capacity and total installed capacity gradually expanding, and the FACTS equipments and HVDC transmission widely using in power system, the electric network of China has entered a period with the characteristic of large capacity, extra voltage, long distance and AC-DC hybrid transmission. Due to the complicated structure and complex operation condition of the grid, more and more attention is paid on the phenomena of subsynchronous oscillation (SSO), about which the research will encounter many new challenges. Considered the practical network, this dissertation focuses on the analysis of SSO and its countermeasures. The main work is as followings:
(1) From the view of frequency response of linear system, the basic formula of the complex torque coefficient approach is further derived, and then the complex frequency domain expression between electromagnetic torque and the rotor angular increment is obtained. From the view of system stability, the applicability of complex torque coefficient method is analyzed. The results show that the complex torque coefficient method can be used in the multi-machine system with asymptotic stability.
Based on IEEE Second Benchmark model for SSO, the impact of the calculation method, the shaft model of non-research unit and equivalent model of non-research model on the analysis results are analyzed. The results show that the electrical damping of non-research unit shaft with a single rigid body model and that with multi-mass models agree with each other well, except near its natural tensional vibration frequency.When non-research unit is equivalent to the power model, it will bring some errors, and analysis accuracy will be influenced. The results further improve the theoretical system of the complex torque coefficient method.
(2) In terms of interaction between the tensional oscillation and HVDC system, the mechanism of SSO caused by HVDC is analyzed in detail which provides the theoretic basis for SSO and its countermeasures. Furthermore, this dissertation proposes a design of SSDC for mitigating SSO caused by HVDC and develops particular software for parameter setting and characteristic analysis. Finally, SSDC is used in HU-LIAO HVDC system and its effectiveness is proved.
(3) Focus on the first AC-DC parallel transmission system with TCSC in China, the impact of operation mode and compensation mode on the SSO characteristic is analyzed, using the complex torque coefficient and time domain simulation method. The results show grid connection mode is more stable than separate grid mode and TCSC can effectively enhance the stability of AC line and HVDC system, thus improve the total power grid stability.
(4) The mechanism of SSSC on active damping SSO is analyzed theoretically. A new method based on single-phase SSSC for mitigating SSO is proposed following the principle that the energy converting between the electrical and mechanical side of generator will be reduced in unbalanced three-phase system. The conclusions provide that the single-phase SSSC can inhibit SSO problem quickly and effectively in the tolerance of three-phase unbalance factor of the network.
(5) The damping characteristic of VSC-HVDC is analyzed in this dissertation. Then the complex torque coefficient method is adopted to investigate the impact of control strategy and operation condition on the damping characteristic. A method of using VSC-HVDC equipped with hybrid SSDC (H-SSDC) is proposed to damp SSO caused by the fixed series compensation, and its effectiveness is verified in a typical system. The results show that the VSC-HVDC can largely improve the electrical damping on the adjacent unites, and with H-SSDC, VSC-HVDC can effectively mitigate SSO resulting from the fixed series compensation.
(1)从线性系统频率响应的角度,对复转矩系数法的基本公式进行了深入推导和分析,得到了发电机电磁功率与转子角增量之间的复转矩复频域表达式,进而从系统稳定性的角度分析了复转矩系数法的适用性。结果表明,复转矩系数法适用于渐进稳定的多机系统。
在此基础上,以IEEE次同步振荡第二标准模型为研究对象,对复转矩系数法应用中的计算方法、非待研机组的轴系模型和非待研机组等效模型对分析结果的影响进行了分析。结果表明,非待研机组轴系采用单刚体模型与采用多质量块模型相比,在其自然扭振频率点附近的电气阻尼存在一定的差异,其他频率点基本一致；非研究发电机采用固定频率电源模型等效时会带来一定的误差,影响分析的准确性。研究结果进一步完善了复转矩系数法的理论体系。
(2)从发电机组扭振与HVDC相互作用的角度,深入阐述HVDC引起SSO的机理；提出了具有工程实用性的用于抑制SSO的附加次同步阻尼控制器(SSDC)方案,并研发了SSDC参数整定和特性分析的系统,通过对呼辽直流输电工程的抑制效果验证了其有效性。
(3)以国内第一个TCSC与HVDC并列运行的交直流系统-伊冯／呼辽系统为研究对象,采用复转矩系数和时域仿真法,分析了运行方式和补偿方式对SSO特性的影响。结果表明,联网运行增强了与交流系统的联系,增大了系统的电气阻尼,从而比解网运行方式更稳定；TCSC不仅改善了交流线路的稳定性,也增强了HVDC的电气阻尼,从而提高了系统的整体稳定性。
(4)对静止同步串联补偿器(SSSC)主动阻尼SSO的机理进行了分析。基于次同步频率下三相不平衡能够减少发电机电气侧与机械侧的能量交互的原理,提出了采用单相SSSC的抑制SSO的新方法。结果表明,该方案能够快速、有效抑制SSO,对系统三相电压不平衡度的影响在允许范围内。该方案大大降低了SSSC的应用成本,推进了SSSC的工程化进程。
(5)从理论上分析了VSC-HVDC阻尼SSO的机理,并采用复转矩系数法研究了控制方式和运行状态对阻尼特性的影响。提出通过为VSC-HVDC配置混合附加次同步阻尼控制器(H-SSDC)抑制串补引发的SSO的方法,并对其抑制效果进行了验证。研究结果表明,VSC-HVDC无论处于整流还是逆变状态,都能够显著提高相邻发电机的阻尼；配置H-SSDC后,VSC-HVDC能有效抑制其相邻机组因串补引发的SSO。
With the unit capacity and total installed capacity gradually expanding, and the FACTS equipments and HVDC transmission widely using in power system, the electric network of China has entered a period with the characteristic of large capacity, extra voltage, long distance and AC-DC hybrid transmission. Due to the complicated structure and complex operation condition of the grid, more and more attention is paid on the phenomena of subsynchronous oscillation (SSO), about which the research will encounter many new challenges. Considered the practical network, this dissertation focuses on the analysis of SSO and its countermeasures. The main work is as followings:
(1) From the view of frequency response of linear system, the basic formula of the complex torque coefficient approach is further derived, and then the complex frequency domain expression between electromagnetic torque and the rotor angular increment is obtained. From the view of system stability, the applicability of complex torque coefficient method is analyzed. The results show that the complex torque coefficient method can be used in the multi-machine system with asymptotic stability.
Based on IEEE Second Benchmark model for SSO, the impact of the calculation method, the shaft model of non-research unit and equivalent model of non-research model on the analysis results are analyzed. The results show that the electrical damping of non-research unit shaft with a single rigid body model and that with multi-mass models agree with each other well, except near its natural tensional vibration frequency.When non-research unit is equivalent to the power model, it will bring some errors, and analysis accuracy will be influenced. The results further improve the theoretical system of the complex torque coefficient method.
(2) In terms of interaction between the tensional oscillation and HVDC system, the mechanism of SSO caused by HVDC is analyzed in detail which provides the theoretic basis for SSO and its countermeasures. Furthermore, this dissertation proposes a design of SSDC for mitigating SSO caused by HVDC and develops particular software for parameter setting and characteristic analysis. Finally, SSDC is used in HU-LIAO HVDC system and its effectiveness is proved.
(3) Focus on the first AC-DC parallel transmission system with TCSC in China, the impact of operation mode and compensation mode on the SSO characteristic is analyzed, using the complex torque coefficient and time domain simulation method. The results show grid connection mode is more stable than separate grid mode and TCSC can effectively enhance the stability of AC line and HVDC system, thus improve the total power grid stability.
(4) The mechanism of SSSC on active damping SSO is analyzed theoretically. A new method based on single-phase SSSC for mitigating SSO is proposed following the principle that the energy converting between the electrical and mechanical side of generator will be reduced in unbalanced three-phase system. The conclusions provide that the single-phase SSSC can inhibit SSO problem quickly and effectively in the tolerance of three-phase unbalance factor of the network.
(5) The damping characteristic of VSC-HVDC is analyzed in this dissertation. Then the complex torque coefficient method is adopted to investigate the impact of control strategy and operation condition on the damping characteristic. A method of using VSC-HVDC equipped with hybrid SSDC (H-SSDC) is proposed to damp SSO caused by the fixed series compensation, and its effectiveness is verified in a typical system. The results show that the VSC-HVDC can largely improve the electrical damping on the adjacent unites, and with H-SSDC, VSC-HVDC can effectively mitigate SSO resulting from the fixed series compensation.
引文
[1]刘振亚.特高压电网[M].北京：中国经济出版社,2005：1-10
[2]周小谦.我国“西电东送”的发展历史、规划和实施.电网技术,2003,27(5)：1-5
[3]周孝信,郭剑波,林集明,武守远.电力系统可控串联电容补偿[M].北京：科学出版社,2009：38-45
[4]P. M. Anderson, R. G. Farmer.电力系统串联补偿[M].北京：中国电力出版社,2008：55-75
[5]任树东.上都电厂串补输电方案次同步谐振专题研究[M].北京： 北京国电华北电力工程有限公司,2005：20-45
[6]杨煜,陈陈.伊敏—大庆500 kV输电系统次同步谐振分析.电网技术,2000,24(5)：10-12
[7]程时杰,曹一家,江全元.电力系统次同步振荡的理论与方法[M].北京：科学出版社,2009：3-19
[8]徐政,交直流电力系统动态特性行为分析[M].北京：机械工业出版社,2005：89-99
[9]文劲宇,孙海顺,程时杰.电力系统的次同步振荡问题[J].电力系统保护与控制,2008,36(12)：1-7
[10]IEEE Subsynchronous Resonance Working Group Terms, definitions and symbols for subsynchronous oscillations[J]. IEEE Transactions on Power Apparatus and Systems,1985,104(6):1326-1333
[11]倪以信,陈寿孙,张宝霖.动态电力系统的理论与分析[M].北京：清华大学出版社,2002：12-23
[12]徐政,罗惠群,祝瑞金.电力系统次同步振荡问题的分析方法概述[J].电网技术,1999,23(6)：36-39
[13]伍凌云.复杂交直流输电系统次同步振荡的分析与控制[博士学位论文].成都：四川大学,2007：38-39
[14]Canay I M. A novel approach to the torsional interaction and electrical damping of the synchronous machine[J]. IEEE transactions on Power Appatatus and Systems. 1982,101(10):3630-3647
[15]张帆.电力系统次同步振荡抑制技术研究[博士学位论文].杭州：浙江大学,2007：20-31
[16]赵洋.静止同步串联补偿器控制策略及抑制次同步谐振的研究[博士学位论文].北京：华北电力大学,2009：31-35
[17]C.E.J.Bowler, D.H.Baker, N.A.Mincer, P.R.Vandiveer. Operation and Test of the Navajo SSR Protective Equipment[J]. IEEE Trans. on Power Apparatus and Systems,1978,97(4):1030-1035
[18]Padiyar K R. Analysis of Subsynchronous Resonance in Power Systems[M]. Massachusetts:Kluwer Academic Pubilisher,1998:32-39
[19]冯辰虎,高永峰,秦俊杰,刘平,刘海东,陈宁,孙瑜.托克托电厂阻塞滤波 器系统二次回路设计的改进[J].电网技术,2010,(05)：24-26
[20]高俊,丁洪发.典型FACTS元件抑制次同步谐振研究综述[J].电力自动化设备,2001,21(5)：45-50
[21]张远取,谢小荣,姜齐荣.应用附加励磁阻尼控制抑制HVDC引起的次同步振荡[J].电力系统保护与控制,2010,(04)：1-5
[22]郭锡玖,谢小荣,刘世宇,等.上都电厂SEDC提高次同步扭振阻尼的现场试验[J].电力系统自动化,2008,32(10)：97-100
[23]谢小荣,刘世宇,张树卿等.附加励磁阻尼控制抑制多模态SSR的机理及其关键技术[J].电力系统自动化,2007,31(21)：10-14
[24]张帆,徐政.采用SVC抑制发电机次同步谐振的理论与实践[J].高电压技术,2007,33(3)：26-31
[25]庞亚东,白秀娟.基于SVC抑制次同步谐振的应用研究[J].电气应用,2010,(17)：32-35
[26]刘世宇,谢小荣,张东辉.多模式次同步谐振的产生机理与抑制方法[J].清华大学学报,2008,48(4)：457-460
[27]刘丽红,张明理,张雪华.伊冯串补动态特性仿真及对电网稳定性影响研究[J].东北电力技术,2010,18(11)：10-12
[28]韩顺实,蔡金博.可控串补及其在500kV冯屯串补站的应用[J].吉林电力2010,23(02)：42-45
[29]谢小荣,姜齐荣.柔性交流输电系统的原理与应用[M].北京：清华大学出版社,2006：102-108
[30]刘黎明,康勇,陈坚,朱鹏程.SSSC建模、控制策略及性能.电工技术学报,2006,21(9)：37-43
[31]Jowder, F.A.R.A., Boon-Teck Ooi. Series Compensation of Radial Power System by a Combination of SSSC and Dielectric Capacitors. IEEE Transactions on Power Delivery,2005,20(1):458-465
[32]李立,洪潮.贵广二回直流输电系统次同步振荡问题分析[J].电力系统自动化,2007,31(7)：90-93
[33]徐大鹏,李兴源,熊萍,艾飞.含串补的交直流输电系统次同步谐振抑制[J].电网技术,2009,33(7)：20-23
[34]周长春.高压直流输电系统次同步振荡阻尼特性研究[博士学位论文].杭州：浙江大学,2004：42-53
[35]倪以信,王艳春,陈寿孙,等.多机系统HVDC的轴系扭振的扫频一复数力矩系数分析[J].电力系统及其自动化学报,1991,3(2)：44-55
[36]倪以信,王艳春,陈寿孙,等.多机系统直流输电引起的次同步振荡的研究[J].中国电机工程学报,1993,13(2)：64-71
[37]徐政.复转矩系数法的适用性分析及其时域仿真实现[J].中国电机工程学报,2000,20(6)：1-4
[38]Chung W T,David A K. Adaptive Pole-placement Controller for HVDC Link[A].In:Proceeding of the 4th International Conference on Advances in Power System Control[C]. Lodz Poland:Institute of Mechatronics and Information Systems,2004:1-6
[39]Bjorklind H, Johansson K E, Liss G..Damping of Subsynchronous Oscillations in Systems Containing Turbine Generators and HVDC Links[J]. IEEE Transactions on Power Systems,2007,22(1):314-323
[40]Y.Y.Hsu, L. Wang. Modal control of HVDC System Oscillations. IEE Proceedings Part C,1989,136(2):78-86
[41]江全元,程时杰,曹一家.基于遗传算法的HVDC附加次同步阻尼控制器的设计.中国电机工程学报,2002,22(11)：87-91
[42]杨秀,王西田,陈陈.高压直流输电系统逆变站对次同步振荡的影响及鲁棒控制设计.上海交通大学学报,2005,39(1)：31-35
[43]曹一家,陶佳,王光增,等FACTS控制器间交互影响及协调控制研究进展.电力系统及其自动化学报,2008,20(1)：1-8
[44]周长春,徐政.串补AC/DC系统次同步振荡阻尼特性分析[J].高电压技术,2004,30(2)：1-3
[45]Tamura T, Sasaki T, Ishikawa S, et al. Analysis of the steady state characteristics of doubly fed synchronous machines[J]. IEEE Transactions on Energy Conversion, 1989,4(2):250-256
[46]Jowder, F.A.L. Influence of mode of operation of the SSSC on the small disturbance and transient stability of a radial power system[J]. IEEE Transactions on Power Systems,2005,20(2):935-942
[47]CANA Y I M. AG.N.Pillai, Arindam Ghosh, Avinash Joshi. Torsional interaction studies on a power system compensated by SSSC and fixed capacitor[J]. IEEE Trans, on Power Delivery,2003,18(3):988-993
[48]Jowder, F.A.R.A., Boon-Teck Ooi. Series Compensation of Radial Power System by a Combination of SSSC and Dielectric Capacitors[J]. IEEE Transactions on Power Delivery,2005,20(1):458-465
[49]B.T.Ooi,S.Z.Dai,X.Wang.Solid state series capacitive reactance compensator. IEEE Trans on Power Del,1992,7(2):914-919.
[50]Abdel-Aty Edris. Series Compensation Schemes reducing the potential of subsynchronous resonance[J]. IEEE Transactions on Power System,1990,5(1): 219-226
[51]K. K. Sen. SSSC-static synchronous series compensator theory modeling and application[J]. IEEE Trans Power Del,1998,13(1):241-246
[52]Wang, H.F. Design of SSSC damping controller to improve power system oscillation stability [A]. In:AFRICON[C]. Cape Town:Institute of Mechatronics and Information Systems,1999:495-500
[53]程汉湘.柔性交流输电系统[M].北京：机械工业出版社,2010：38-35
[54]M. R. Iravani and A. Edris, Eigen analysis of series compensation schemes reducing the potential of subsynchronous resonance[J]. IEEE Trans. Power Syst., 1995,10(2):876-883
[55]Dipendra Rai, G. Ramakrishna, Sherif O. Faried, Abdel-Aty Edris. Enhancement of Power System Dynamics Using a Phase Imbalanced Series Compensation Scheme. IEEE Transaction on Power System,2010,25(2):966-974
[56]D. Rai, S.O. Faried, G. Ramakrishna, A. Edris. Hybrid series compensation scheme capable of damping subsynchronous resonance. IET Generation, Transmission & Distribution,2010,4(3):456-466
[57]梁海峰,李庚银,李广凯,等.向无源网络供电的VSC-HVDC系统仿真研究[J].电网技术,2005,29(8)：45-50
[58]李庚银,吕鹏飞,李广凯,等.轻型高压直流输电的发展与展望[J].电力系统自动化,2003,27(4)：77-81
[59]Xiao Wang, Boon-Tech Ooi. High voltage direct current transmission system based on voltage source converters[A]. In:Power Electronics Specialists Conference[C].San Antonio:21st Annual IEEE,2009:325-332
[60]汤广福.基于电压源换流器的高压直流输电技术[M].北京：中国电力出版社,2010：34-44
[61]徐政,陈海荣.电压源换流器型直流输电技术综述[J].高电压技术,2007,33(1)：1-10
[62]王凤川.电压源换流器式轻型高压直流输电[J].电网技术,1999,23(4)：74-76
[63]武娟,任震,黄雯莹.轻型直流输电的运行机理和特性分析[J].华南理工大学学报,2001,29(8)：41-44
[64]尹明,李庚银,李广凯.VSC-HVDC连续时间状态空间模型及其控制策略研究[J].中国电机工程学报,2005,18(3)：34-39
[65]张桂斌,徐政,王广柱.基于VSC的直流输电系统的稳态建模及其非线性控制.中国电机工程学报,2002,22(1)：17-22
[66]刘洪涛,徐政. 基于三电平电压源换流器的高压直流输电系统的控制策略研究.电工技术学报,2003,18(3)：31-34
[67]L Ronstrm, B D Railing, J J Miller, et al.Cross sound cable project second generation VSC technology for HVDC[A]. Institute of Electrical and Electronics Engineers Computer Society,2005:2481-2486
[68]F.A.R. Al Jowder, B.T. Ooi. VSC-HVDC station with SSSC characteristics[J]. IEEE Trans. Power Electron,2004,19(4):1053-1059
[69]G.Asplun. Application of HVDC light to power system enhancement A]. In:IEEE Power Engineering Society Winter Meeting[C]. USA:IEEE,2000:2498-2503
[70]Ying, J.-H., H.Duchen, et. Improvement of subsynchronous torsional damping using VSC HVDC[A]. In:Power System Technology[C]. Sweden:Institute of Electrical and Electronics Engineers Computer Society,2002:443-449
[71]Prabhu, N. and K. R. Padiyar. Investigation of Subsynchronous Resonance With VSC-Based HVDC Transmission Systems[J]. IEEE Transactions on Power Delivery,2009,24(1):433-440
[72]Guosheng Tang. Damping subsynchronous resonance oscillations using a VSC-HVDC Back to Back system[D]. Canada:University of Saskatchewan, 2006:68-90
[73]郑超,汤涌,等.基于等效仿真模型的VSC-HVDC次同步振荡阻尼特性分析[J].中国电机工程学报,2007,27(31)：34-39
[74]李吉芳.复转矩系数法应用于多机电力系统的修正[J].继电器,2004,32(8)： 5-8
[75]姜齐荣,陈湘,多机系统复转矩系数分析及PSS参数计算[J].电力系统及其自动化学报,2010,22(1)：20-25
[76]夏道止.电力系统分析[M].北京：中国电力出版社,2004：185,237-247
[77]IEEE subsynchronous resonance working group. Second benchmark model for computer simulation of subsynchronous resonance[J]. IEEE Trans on Power Apparatus and System,1985, Vol PAS-104(5):1057-1066
[78]周长春,徐政.由直流输电引起的次同步振荡的阻尼特性分析[J].中国电机工程学报,2003,23(10)：6-10
[79]周长春,刘前进.抑制次同步谐振的TCSC主动阻尼控制[J].中国电机工程学报,2008,8(15)：130-135
[80]王成祥,李建设.南方电网交直流联网运行特性分析[J].电力系统自动化,2003,27(16)：84-86
[81]杨秀,陈陈,王西田.HVDC控制系统对汽轮发电机组次同步振荡的影响[J].电网技术,2004,28(5)：5-8
[82]J.D.Ainsworth. Proposed benchmark model for study of HVDC controls by simulator or digital computer[A]. In:Proc.CIGRE SC-14 [C]. Calgary Canada: IEEE Computer Society,2009:1-11
[83]V. Atarod, P. L. Dandeno, M. R. Iravani. Impact of synchronous machine constants and models on the analysis of torsional dynamics[J]. IEEE Trans, on Power System,1992,7(4):1456-1463
[84]D. N. Walker, C. E. J. Bowler, D. H. Baker. Torsional dynamics of closely coupled turbine-generators[J]. IEEE Trans. on Power Apparatus and Systems, 1978,97(4):1458-1466
[85]Kundur P. Power System Stability and Control[M]. New York:McGraw-Hill Inc, 2002:345-356
[86]IEEE Subsynchronous Resonance Working Group. First benchmark model for computer simulation of subsynchronous resonance[J]. IEEE Trans. on Power Apparatus and Systems,1977,96(5):1565-1672
[87]EPRI. HVDC system control for damping of subsynchronous oscillations[R].New York:HVDC Research group,1982:23-26
[88]东北-华北联网高岭背靠背换流站工程功能规范书[Z].北京：网联直流工程技术有限公司,2007：35-39
[89]曹路,陈珩.可控串联补偿抑制次同步谐振的机理[J].电力系统自动化,2001,25(4)：25-31
[90]吕世荣,刘晓鹏,郭强,等.TCSC对抑制次同步谐振的机理分析[J].电力系统自动化,1999,23(6)：14-18
[91]汤海雁,武守远,周孝信.可控串补次同步频率等效阻抗特性的机理分析[J].中国电机工程学报,2008,25(6)：16-23
[92]童陆园,葛俊.TCSC抑制次同步谐振的机理分析[J].电力系统自动化,2002,26(2)：18-21
[93]GB/T 15543.三相电压允许不平衡度[S].北京：中国电力出版社,1995：1-2
[2]周小谦.我国“西电东送”的发展历史、规划和实施.电网技术,2003,27(5)：1-5
[3]周孝信,郭剑波,林集明,武守远.电力系统可控串联电容补偿[M].北京：科学出版社,2009：38-45
[4]P. M. Anderson, R. G. Farmer.电力系统串联补偿[M].北京：中国电力出版社,2008：55-75
[5]任树东.上都电厂串补输电方案次同步谐振专题研究[M].北京： 北京国电华北电力工程有限公司,2005：20-45
[6]杨煜,陈陈.伊敏—大庆500 kV输电系统次同步谐振分析.电网技术,2000,24(5)：10-12
[7]程时杰,曹一家,江全元.电力系统次同步振荡的理论与方法[M].北京：科学出版社,2009：3-19
[8]徐政,交直流电力系统动态特性行为分析[M].北京：机械工业出版社,2005：89-99
[9]文劲宇,孙海顺,程时杰.电力系统的次同步振荡问题[J].电力系统保护与控制,2008,36(12)：1-7
[10]IEEE Subsynchronous Resonance Working Group Terms, definitions and symbols for subsynchronous oscillations[J]. IEEE Transactions on Power Apparatus and Systems,1985,104(6):1326-1333
[11]倪以信,陈寿孙,张宝霖.动态电力系统的理论与分析[M].北京：清华大学出版社,2002：12-23
[12]徐政,罗惠群,祝瑞金.电力系统次同步振荡问题的分析方法概述[J].电网技术,1999,23(6)：36-39
[13]伍凌云.复杂交直流输电系统次同步振荡的分析与控制[博士学位论文].成都：四川大学,2007：38-39
[14]Canay I M. A novel approach to the torsional interaction and electrical damping of the synchronous machine[J]. IEEE transactions on Power Appatatus and Systems. 1982,101(10):3630-3647
[15]张帆.电力系统次同步振荡抑制技术研究[博士学位论文].杭州：浙江大学,2007：20-31
[16]赵洋.静止同步串联补偿器控制策略及抑制次同步谐振的研究[博士学位论文].北京：华北电力大学,2009：31-35
[17]C.E.J.Bowler, D.H.Baker, N.A.Mincer, P.R.Vandiveer. Operation and Test of the Navajo SSR Protective Equipment[J]. IEEE Trans. on Power Apparatus and Systems,1978,97(4):1030-1035
[18]Padiyar K R. Analysis of Subsynchronous Resonance in Power Systems[M]. Massachusetts:Kluwer Academic Pubilisher,1998:32-39
[19]冯辰虎,高永峰,秦俊杰,刘平,刘海东,陈宁,孙瑜.托克托电厂阻塞滤波 器系统二次回路设计的改进[J].电网技术,2010,(05)：24-26
[20]高俊,丁洪发.典型FACTS元件抑制次同步谐振研究综述[J].电力自动化设备,2001,21(5)：45-50
[21]张远取,谢小荣,姜齐荣.应用附加励磁阻尼控制抑制HVDC引起的次同步振荡[J].电力系统保护与控制,2010,(04)：1-5
[22]郭锡玖,谢小荣,刘世宇,等.上都电厂SEDC提高次同步扭振阻尼的现场试验[J].电力系统自动化,2008,32(10)：97-100
[23]谢小荣,刘世宇,张树卿等.附加励磁阻尼控制抑制多模态SSR的机理及其关键技术[J].电力系统自动化,2007,31(21)：10-14
[24]张帆,徐政.采用SVC抑制发电机次同步谐振的理论与实践[J].高电压技术,2007,33(3)：26-31
[25]庞亚东,白秀娟.基于SVC抑制次同步谐振的应用研究[J].电气应用,2010,(17)：32-35
[26]刘世宇,谢小荣,张东辉.多模式次同步谐振的产生机理与抑制方法[J].清华大学学报,2008,48(4)：457-460
[27]刘丽红,张明理,张雪华.伊冯串补动态特性仿真及对电网稳定性影响研究[J].东北电力技术,2010,18(11)：10-12
[28]韩顺实,蔡金博.可控串补及其在500kV冯屯串补站的应用[J].吉林电力2010,23(02)：42-45
[29]谢小荣,姜齐荣.柔性交流输电系统的原理与应用[M].北京：清华大学出版社,2006：102-108
[30]刘黎明,康勇,陈坚,朱鹏程.SSSC建模、控制策略及性能.电工技术学报,2006,21(9)：37-43
[31]Jowder, F.A.R.A., Boon-Teck Ooi. Series Compensation of Radial Power System by a Combination of SSSC and Dielectric Capacitors. IEEE Transactions on Power Delivery,2005,20(1):458-465
[32]李立,洪潮.贵广二回直流输电系统次同步振荡问题分析[J].电力系统自动化,2007,31(7)：90-93
[33]徐大鹏,李兴源,熊萍,艾飞.含串补的交直流输电系统次同步谐振抑制[J].电网技术,2009,33(7)：20-23
[34]周长春.高压直流输电系统次同步振荡阻尼特性研究[博士学位论文].杭州：浙江大学,2004：42-53
[35]倪以信,王艳春,陈寿孙,等.多机系统HVDC的轴系扭振的扫频一复数力矩系数分析[J].电力系统及其自动化学报,1991,3(2)：44-55
[36]倪以信,王艳春,陈寿孙,等.多机系统直流输电引起的次同步振荡的研究[J].中国电机工程学报,1993,13(2)：64-71
[37]徐政.复转矩系数法的适用性分析及其时域仿真实现[J].中国电机工程学报,2000,20(6)：1-4
[38]Chung W T,David A K. Adaptive Pole-placement Controller for HVDC Link[A].In:Proceeding of the 4th International Conference on Advances in Power System Control[C]. Lodz Poland:Institute of Mechatronics and Information Systems,2004:1-6
[39]Bjorklind H, Johansson K E, Liss G..Damping of Subsynchronous Oscillations in Systems Containing Turbine Generators and HVDC Links[J]. IEEE Transactions on Power Systems,2007,22(1):314-323
[40]Y.Y.Hsu, L. Wang. Modal control of HVDC System Oscillations. IEE Proceedings Part C,1989,136(2):78-86
[41]江全元,程时杰,曹一家.基于遗传算法的HVDC附加次同步阻尼控制器的设计.中国电机工程学报,2002,22(11)：87-91
[42]杨秀,王西田,陈陈.高压直流输电系统逆变站对次同步振荡的影响及鲁棒控制设计.上海交通大学学报,2005,39(1)：31-35
[43]曹一家,陶佳,王光增,等FACTS控制器间交互影响及协调控制研究进展.电力系统及其自动化学报,2008,20(1)：1-8
[44]周长春,徐政.串补AC/DC系统次同步振荡阻尼特性分析[J].高电压技术,2004,30(2)：1-3
[45]Tamura T, Sasaki T, Ishikawa S, et al. Analysis of the steady state characteristics of doubly fed synchronous machines[J]. IEEE Transactions on Energy Conversion, 1989,4(2):250-256
[46]Jowder, F.A.L. Influence of mode of operation of the SSSC on the small disturbance and transient stability of a radial power system[J]. IEEE Transactions on Power Systems,2005,20(2):935-942
[47]CANA Y I M. AG.N.Pillai, Arindam Ghosh, Avinash Joshi. Torsional interaction studies on a power system compensated by SSSC and fixed capacitor[J]. IEEE Trans, on Power Delivery,2003,18(3):988-993
[48]Jowder, F.A.R.A., Boon-Teck Ooi. Series Compensation of Radial Power System by a Combination of SSSC and Dielectric Capacitors[J]. IEEE Transactions on Power Delivery,2005,20(1):458-465
[49]B.T.Ooi,S.Z.Dai,X.Wang.Solid state series capacitive reactance compensator. IEEE Trans on Power Del,1992,7(2):914-919.
[50]Abdel-Aty Edris. Series Compensation Schemes reducing the potential of subsynchronous resonance[J]. IEEE Transactions on Power System,1990,5(1): 219-226
[51]K. K. Sen. SSSC-static synchronous series compensator theory modeling and application[J]. IEEE Trans Power Del,1998,13(1):241-246
[52]Wang, H.F. Design of SSSC damping controller to improve power system oscillation stability [A]. In:AFRICON[C]. Cape Town:Institute of Mechatronics and Information Systems,1999:495-500
[53]程汉湘.柔性交流输电系统[M].北京：机械工业出版社,2010：38-35
[54]M. R. Iravani and A. Edris, Eigen analysis of series compensation schemes reducing the potential of subsynchronous resonance[J]. IEEE Trans. Power Syst., 1995,10(2):876-883
[55]Dipendra Rai, G. Ramakrishna, Sherif O. Faried, Abdel-Aty Edris. Enhancement of Power System Dynamics Using a Phase Imbalanced Series Compensation Scheme. IEEE Transaction on Power System,2010,25(2):966-974
[56]D. Rai, S.O. Faried, G. Ramakrishna, A. Edris. Hybrid series compensation scheme capable of damping subsynchronous resonance. IET Generation, Transmission & Distribution,2010,4(3):456-466
[57]梁海峰,李庚银,李广凯,等.向无源网络供电的VSC-HVDC系统仿真研究[J].电网技术,2005,29(8)：45-50
[58]李庚银,吕鹏飞,李广凯,等.轻型高压直流输电的发展与展望[J].电力系统自动化,2003,27(4)：77-81
[59]Xiao Wang, Boon-Tech Ooi. High voltage direct current transmission system based on voltage source converters[A]. In:Power Electronics Specialists Conference[C].San Antonio:21st Annual IEEE,2009:325-332
[60]汤广福.基于电压源换流器的高压直流输电技术[M].北京：中国电力出版社,2010：34-44
[61]徐政,陈海荣.电压源换流器型直流输电技术综述[J].高电压技术,2007,33(1)：1-10
[62]王凤川.电压源换流器式轻型高压直流输电[J].电网技术,1999,23(4)：74-76
[63]武娟,任震,黄雯莹.轻型直流输电的运行机理和特性分析[J].华南理工大学学报,2001,29(8)：41-44
[64]尹明,李庚银,李广凯.VSC-HVDC连续时间状态空间模型及其控制策略研究[J].中国电机工程学报,2005,18(3)：34-39
[65]张桂斌,徐政,王广柱.基于VSC的直流输电系统的稳态建模及其非线性控制.中国电机工程学报,2002,22(1)：17-22
[66]刘洪涛,徐政. 基于三电平电压源换流器的高压直流输电系统的控制策略研究.电工技术学报,2003,18(3)：31-34
[67]L Ronstrm, B D Railing, J J Miller, et al.Cross sound cable project second generation VSC technology for HVDC[A]. Institute of Electrical and Electronics Engineers Computer Society,2005:2481-2486
[68]F.A.R. Al Jowder, B.T. Ooi. VSC-HVDC station with SSSC characteristics[J]. IEEE Trans. Power Electron,2004,19(4):1053-1059
[69]G.Asplun. Application of HVDC light to power system enhancement A]. In:IEEE Power Engineering Society Winter Meeting[C]. USA:IEEE,2000:2498-2503
[70]Ying, J.-H., H.Duchen, et. Improvement of subsynchronous torsional damping using VSC HVDC[A]. In:Power System Technology[C]. Sweden:Institute of Electrical and Electronics Engineers Computer Society,2002:443-449
[71]Prabhu, N. and K. R. Padiyar. Investigation of Subsynchronous Resonance With VSC-Based HVDC Transmission Systems[J]. IEEE Transactions on Power Delivery,2009,24(1):433-440
[72]Guosheng Tang. Damping subsynchronous resonance oscillations using a VSC-HVDC Back to Back system[D]. Canada:University of Saskatchewan, 2006:68-90
[73]郑超,汤涌,等.基于等效仿真模型的VSC-HVDC次同步振荡阻尼特性分析[J].中国电机工程学报,2007,27(31)：34-39
[74]李吉芳.复转矩系数法应用于多机电力系统的修正[J].继电器,2004,32(8)： 5-8
[75]姜齐荣,陈湘,多机系统复转矩系数分析及PSS参数计算[J].电力系统及其自动化学报,2010,22(1)：20-25
[76]夏道止.电力系统分析[M].北京：中国电力出版社,2004：185,237-247
[77]IEEE subsynchronous resonance working group. Second benchmark model for computer simulation of subsynchronous resonance[J]. IEEE Trans on Power Apparatus and System,1985, Vol PAS-104(5):1057-1066
[78]周长春,徐政.由直流输电引起的次同步振荡的阻尼特性分析[J].中国电机工程学报,2003,23(10)：6-10
[79]周长春,刘前进.抑制次同步谐振的TCSC主动阻尼控制[J].中国电机工程学报,2008,8(15)：130-135
[80]王成祥,李建设.南方电网交直流联网运行特性分析[J].电力系统自动化,2003,27(16)：84-86
[81]杨秀,陈陈,王西田.HVDC控制系统对汽轮发电机组次同步振荡的影响[J].电网技术,2004,28(5)：5-8
[82]J.D.Ainsworth. Proposed benchmark model for study of HVDC controls by simulator or digital computer[A]. In:Proc.CIGRE SC-14 [C]. Calgary Canada: IEEE Computer Society,2009:1-11
[83]V. Atarod, P. L. Dandeno, M. R. Iravani. Impact of synchronous machine constants and models on the analysis of torsional dynamics[J]. IEEE Trans, on Power System,1992,7(4):1456-1463
[84]D. N. Walker, C. E. J. Bowler, D. H. Baker. Torsional dynamics of closely coupled turbine-generators[J]. IEEE Trans. on Power Apparatus and Systems, 1978,97(4):1458-1466
[85]Kundur P. Power System Stability and Control[M]. New York:McGraw-Hill Inc, 2002:345-356
[86]IEEE Subsynchronous Resonance Working Group. First benchmark model for computer simulation of subsynchronous resonance[J]. IEEE Trans. on Power Apparatus and Systems,1977,96(5):1565-1672
[87]EPRI. HVDC system control for damping of subsynchronous oscillations[R].New York:HVDC Research group,1982:23-26
[88]东北-华北联网高岭背靠背换流站工程功能规范书[Z].北京：网联直流工程技术有限公司,2007：35-39
[89]曹路,陈珩.可控串联补偿抑制次同步谐振的机理[J].电力系统自动化,2001,25(4)：25-31
[90]吕世荣,刘晓鹏,郭强,等.TCSC对抑制次同步谐振的机理分析[J].电力系统自动化,1999,23(6)：14-18
[91]汤海雁,武守远,周孝信.可控串补次同步频率等效阻抗特性的机理分析[J].中国电机工程学报,2008,25(6)：16-23
[92]童陆园,葛俊.TCSC抑制次同步谐振的机理分析[J].电力系统自动化,2002,26(2)：18-21
[93]GB/T 15543.三相电压允许不平衡度[S].北京：中国电力出版社,1995：1-2