基于随机矩阵谱分析的输电线路故障检测算法
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摘要
针对基于基波相量体系和时域波形相似度的故障检测算法抗干扰能力不强,提出了一种基于随机矩阵谱分析的输电线路故障检测算法。首先,利用故障线路两侧电流故障分量波形几乎反向的特性,通过滑动的定长时间窗,将线路的一侧电流故障分量与另一侧电流故障分量相反量形成原始矩阵,进行复制、平移、加噪声等处理构造随机矩阵,计算其平均谱半径,并进行谱分析,给出了线路的两个故障检测判据。然后,结合随机矩阵理论的单环定理,给出了阈值的确定办法,分析了各种因素对所提算法的影响。最后,利用IEEE 39节点系统的大量仿真算例验证了算法的有效性,实验表明该算法不受故障点位置、线路重载、非全相运行等因素的影响,在系统发生振荡时也不会误切除正常线路,耐受过渡电阻能力强,对信息的同步性要求不高。
Considering the lack of anti-interference ability of fault detection algorithm based on the fundamental wave phasor system and similarity of time-domain waveform, a novel transmission line fault detection algorithm based on random matrix spectrum analysis is proposed. Firstly, using the almost reverse characteristics of waveforms for the current fault components at both ends of the line, the original matrix is formed by a fixed time window that consists of current fault component on one side and opposite current fault component on the other side. A random matrix is constructed by copying, translating, and adding noise, its mean spectral radius is calculated and spectrum analysis is taken, which brings about two criteria of fault detections for lines. Then, the single ring theorem of the theory for random matrix is used to set the threshold and the influence of various factors on the proposed algorithm is analyzed. Finally, a large number of simulation examples in the IEEE-39 bus system prove the effectiveness of the algorithm. The simulation results show that the algorithm is not affected by the fault location, non-full-phase operation and heavy load and it will not cut off the normal line when the system oscillates. It also has a strong ability of resisting the transition resistance and does not require high information of synchronization.
Considering the lack of anti-interference ability of fault detection algorithm based on the fundamental wave phasor system and similarity of time-domain waveform, a novel transmission line fault detection algorithm based on random matrix spectrum analysis is proposed. Firstly, using the almost reverse characteristics of waveforms for the current fault components at both ends of the line, the original matrix is formed by a fixed time window that consists of current fault component on one side and opposite current fault component on the other side. A random matrix is constructed by copying, translating, and adding noise, its mean spectral radius is calculated and spectrum analysis is taken, which brings about two criteria of fault detections for lines. Then, the single ring theorem of the theory for random matrix is used to set the threshold and the influence of various factors on the proposed algorithm is analyzed. Finally, a large number of simulation examples in the IEEE-39 bus system prove the effectiveness of the algorithm. The simulation results show that the algorithm is not affected by the fault location, non-full-phase operation and heavy load and it will not cut off the normal line when the system oscillates. It also has a strong ability of resisting the transition resistance and does not require high information of synchronization.
引文
[1] 杨春生,周步祥,林楠,等.广域保护研究现状及展望[J].电力系统保护与控制,2010,38(9):147-150.YANG Chunsheng,ZHOU Buxiang,LIN Nan,et al.Research current status and prospect of wide-area protection[J].Power System Protection and Control,2010,38(9):147-150.
[2] 陈乐,薄志谦,林湘宁,等.基于波形相似度比较的线路快速纵联保护研究[J].中国电机工程学报,2017,37(17):5018-5027.CHEN Le,BO Zhiqian,LIN Xiangning,et al.Waveform similarity comparison based high-speed pilot protection for transmission line[J].Proceedings of the CSEE,2017,37(17):5018-5027.
[3] 孔令号,焦彦军,戴志辉.基于灰色关联度的站域保护原理[J].电网技术,2014,38(8):2274-2279.KONG Linghao,JIAO Yanjun,DAI Zhihui.New substation area protection principle based on gray correlation degree[J].Power System Technology,2014,38(8):2274-2279.
[4] 宋国兵,王晨清,唐吉斯,等.适用于风电接入系统的时域模型识别纵联保护新原理[J].电网技术,2016,40(11):3580-3585.SONG Guobing,WANG Chenqing,Tengis,et al.Novel pilot protection based on time-domain model identification for wind power integration[J].Power System Technology,2016,40(11):3580-3585.
[5] 孔德洪,吕飞鹏,韩康,等.基于采样值相关度的广域后备保护算法[J].电测与仪表,2017,54(9):6-11.KONG Dehong,Lü Feipeng,HAN Kang,et al.A wide area back-up protection algorithm based on the correlation of sample value[J].Electrical Measurement & Instrumentation,2017,54(9):6-11.
[6] DUBEY R,SAMANTARAY S R,PANIGRAHI B K.An spatiotemporal information system based wide-area protection fault identification scheme[J].International Journal of Electrical Power & Energy Systems,2017,89:136-145.
[7] 贺兴,艾芊,邱才明,等.随机矩阵理论在电力系统认知中的应用初探[J].电网技术,2017,41(4):1165-1173.HE Xing,AI Qian,QIU Caiming,et al.A primary study on the situation awareness of power systems using random matrix theory[J].Power System Technology,2017,41(4):1165-1173.
[8] 王磊,郑宝玉,崔景伍.基于随机矩阵理论的频谱感知技术研究综述[J].信号处理,2011,27(12):1889-1897.WANG Lei,ZHENG Baoyu,CUI Jingwu.Survey on the research of spectrum sensing technologies based on random matrix theory[J].Signal Processing,2011,27(12):1889-1897.
[9] KUMAR S,DEO N.Correlation and network analysis of global financial indices[J].Physical Review E,2012,86(2):026101.
[10] LIANG Y,PAN G,BAI Z.Asymptotic performance of MMSE receivers for large systems using random matrix theory[J].IEEE Transactions on Information Theory,2007,53(11):4173-4190.
[11] HE X,AI Q,QIU R,et al.A big data architecture design for smart grids based on random matrix theory[J].IEEE Transactions on Smart Grid,2017,8(2):674-686.
[12] 徐心怡,贺兴,艾芊,等.基于随机矩阵理论的配电网运行状态相关性分析方法[J].电网技术,2016,40(3):781-790.XU Xinyi,HE Xing,AI Qian,et al.A correlation analysis method for operation status of distribution network based on random matrix theory[J].Power System Technology,2016,40(3):781-790.
[13] 张力,张子仲,顾建炜.基于随机矩阵理论的电网状态分析与扰动定位方法[J].电力系统自动化,2018,42(12):93-99.DOI:10.7500/AEPS20171106006.ZHANG Li,ZHANG Zizhong,GU Jianwei.State analysis and disturbance positioning method of power grid based on random matrix theory[J].Automation of Electric Power Systems,2018,42(12):93-99.DOI:10.7500/AEPS20171106006.
[14] 刘威,张东霞,王新迎,等.基于随机矩阵理论的电力系统暂态稳定性分析[J].中国电机工程学报,2016,36(18):4854-4863.LIU Wei,ZHANG Dongxia,WANG Xinying,et al.Power system transient stability analysis based on random matrix theory[J].Proceedings of the CSEE,2016,36(18):4854-4863.
[15] 吴茜,张东霞,刘道伟,等.基于随机矩阵的电网静态稳定态势评估方法[J].中国电机工程学报,2016,36(20):5414-5420.WU Qian,ZHANG Dongxia,LIU Daowei,et al.A method for power system steady stability situation assessment based on random matrix theory[J].Proceedings of the CSEE,2016,36(20):5414-5420.
[16] 余森林.基于故障分量和随机矩阵谱分析的广域后备保护研究[D].成都:西南交通大学,2018.YU Senlin.Study on wide-area backup protection based on fault component and random matrix spectrum analysis[D].Chengdu:Southwest Jiaotong University,2018.
[17] GUIONNET A,KRISHNAPUR M,ZEITOUNI O.The single ring theorem[J].Annals of Mathematics,2011,174(2):1189-1217.
[18] GUIONNET A,ZEITOUNI O.Support convergence in the single ring theorem[J].Probability Theory & Related Fields,2012,154(4):661-675.
[19] JANA I,SAHA K,SOSHNIKOV A.Fluctuations of linear eigenvalue statistics of random band matrices[J].Journal of Magnetism & Magnetic Materials,2014,34(31):181-182.
[20] 李斌,曾红艳,范瑞卿,等.基于故障分量的相位相关电流差动保护[J].电力系统自动化,2011,35(3):54-58.LI Bin,ZENG Hongyan,FAN Ruiqing,et al.Phase correlation current differential protection based on fault component[J].Automation of Electric Power Systems,2011,35(3):54-58.
[21] 刘凯,李幼仪,伊沃布林西奇,等.自适应线路差动保护新原理[J].中国电机工程学报,2016,36(13):3440-3450.LIU Kai,LI Youyi,BRNCIC Ivo,et al.A novel adaptive differential line protection principle[J].Proceedings of the CSEE,2016,36(13):3440-3450.
[22] 王宾,董新洲,薄志谦,等.非全相运行输电线路负序方向纵联保护方法[J].电力系统自动化,2009,33(12):61-66.WANG Bin,DONG Xinzhou,BO Zhiqian,et al.A novel algorithm for negative sequence pilot protection applicable to open-phase transmission lines[J].Automation of Electric Power Systems,2009,33(12):61-66.
[23] NAYAK P K,PRADHAN A K,BAJPAI P.Wide-area measurement-based backup protection for power network with series compensation[J].IEEE Transactions on Power Delivery,2014,29(4):1970-1977.
[2] 陈乐,薄志谦,林湘宁,等.基于波形相似度比较的线路快速纵联保护研究[J].中国电机工程学报,2017,37(17):5018-5027.CHEN Le,BO Zhiqian,LIN Xiangning,et al.Waveform similarity comparison based high-speed pilot protection for transmission line[J].Proceedings of the CSEE,2017,37(17):5018-5027.
[3] 孔令号,焦彦军,戴志辉.基于灰色关联度的站域保护原理[J].电网技术,2014,38(8):2274-2279.KONG Linghao,JIAO Yanjun,DAI Zhihui.New substation area protection principle based on gray correlation degree[J].Power System Technology,2014,38(8):2274-2279.
[4] 宋国兵,王晨清,唐吉斯,等.适用于风电接入系统的时域模型识别纵联保护新原理[J].电网技术,2016,40(11):3580-3585.SONG Guobing,WANG Chenqing,Tengis,et al.Novel pilot protection based on time-domain model identification for wind power integration[J].Power System Technology,2016,40(11):3580-3585.
[5] 孔德洪,吕飞鹏,韩康,等.基于采样值相关度的广域后备保护算法[J].电测与仪表,2017,54(9):6-11.KONG Dehong,Lü Feipeng,HAN Kang,et al.A wide area back-up protection algorithm based on the correlation of sample value[J].Electrical Measurement & Instrumentation,2017,54(9):6-11.
[6] DUBEY R,SAMANTARAY S R,PANIGRAHI B K.An spatiotemporal information system based wide-area protection fault identification scheme[J].International Journal of Electrical Power & Energy Systems,2017,89:136-145.
[7] 贺兴,艾芊,邱才明,等.随机矩阵理论在电力系统认知中的应用初探[J].电网技术,2017,41(4):1165-1173.HE Xing,AI Qian,QIU Caiming,et al.A primary study on the situation awareness of power systems using random matrix theory[J].Power System Technology,2017,41(4):1165-1173.
[8] 王磊,郑宝玉,崔景伍.基于随机矩阵理论的频谱感知技术研究综述[J].信号处理,2011,27(12):1889-1897.WANG Lei,ZHENG Baoyu,CUI Jingwu.Survey on the research of spectrum sensing technologies based on random matrix theory[J].Signal Processing,2011,27(12):1889-1897.
[9] KUMAR S,DEO N.Correlation and network analysis of global financial indices[J].Physical Review E,2012,86(2):026101.
[10] LIANG Y,PAN G,BAI Z.Asymptotic performance of MMSE receivers for large systems using random matrix theory[J].IEEE Transactions on Information Theory,2007,53(11):4173-4190.
[11] HE X,AI Q,QIU R,et al.A big data architecture design for smart grids based on random matrix theory[J].IEEE Transactions on Smart Grid,2017,8(2):674-686.
[12] 徐心怡,贺兴,艾芊,等.基于随机矩阵理论的配电网运行状态相关性分析方法[J].电网技术,2016,40(3):781-790.XU Xinyi,HE Xing,AI Qian,et al.A correlation analysis method for operation status of distribution network based on random matrix theory[J].Power System Technology,2016,40(3):781-790.
[13] 张力,张子仲,顾建炜.基于随机矩阵理论的电网状态分析与扰动定位方法[J].电力系统自动化,2018,42(12):93-99.DOI:10.7500/AEPS20171106006.ZHANG Li,ZHANG Zizhong,GU Jianwei.State analysis and disturbance positioning method of power grid based on random matrix theory[J].Automation of Electric Power Systems,2018,42(12):93-99.DOI:10.7500/AEPS20171106006.
[14] 刘威,张东霞,王新迎,等.基于随机矩阵理论的电力系统暂态稳定性分析[J].中国电机工程学报,2016,36(18):4854-4863.LIU Wei,ZHANG Dongxia,WANG Xinying,et al.Power system transient stability analysis based on random matrix theory[J].Proceedings of the CSEE,2016,36(18):4854-4863.
[15] 吴茜,张东霞,刘道伟,等.基于随机矩阵的电网静态稳定态势评估方法[J].中国电机工程学报,2016,36(20):5414-5420.WU Qian,ZHANG Dongxia,LIU Daowei,et al.A method for power system steady stability situation assessment based on random matrix theory[J].Proceedings of the CSEE,2016,36(20):5414-5420.
[16] 余森林.基于故障分量和随机矩阵谱分析的广域后备保护研究[D].成都:西南交通大学,2018.YU Senlin.Study on wide-area backup protection based on fault component and random matrix spectrum analysis[D].Chengdu:Southwest Jiaotong University,2018.
[17] GUIONNET A,KRISHNAPUR M,ZEITOUNI O.The single ring theorem[J].Annals of Mathematics,2011,174(2):1189-1217.
[18] GUIONNET A,ZEITOUNI O.Support convergence in the single ring theorem[J].Probability Theory & Related Fields,2012,154(4):661-675.
[19] JANA I,SAHA K,SOSHNIKOV A.Fluctuations of linear eigenvalue statistics of random band matrices[J].Journal of Magnetism & Magnetic Materials,2014,34(31):181-182.
[20] 李斌,曾红艳,范瑞卿,等.基于故障分量的相位相关电流差动保护[J].电力系统自动化,2011,35(3):54-58.LI Bin,ZENG Hongyan,FAN Ruiqing,et al.Phase correlation current differential protection based on fault component[J].Automation of Electric Power Systems,2011,35(3):54-58.
[21] 刘凯,李幼仪,伊沃布林西奇,等.自适应线路差动保护新原理[J].中国电机工程学报,2016,36(13):3440-3450.LIU Kai,LI Youyi,BRNCIC Ivo,et al.A novel adaptive differential line protection principle[J].Proceedings of the CSEE,2016,36(13):3440-3450.
[22] 王宾,董新洲,薄志谦,等.非全相运行输电线路负序方向纵联保护方法[J].电力系统自动化,2009,33(12):61-66.WANG Bin,DONG Xinzhou,BO Zhiqian,et al.A novel algorithm for negative sequence pilot protection applicable to open-phase transmission lines[J].Automation of Electric Power Systems,2009,33(12):61-66.
[23] NAYAK P K,PRADHAN A K,BAJPAI P.Wide-area measurement-based backup protection for power network with series compensation[J].IEEE Transactions on Power Delivery,2014,29(4):1970-1977.