汽轮机发电机组宽频带阻抗建模及次/超同步振荡分析

doi:10.11930/j.issn.1004-9649.202312081

摘要/Abstract

摘要：

基于阻抗的建模与分析方法是目前分析和解决新能源并网宽频带振荡问题的有效工具之一。集中开发远距离输送是中国新能源开发利用的重要形式，在新能源基地的发电装备中，风光发电装备的阻抗模型已经较为完善，但是现有汽轮发电机组的宽频带阻抗模型均存在一定的简化，不能完整地反映汽轮发电机组的宽频带阻抗特性。基于频域小信号建模方法，建立了计及原动机、调速器、励磁系统、轴系和同步机的汽轮发电机宽频阻抗模型，在Matlab/Simulink中建立了汽轮发电机的仿真模型，通过扫频验证了所提模型的正确性，分析了不同环节对阻抗的影响，最后以汽轮发电机组经串联补偿装置并网系统为例，验证了所提模型在次/超同步振荡问题分析上的有效性。

关键词: 阻抗建模, 汽轮发电机, 次同步振荡, 轴系建模, 串联补偿

Abstract:

Impedance-based modeling and analysis method is currently one of the effective tools to analyze and solve the problem of renewable energy grid-connected broadband oscillation. Centralized development of long-distance transmission is an important form of renewable energy development and utilization in China. Among the power generation equipment in the renewable energy base, the impedance model of wind and solar power generation equipment has been built perfectly, but the current broadband impedance model of the steam turbine generator has some simplification, failing to completely reflect the broadband impedance characteristics of the steam turbine generator. Based on the frequency-domain small-signal modeling method, a broadband impedance model of the steam turbine generator containing the prime mover, speed governor, exciter system, shaft system, and synchronous generator was established. A simulation model of a steam turbine generator was built in Matlab/Simulink, and the correctness of the proposed model was verified by frequency sweeping. The influence of different links on the impedance was analyzed. Finally, the effectiveness of the proposed model in the analysis of the sub/super-synchronous oscillation problem was verified by studying a steam turbine generator connected to the grid via a series compensation device.

Key words: impedance modeling, steam turbine generator, sub-synchronous oscillation, shaft system modeling, series compensation

赵牧驰, 汪海蛟, 刘纯, 何国庆, 孙艳霞, 王盼盼. 汽轮机发电机组宽频带阻抗建模及次/超同步振荡分析[J]. 中国电力, 2024, 57(7): 238-246.

Muchi ZHAO, Haijiao WANG, Chun LIU, Guoqing HE, Yanxia SUN, Panpan WANG. Broadband Impedance Modeling and Sub/Super-synchronous Oscillation Analysis of Steam Turbine Generator[J]. Electric Power, 2024, 57(7): 238-246.

导出引用管理器 EndNote|Ris|BibTeX

链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202312081

https://www.electricpower.com.cn/CN/Y2024/V57/I7/238

图/表 12

图 1 汽轮发电机组整体结构

Fig.1 Overall structure of steam turbine generator

图 2 调速器及原动机模型

Fig.2 Models of speed governor and prime mover

图 3 励磁系统模型

Fig.3 Model of exciter system

表 1 仿真案例参数

Table 1 Parameters in simulation case

参数		取值
U_SG/kV		22
P_SG/(MV·A)		600
x_d, x_ls, x_f, x_D(p.u.)		1.65, 0.14, 1.628, 1.642
x_q, x_g, x_Q(p.u.)		1.59, 1.8606, 1.5238
R_a(p.u.)		0.0045
$ T'_{d 0}, T''_{ d 0}, T'_{ q 0}, T''_{ q 0}/\rm s$		4.5, 0.04, 0.67, 0.09
T_SR, T_SM, T_RH, T_CH/s		0.001, 0.15, 3.3, 0.5
H₁, H₂, H₃/s		0.8788, 1.5498, 0.249
D₁₁, D₂₂, D₃₃(p.u.)		0.0001, 2.4832, 0.4
K₁₂, K₂₃ /((p.u.)·rad^–1)		83.47, 42.702

图 4 汽轮机解析阻抗和仿真结果对比

Fig.4 Comparison of calculated impedance and simulation results of steam turbine generator

图 5 同步机和汽轮机阻抗对比

Fig.5 Comparison of impedance between synchronous generator and steam turbine generator

表 2 轴系固有振荡频率

Table 2 Inherent oscillation frequency of shaft system

轴系参数	模态1固有频率/Hz	模态2固有频率/Hz
参数1	27.43	20.42
参数2	34.04	29.09
参数3	23.94	15.84

图 6 轴系固有振荡频率对阻抗的影响

Fig.6 Influence of inherent oscillation frequency of shaft system on impedance

图 7 不同串补度阻抗和汽轮机阻抗的交互情况

Fig.7 Interaction between impedance at different series compensation ratios and impedance of steam turbine generator

图 8 不同串补度下的并网点电流

Fig.8 Point-of-common coupling current at different series compensation ratios

图 9 不同串补度下并网点电流FFT分析结果

Fig.9 Fast Fourier transform analysis of point-of-common coupling current at different series compensation ratios

图 10 不同串补度下同步电机-低压缸之间的扭矩

Fig.10 Torque between synchronous generator and low pressure cylinder at different series compensation ratios

参考文献 26

1	李博浩, 郭昆丽, 吕家君, 等. 弱电网下改进LADRC抑制直驱风机次同步振荡研究[J]. 中国电力, 2023, 56 (4): 56- 67.
	LI Bohao, GUO Kunli, LV Jiajun, et al. Inhibition of subsynchronous oscillation of direct-drive wind turbine by improved LADRC in weak grids[J]. Electric Power, 2023, 56 (4): 56- 67.
2	蔡维正, 郭昆丽, 刘璐雨, 等. 基于一阶LADRC控制的直驱风机次同步振荡抑制策略[J]. 中国电力, 2022, 55 (4): 175- 184.
	CAI Weizheng, GUO Kunli, LIU Luyu, et al. Subsynchronous oscillation mitigation strategy based on first-order LADRC for direct-drive wind turbines[J]. Electric Power, 2022, 55 (4): 175- 184.
3	陈作舟, 余浩, 王盼盼, 等. 海上风电集群与火电打捆外送系统短路比定义及影响因素分析[J]. 发电技术, 2022, 43 (2): 207- 217.
	CHEN Zuozhou, YU Hao, WANG Panpan, et al. Definition and influencing factors of short-circuit ratio between offshore wind power cluster and thermal power bundling system[J]. Power Generation Technology, 2022, 43 (2): 207- 217.
4	张帆, 尹聪琦, 袁豪, 等. 风电-柔直系统次同步振荡的耦合阻抗模型分析[J]. 南方电网技术, 2022, 16 (3): 24- 31.
	ZHANG Fan, YIN Congqi, YUAN Hao, et al. Impedance coupling model based sub-synchronous oscillation analysis of wind farms connected to VSC-HVDC transmission system[J]. Southern Power System Technology, 2022, 16 (3): 24- 31.
5	李长宇, 刘博昊, 肖仕武, 等. 基于功率外环附加阻尼控制的柔性直流抑制送端火电机组次同步振荡研究[J]. 电力科学与技术学报, 2024, 39 (2): 20- 27, 73.
	LI Changyu, LIU Bohao, XIAO Shiwu, et al. Research on subsynchronous oscillation suppression of flexible HVDC with thermal power units based on external loop damping control[J]. Journal of Electric Power Science and Technology, 2024, 39 (2): 20- 27, 73.
6	First benchmark model for computer simulation of subsynchronous resonance[J]. IEEE Transactions on Power Apparatus and Systems, 1977, 96(5): 1565–1572.
7	倪以信. 动态电力系统的理论和分析[M]. 北京: 清华大学出版社, 2002.
8	LARSEN E V, BAKER D H. Series compensation operating limits - A new concept for subsynchronous resonance stability analysis[J]. IEEE Transactions on Power Apparatus and Systems, 1980, PAS-99 (5): 1855- 1863. DOI
9	UCHIDA N, NAGAO T. A new eigen-analysis method of steady-state stability studies for large power systems: S matrix method[J]. IEEE Transactions on Power Systems, 1988, 3 (2): 706- 714. DOI
10	CANAY I M. A novel approach to the torsional interaction and electrical damping of the synchronous machine. part I: theory[J]. IEEE Power Engineering Review, 1982, PER-2 (10): 24. DOI
11	伍凌云, 李兴源, 孙衢, 等. 时域和频域相结合的次同步振荡分析方法[J]. 中国电力, 2007, 40 (5): 13- 18. DOI
	WU Lingyun, LI Xingyuan, SUN Qu, et al. Analysis methods of sub-synchronous oscillation in time and frequency domains[J]. Electric Power, 2007, 40 (5): 13- 18. DOI
12	WALKER D N, BOWLER C E J, JACKSON R L, et al. Results of subsynchronous resonance test at Mohave[J]. IEEE Transactions on Power Apparatus and Systems, 1975, 94 (5): 1878- 1889. DOI
13	李明节, 于钊, 许涛, 等. 新能源并网系统引发的复杂振荡问题及其对策研究[J]. 电网技术, 2017, 41 (4): 1035- 1042.
	LI Mingjie, YU Zhao, XU Tao, et al. Study of complex oscillation caused by renewable energy integration and its solution[J]. Power System Technology, 2017, 41 (4): 1035- 1042.
14	汪宁渤, 马明, 强同波, 等. 高比例新能源电力系统的发展机遇、挑战及对策[J]. 中国电力, 2018, 51 (1): 29- 35, 50.
	WANG Ningbo, MA Ming, QIANG Tongbo, et al. High-penetration new energy power system development: challenges, opportunities and countermeasures[J]. Electric Power, 2018, 51 (1): 29- 35, 50.
15	CESPEDES M, SUN J. Impedance modeling and analysis of grid-connected voltage-source converters[J]. IEEE Transactions on Power Electronics, 2014, 29 (3): 1254- 1261. DOI
16	HUANG J, CORZINE K A, BELKHAYAT M. Online synchronous machine parameter extraction from small-signal injection techniques[J]. IEEE Transactions on Energy Conversion, 2009, 24 (1): 43- 51. DOI
17	高磊, 马骏超, 吕敬, 等. 基于频域模态法的新能源电力系统振荡稳定性评估[J/OL]. 上海交通大学学报: 1–32[2024-05-16].https://doi.org/10.16183/j.cnki.jsjtu.2023.358.
	GAO Lei, MA Junchao, LÜ Jing, et al. Oscillatory Stability Assessment of Renewable Power Systems Based on Frequency-Domain Modal Analysis[J]. Journal of Shanghai Jiaotong University: 1–32[2024-05-16].https://doi.org/10.16183/j.cnki.jsjtu.2023.358.
18	田颖池. 大型风电场与火电打捆系统次同步振荡相互作用分析[D]. 北京: 华北电力大学, 2022.
	TIAN Yingchi. Interaction analysis of subsynchronous oscillation between large wind farm and thermal power plant bundling system[D]. Beijing: North China Electric Power University, 2022.
19	WEN B, DONG D, BOROYEVICH D, et al. Impedance-based analysis of grid-synchronization stability for three-phase paralleled converters[J]. IEEE Transactions on Power Electronics, 2016, 31 (1): 26- 38. DOI
20	金铁铮, 张磊, 徐亚涛, 等. 汽轮发电机组轴系扭振模型参数识别方法[J]. 中国电力, 2017, 50 (4): 100- 105. DOI
	JIN Tiezheng, ZHANG Lei, XU Yatao, et al. Parameter estimation method for torsional vibration model of turbine-generator shafts[J]. Electric Power, 2017, 50 (4): 100- 105. DOI
21	和鹏, 白菲菲, 张鹏, 等. 电力系统次同步振荡轴系模型研究[J]. 电力系统保护与控制, 2012, 40 (4): 107- 112. DOI
	HE Peng, BAI Feifei, ZHANG Peng, et al. Shaft models of subsynchronous oscillation in power system[J]. Power System Protection and Control, 2012, 40 (4): 107- 112. DOI
22	RYGG A, MOLINAS M, ZHANG C, et al. On the equivalence and impact on stability of impedance modeling of power electronic converters in different domains[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2017, 5 (4): 1444- 1454. DOI
23	RYGG A, MOLINAS M, ZHANG C, et al. A modified sequence-domain impedance definition and its equivalence to the dq-domain impedance definition for the stability analysis of AC power electronic systems[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2016, 4 (4): 1383- 1396. DOI
24	汪海蛟, 何国庆, 刘纯, 等. 计及频率耦合和汇集网络的风电场序阻抗模型等值方法[J]. 电力系统自动化, 2019, 43 (15): 87- 92. DOI
	WANG Haijiao, HE Guoqing, LIU Chun, et al. Equivalent method for sequence impedance model of wind farms considering frequency coupling and collecting network[J]. Automation of Electric Power Systems, 2019, 43 (15): 87- 92. DOI
25	吴旭, 王伟, 肖华锋, 等. 并网逆变器整体序阻抗建模方法及其稳定性分析[J/OL]. 中国电机工程学报: 1–12[2024-05-16]. http://kns.cnki.net/kcms/detail/11.2107.TM.20230713.1946.004.html.
	WU Xu, WANG Wei, XIAO Huafeng, et al. Overall Sequence Impedance Model of Grid-connected Inverter and Its Stability Analysis[J]. Proceedings of the CSEE: 1–12[2024-05-16]. http://kns.cnki.net/kcms/detail/11.2107.TM.20230713.1946.004.html.
26	SUN J. Impedance-based stability criterion for grid-connected inverters[J]. IEEE Transactions on Power Electronics, 2011, 26 (11): 3075- 3078. DOI

[1]	潘鹏程, 韩文舜, 郭雪丽. 基于有源和无源阻尼协同控制的光伏直流升压汇集系统谐振抑制[J]. 中国电力, 2025, 58(3): 20-30.
[2]	周于清, 李大虎, 姚伟, 宗启航, 周泓宇, 文劲宇. 受端近区光伏电站对LCC-HVDC系统稳定性影响分析[J]. 中国电力, 2024, 57(3): 170-182.
[3]	李博浩, 郭昆丽, 吕家君, 蔡维正, 刘璐豪, 刘凤仪, 郝翊帆. 弱电网下改进LADRC抑制直驱风机次同步振荡研究[J]. 中国电力, 2023, 56(4): 56-67.
[4]	蔡维正, 郭昆丽, 刘璐雨, 吴朝俊. 基于一阶LADRC控制的直驱风机次同步振荡抑制策略[J]. 中国电力, 2022, 55(4): 175-184.
[5]	苗硕, 李奇南, 查鲲鹏, 李兰芳, 曹建春, 张帆. 基于加窗FFT的风电场自适应振荡抑制策略[J]. 中国电力, 2022, 55(10): 112-123.
[6]	张帆, 高本锋, 李铁成. 基于SVG的光伏并网SSO附加阻尼抑制策略[J]. 中国电力, 2021, 54(12): 11-19,44.
[7]	王胜利, 许刚. 特高压近区风电汇集地区次同步振荡特征及防控措施[J]. 中国电力, 2020, 53(3): 28-34,65.
[8]	张学延, 屈杰, 何国安, 朱蓬勃, 姜广政, 潘渤. 大型汽轮发电机组非典型故障分析[J]. 中国电力, 2020, 53(12): 284-292,300.
[9]	杨京, 王彤, 唐俊刺. 基于滑窗FFT的次同步振荡时变幅频在线监测方法[J]. 中国电力, 2020, 53(11): 139-146.
[10]	蒋小利, 何荣尧. 弹簧基础的汽轮发电机振动异常原因分析及处理[J]. 中国电力, 2018, 51(7): 95-102.
[11]	金铁铮, 张磊, 徐亚涛, 张俊杰, 崔亚辉, 顾煜炯. 汽轮发电机组轴系扭振模型参数识别方法[J]. 中国电力, 2017, 50(4): 100-105.
[12]	李汪繁, 蒋俊, 孙庆, 王超, 王坤. 大型汽轮发电机组轴系静特性分析方法研究[J]. 中国电力, 2017, 50(2): 52-56.
[13]	黎瑜春, 陈涛, 杨为民, 齐敏芳. 某600 MW超临界机组1号瓦振动异常分析与处理[J]. 中国电力, 2016, 49(11): 135-139.
[14]	王浩. 一次加准法在1 000 MW汽轮发电机组现场动平衡中的应用[J]. 中国电力, 2016, 49(10): 38-42.
[15]	郑志萍，吴军，杨武盖，岑炳成，柯丽娜. 一种新的阻尼正弦原子分解算法辨识SSO模态参数[J]. 中国电力, 2016, 49(1): 75-79.