电力系统小干扰稳定性评估的多重谱变换方法

曹玉磊; 李崇涛; 何劲捷

doi:10.7652/xjtuxb202401020

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电力系统小干扰稳定性评估的多重谱变换方法

更新时间：2025-05-13

- 电力系统小干扰稳定性评估的多重谱变换方法
- A Multi-Spectral Transform Approach for Assessing Small Signal Stability in Power Systems
- 西安交通大学学报 2024年58卷第1期页码：208-216
- 作者机构：
  
  西安交通大学电气工程学院,西安,710049
- 作者简介：
  
  : 2023-04-01。作者简介: 曹玉磊(1997—),男,博士生
  李崇涛(通信作者),男,教授,博士生导师。基金项目: 国家重点研发计划资助项目(2022YFA1004600)
- 基金信息：
  
  : 2023-04-01。作者简介: 曹玉磊(1997—),男,博士生;李崇涛(通信作者),男,教授,博士生导师。基金项目: 国家重点研发计划资助项目(2022YFA1004600);国家自然科学基金资助项目(51977167)。
- DOI：10.7652/xjtuxb202401020
  中图分类号： TM744
- 网络首发：2024-01-10，
  
  纸质出版：2024
- 稿件说明：
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曹玉磊, 李崇涛, 何劲捷. 电力系统小干扰稳定性评估的多重谱变换方法[J]. 西安交通大学学报, 2024,58(1):208-216.

A Multi-Spectral Transform Approach for Assessing Small Signal Stability in Power Systems[J]. 2024, 58(1): 208-216.
曹玉磊, 李崇涛, 何劲捷. 电力系统小干扰稳定性评估的多重谱变换方法[J]. 西安交通大学学报, 2024,58(1):208-216. DOI： 10.7652/xjtuxb202401020.

A Multi-Spectral Transform Approach for Assessing Small Signal Stability in Power Systems[J]. 2024, 58(1): 208-216. DOI： 10.7652/xjtuxb202401020.

摘要

针对电力系统小干扰稳定性分析过程中遗漏不稳定特征值的问题

提出了一种求解大规模系统不稳定特征值的多重谱变换方法。该方法首先利用所提出的多重谱变换将全部不稳定特征值映射为主导特征值; 在利用Krylov-Schur方法收敛得到全部主导特征值之后

通过逆变换得到相应的不稳定特征值; 该方法还揭示了指数变换与位移逆变换以及凯莱变换之间的内在联系。相较于位移逆变换和凯莱变换

多重谱变换方法由于具有类似于指数变换的良好谱特性

从而有利于特征值收敛; 同时其又避免了指数变换引起的指数矩阵与向量的乘积

从而具有更高的计算效率和计算精度。在Xingo6u和Xingo3012这两个源于巴西互联电网上的算例分析结果表明

所提出的多重谱变换方法不仅保证了不遗漏不稳定特征值

而且相较于指数变换方法

计算精度提升了约3个数量级

计算耗时减少了90%以上。

Abstract

To address missing unstable eigenvalues in small signal stability analysis of power systems

a multi-spectral transform method for calculating the unstable eigenvalues of large-scale systems is proposed. Firstly

this method utilizes the proposed multi-spectral transform technique to map all unstable eigenvalues into dominant eigenvalues. Subsequently

the Krylov-Schur method is employed to ensure convergence and obtain all dominant eigenvalues. Finally

the inverse transformation allows for the retrieval of the corresponding unstable eigenvalues. Furthermore

this method establishes the intrinsic relationship between various transforms

including the exponential transform

shift-and-invert transform

and Cayley transform. Compared with the shift-and-invert transform and Cayley transform

the multi-spectral transform exhibits superior spectral performance akin to the exponential transform

facilitating eigenvalue convergence. At the same time

it avoids calculating the multiplication of exponential matrix and vector caused by the exponential transform

thereby having higher computational efficiency and accuracy. Experimental results obtained from the Xingo6u and Xingo3012 system of the Brazilian interconnected power grid demonstrate the effectiveness of this method. Notably

it ensures that unstable eigenvalues are not overlooked

enhances calculation accuracy by about 3 orders of magnitude

and reduces the calculation time by more than 90% compared to the exponential transform method.

关键词

Keywords

references

王锡凡. 现代电力系统分析 [M]. 北京: 科学出版社, 2003

KUNDUR P. Power system stability and control [M]. New York, USA: McGraw-Hill, 1994

王康, 李子恒, 杨超然, 等. 面向大型新能源基地小干扰稳定性提升的调相机选址方法 [J]. 电力系统自动化, 2022, 46(4): 66-74.WANG Kang, LI Ziheng, YANG Chaoran, et al. Siting method of synchronous condenser for small-signal stability improvement of large-scale renewable energy base [J]. Automation of Electric Power Systems, 2022, 46(4): 66-74

索江镭, 胡志坚, 刘宇凯, 等. 大规模光伏发电并网对互联电力系统阻尼特性的影响及其阻尼控制策略 [J]. 西安交通大学学报, 2015, 49(2): 99-105.SUO Jianglei, HU Zhijian, LIU Yukai, et al. Influence of large-scale photovoltaic system integration on damping characteristics of interconnected grid and damping control [J]. Journal of Xi'an Jiaotong University, 2015, 49(2): 99-105

朱振青, 王新. 复杂电力系统中电力系统稳定器的参数优化 [J]. 西安交通大学学报, 1989, 23(S1): 71-77.ZHU Zhenqing, WANG Xin. Parameter optimization of PSS in multimachines power systems [J]. Journal of Xi'an Jiaotong University, 1989, 23(S1): 71-77

MA Jian, DONG Zhaoyang, ZHANG Pei. Comparison of BR and QR eigenvalue algorithms for power system small signal stability analysis [J]. IEEE Transactions on Power Systems, 2006, 21(4): 1848-1855

赵文恺, 严正, 房鑫炎, 等. 电力系统小信号稳定全特征值分析的改进BR算法 [J]. 中国电机工程学报, 2014, 34(10): 1599-1608.ZHAO Wenkai, YAN Zheng, FANG Xinyan, et al. Complete eigen analysis of power system small signal stability using the improved BR algorithm [J]. Proceedings of the CSEE, 2014, 34(10): 1599-1608

张逸飞, 严正, 赵文恺, 等. 基于GPU的分块约化算法在小干扰稳定分析中的应用 [J]. 电力系统自动化, 2015, 39(22): 90-97.ZHANG Yifei, YAN Zheng, ZHAO Wenkai, et al. Application of GPU-based block reduction algorithm in power system small-signal stability analysis [J]. Automation of Electric Power Systems, 2015, 39(22): 90-97

岳涵, 赵登福, 夏道止, 等. 求解大型电力系统机电振荡模态的逆幂方法 [J]. 西安交通大学学报, 2010, 44(10): 93-98.YUE Han, ZHAO Dengfu, XIA Daozhi, et al. Inverse power algorithm for solving electromechanical modes of large-scale power system [J]. Journal of Xi'an Jiaotong University, 2010, 44(10): 93-98

杜正春, 刘伟, 方万良, 等. 大规模电力系统关键特征值计算的Arnoldi-Chebyshev方法 [J]. 西安交通大学学报, 2004, 38(10): 995-999.DU Zhengchun, LIU Wei, FANG Wanliang, et al. Calculation of critical eigenvalues in large-scale power systems using Arnoldi-Chebyshev method [J]. Journal of Xi'an Jiaotong University, 2004, 38(10): 995-999

田鹏飞, 刘崇茹, 贠飞龙, 等. 一种动态扩维的IRA算法及其在电力系统关键特征值计算中的应用 [J]. 中国电机工程学报, 2015, 35(17): 4318-4325.TIAN Pengfei, LIU Chongru, YUN Feilong, et al. An improved IRA algorithm and its application in computation of critical eigenvalues in small signal stability analysis [J]. Proceedings of the CSEE, 2015, 35(17): 4318-4325

LIU Chongru, LI Xiao, TIAN Pengfei, et al. An improved IRA algorithm and its application in critical eigenvalues searching for low frequency oscillation analysis [J]. IEEE Transactions on Power Systems, 2017, 32(4): 2974-2983

杜正春, 李崇涛, 潘艳菲, 等. 一种求取大规模电力系统关键特征值的有效方法 [J]. 电力系统自动化, 2014, 38(2): 53-58.DU Zhengchun, LI Chongtao, PAN Yanfei, et al. An efficient method for computing critical eigenvalues of large-scale power systems [J]. Automation of Electric Power Systems, 2014, 38(2): 53-58

LI Yongjie, GENG Guangchao, JIANG Quanyuan. An efficient parallel Krylov-Schur method for eigen-analysis of large-scale power systems [J]. IEEE Transactions on Power Systems, 2016, 31(2): 920-930

仲悟之. 大型电力系统小干扰稳定性分析方法研究和软件开发 [D]. 北京: 中国电力科学研究院, 2005

励刚, 苏寅生, 陈陈. 面向对象的多谱变换隐式重启动Arnoldi算法 [J]. 电力系统自动化, 2001, 25(8): 24-27.LI Gang, SU Yinsheng, CHEN Chen. Object-oriented multi-spectrum transformation implicit restarted Arnoldi algorithm [J]. Automation of Electric Power Systems, 2001, 25(8): 24-27

谷寒雨, 陈陈. 一种新的大型电力系统低频机电模式计算方法 [J]. 中国电机工程学报, 2000, 20(9): 50-54.GU Hanyu, CHEN Chen. A new algorithm for the computation of low frequency electro-mechanical oscillation modes of large power systems [J]. Proceedings of the CSEE, 2000, 20(9): 50-54

MEERBERGEN K, SPENCE A, ROOSE D. Shift-invert and Cayley transforms for detection of rightmost eigenvalues of nonsymmetric matrices [J]. Bit Numerical Mathematics, 1994, 34(3): 409-423

陈亦平, 曹玉磊, 赵利刚, 等. 基于指数变换的电力系统不稳定特征值计算方法 [J]. 电力系统自动化, 2023, 47(3): 161-168.CHEN Yiping, CAO Yulei, ZHAO Ligang, et al. Calculation method for unstable eigenvalue of power system based on exponential transformation [J]. Automation of Electric Power Systems, 2023, 47(3): 161-168

CAO Yulei, LI Chongtao, YAN Chenguang, et al. An exponential transform based dual-layer Krylov subspace method for computing unstable modes of power systems [J]. IEEE Transactions on Power Systems, 2023, 38(2): 1596-1607

ROSTAMI M W, XUE Fei. Robust linear stability analysis and a new method for computing the action of the matrix exponential [J]. SIAM Journal on Scientific Computing, 2018, 40(5): A3344-A3370

杜正春, 刘伟, 方万良, 等. 小干扰稳定性分析中一种关键特征值计算的稀疏实现 [J]. 中国电机工程学报, 2005, 25(2): 17-21.DU Zhengchun, LIU Wei, FANG Wanliang, et al. A sparse method for the calculation of critical eigenvalue in small signal stability analysis [J]. Proceedings of the CSEE, 2005, 25(2):17-21

MOLER C, VAN LOAN C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later [J]. SIAM Review, 2003, 45(1): 3-49

ROMMES J, MARTINS N, FREITAS F D. Computing rightmost eigenvalues for small-signal stability assessment of large-scale power systems [J]. IEEE Transactions on Power Systems, 2010, 25(2): 929-938

ROMMES J. Examples from the Brazilian power system [EB/OL]. [2023-03-08]. http://sites.google.com/site/rommes.

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