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| Impedance Model of Turbo-Generator Considering Torsional Characteristics of Shafting |
| Li Jialong1, Lu Xinyu1, Du Xiong1, Liu Junliang1, Fan Lijuan2 |
1. State Key Laboratory of Power Transmission Equipment and System Security and New Technology Chongqing University Chongqing 400044 China;
2. System Research Institute CSG Electric Power Research Institute Guangzhou 510663 China |
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Abstract Due to the increasing number of electronic power devices in power systems, power system structures have become complicated, and analyzing power system stability containing power electronic devices and turbo-generators is difficult. The impedance-based analysis method is a good choice because extending the system topology and establishing the black box system model is easy. However, the impedance of the turbo-generator only reflects electrical characteristics. This paper establishes an impedance model of the turbo-generator considering the mechanical part of the turbine, governor, and shafting mass-spring.
The turbo-generator is divided into electrical and mechanical parts. For the electrical part modeling, an ideal state is assumed, and the small signal equation of the synchronous motor is standardized. For the mechanical part modeling, a small signal model is established for the shafting part, steam turbine, and speed regulator. Calculation results show that the impedance model of the turbo-generator in the d-q coordinate system is a 2nd-order matrix. Finally, the impedance model of the turbo-generator considering the shafting part is obtained by converting it into a sequence impedance model and considering the frequency coupling effect.
The theoretical model is verified by the frequency scanning method. The experimental results of frequency scanning points agree with the theoretical model, which verifies the correctness of the impedance model. Taking the wind-thermal bundling delivery system as the research object, compared with the oscillation analysis based on the RL equivalent impedance model, the proposed impedance model can identify the sub-/super-synchronous oscillation risk. The proposed model for stability analysis in power systems containing new energy and power electronic equipment is verified. Finally, the classical turbo-generator stability analysis, i.e., the complex torque coefficient method, is used to analyze the oscillation of the wind-thermal bundled system.
This study draws the following conclusions. (1) Compared with the equivalent circuit impedance of the synchronous motor, the proposed impedance model is more accurate near the natural torsional vibration frequency of the turbo-generator shafting, improving the model’s accuracy. (2) The turbo-generator impedance model can perform stability analysis well in complex power systems containing new energy systems and power electronic equipment. It is more accurate than the traditional turbo-generator impedance model in the sub-/super-synchronous frequency band. (3) Compared with the complex torque coefficient method, the impedance-based analysis has advantages in accuracy in multi-machine systems containing electronic power devices.
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Received: 26 May 2023
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[1] 刘欣, 郭志博, 贾焦心, 等. 基于序阻抗的虚拟同步发电机并网稳定性分析及虚拟阻抗设计[J]. 电工技术学报, 2023, 38(15): 4130-4146.
Liu Xin, Guo Zhibo, Jia Jiaoxin, et al.Stability analysis and virtual impedance design of virtual synchronous machine based on sequence impe- dance[J]. Transactions of China Electrotechnical Society, 2023, 38(15): 4130-4146.
[2] 于彦雪, 关万琳, 陈晓光, 等. 基于序阻抗的虚拟同步机同步频率谐振现象[J]. 电工技术学报, 2022, 37(10): 2584-2595.
Yu Yanxue, Guan Wanlin, Chen Xiaoguang, et al.Synchronous frequency resonance in virtual syn- chronous generator based on sequence-impedance[J]. Transactions of China Electrotechnical Society, 2022, 37(10): 2584-2595.
[3] 刘朋印, 谢小荣, 马宁宁, 等. 风电次/超同步振荡激发汽轮机组轴系扭振风险的在线评估与预警技术[J]. 中国电机工程学报, 2021, 41(增刊1): 52-58.
Liu Pengyin, Xie Xiaorong, Ma Ningning, et al.Online assessment and early warning of torsional vibration risk for turbine generators stimulated by sub-/super-synchronous oscillations associated with wind power[J]. Proceedings of the CSEE, 2021, 41(S1): 52-58.
[4] 李宽, 王军, 赵斌超, 等. 风火捆绑经HVDC送电引起轴系扭振研究[J]. 电工技术学报, 2017, 32(6): 115-122.
Li Kuan, Wang Jun, Zhao Binchao, et al.Shafting vibration research of wind power and thermal power bundle supply through HVDC[J]. Transactions of China Electrotechnical Society, 2017, 32(6): 115-122.
[5] 刘其辉, 洪晨威, 逄思敏, 等. 基于弹性系数的双馈风电机组控制参数对次同步振荡作用分析及调整方法[J]. 电工技术学报, 2022, 37(14): 3528-3541.
Liu Qihui, Hong Chenwei, Pang Simin, et al.Analysis and adjustment method of doubly-fed fan control parameters on subsynchronous oscillation based on impedance elastic sensitivity[J]. Transactions of China Electrotechnical Society, 2022, 37(14): 3528-3541.
[6] Chi Yongning, Tang Bingjie, Hu Jiabing, et al.Overview of mechanism and mitigation measures on multi-frequency oscillation caused by large-scale integration of wind power[J]. CSEE Journal of Power and Energy Systems, 2019, 5(4): 433-443.
[7] Liu Huakun, Xie Xiaorong, He Jingbo, et al.Subsynchronous interaction between direct-drive PMSG based wind farms and weak AC networks[J]. IEEE Transactions on Power Systems, 2017, 32(6): 4708-4720.
[8] 孙东阳, 孟繁易, 王南, 等. 基于反步自适应准谐振控制的双馈风机次同步振荡抑制策略[J]. 电工技术学报, 2023, 38(9): 2375-2390, 2434.
Sun Dongyang, Meng Fanyi, Wang Nan, et al.DFIG sub-synchronous oscillation suppression strategy based on backstepping adaptive quasi-resonant control[J]. Transactions of China Electrotechnical Society, 2023, 38(9): 2375-2390, 2434.
[9] 付强, 杜文娟, 王海风. 柔性直流输电控制与交流系统次同步交互机理研究[J]. 中国电机工程学报, 2018, 38(13): 3717-3726, 4013.
Fu Qiang, Du Wenjuan, Wang Haifeng.The mechanism of sub-synchronous interactions between converter control of VSC HVDC and power systems[J]. Proceedings of the CSEE, 2018, 38(13): 3717-3726, 4013.
[10] 王晖, 吴命利. 电气化铁路低频振荡研究综述[J]. 电工技术学报, 2015, 30(17): 70-78.
Wang Hui, Wu Mingli.Review of low-frequency oscillation in electric railways[J]. Transactions of China Electrotechnical Society, 2015, 30(17): 70-78.
[11] 郭春义, 吕乃航, 张加卿. 提高LCC-HVDC在弱交流系统下的稳定性和动态性能的控制参数优化方法[J]. 电工技术学报, 2023, 38(7): 1751-1764, 1779.
Guo Chunyi, Lü Naihang, Zhang Jiaqing.Optimi- zation of control parameters to enhance stability and dynamic performance of LCC-HVDC under weak AC condition[J]. Transactions of China Electrotechnical Society, 2023, 38(7): 1751-1764, 1779.
[12] 朱晓娟, 胡海涛, 陶海东, 等. 光伏并网系统的谐波不稳定产生机理及影响规律[J]. 电工技术学报, 2017, 32(10): 33-41.
Zhu Xiaojuan, Hu Haitao, Tao Haidong, et al.The mechanism and influence of harmonic instability for photovoltaic grid-connected system[J]. Transactions of China Electrotechnical Society, 2017, 32(10): 33-41.
[13] Canay I M.A novel approach to the torsional interaction and electrical damping of the synchronous machine part Ⅱ: application to an arbitrary net- work[J]. IEEE Transactions on Power Apparatus and Systems, 1982, 101(10): 3639-3647.
[14] Tabesh A, Iravani R.On the application of the complex torque coefficients method to the analysis of torsional dynamics[J]. IEEE Transactions on Energy Conversion, 2005, 20(2): 268-275.
[15] Zhao Wei, Wang Shihao, Sun Xiaofeng, et al.Impedance modeling and stability research of hybrid parallel system with synchronous generator and inverters[C]//2018 IEEE International Power Elec- tronics and Application Conference and Exposition (PEAC), Shenzhen, China, 2018: 1-6.
[16] Gu Yunjie, Li Yitong, Zhu Yue, et al.Impedance- based whole-system modeling for a composite grid via embedding of frame dynamics[J]. IEEE Transa- ctions on Power Systems, 2021, 36(1): 336-345.
[17] IEEE Subsynchronous Resonance Working Group. First benchmark model for computer simulation of subsynchronous resonance[J]. IEEE Transactions on Power Apparatus and Systems, 1977, 96(5): 1565-1572.
[18] Zou Xiaoming, Du Xiong, Tai Hengming.Two- variable admittance model for D-PMSG-based wind turbine and stability criterion based on magnitude and phase contour plot[J]. IEEE Transactions on Power Electronics, 2020, 35(2): 1484-1498.
[19] IEEE Committee Report.Dynamic models for steam and hydro turbines in power system studies[J]. IEEE Transa- ctions on Power Apparatus and Systems, 1973, 92(6): 1904-1915.
[20] 谢小荣, 韩英铎, 郭锡玖. 电力系统次同步谐振的分析与控制[M]. 北京: 科学出版社, 2015.
[21] IEEE Subsynchronous Resonance Working Group. Terms, definitions and symbols for subsynchronous oscillations[J]. IEEE Transactions on Power Apparatus and Systems, 1985, 104(6): 1326-1334.
[22] Rygg A, Molinas M, Zhang Chen, 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.
[23] 杜程茂, 杜雄, 邹小明, 等. 考虑频率耦合效应的并网模块化多电平变流器阻抗建模及稳定性分析[J]. 中国电机工程学报, 2020, 40(9): 2866-2877.
Du Chengmao, Du Xiong, Zou Xiaoming, et al.Impedance modeling and stability analysis of grid-connected modular multilevel converter con- sidering frequency coupling effect[J]. Proceedings of the CSEE, 2020, 40(9): 2866-2877.
[24] 邹小明, 杜雄, 王国宁, 等. 三相并网逆变器频率耦合机理分析及稳定性判定[J]. 电力系统自动化, 2018, 42(18): 57-63.
Zou Xiaoming, Du Xiong, Wang Guoning, et al.Frequency coupling mechanism analysis and stability judgement for three-phase grid-connected inverter[J]. Automation of Electric Power Systems, 2018, 42(18): 57-63.
[25] 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.
[26] 王一珺, 杜文娟, 陈晨, 等. 基于改进复转矩系数法的风电场并网引发电力系统次同步振荡研究[J]. 电工技术学报, 2020, 35(15): 3258-3269.
Wang Yijun, Du Wenjuan, Chen Chen, et al.Study on sub-synchronous oscillations of power systems caused by grid-connected wind farms based on the improved complex torque coefficients method[J]. Transactions of China Electrotechnical Society, 2020, 35(15): 3258-3269.
[27] Mortensen K, Larsen E V, Piwko R J.Field tests and analysis of torsional interaction between the coal creek turbine-generators and the CU HVDC system[J]. IEEE Transactions on Power Apparatus and Systems, 1981, 100(1): 336-344.
[28] 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.
Xu Zheng.The complex torque coefficient approach’s applicability analysis and its realization by time domain simulation[J]. Proceedings of the CSEE, 2000, 20(6): 1-4.
[29] Bosetti H, Khan S.Transient stability in oscillating multi-machine systems using Lyapunov vectors[J]. IEEE Transactions on Power Systems, 2018, 33(2): 2078-2086. |
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2024, Vol. 39 
