摘 要:针对世界上连续发生的电网连锁性大停电事故,论述了长期以来采用的还原法的思想方法已不完全适应对电网整体动态特性的研究.简述了复杂网络的基本概念;综述了应用复杂网络理论,对美国和中国电网大停电事故的部分数据统计分析的结果.发现电力系统的无标度特性:大停电的规模与出现的概率具有幂律特征,而电网的自组织临界性是发生连锁性大停电事故的内在动力.提出建立实时动态的全国沙堆模型,为预测大停电事故提供实时信息和应用复杂网络的控制理论对电网关键节点进行保护和控制,以缓解大停电事故发生的设想.
关键词:连锁性大停电事故;复杂网络;幂律分布;无标度网络;自组织临界性;沙堆模型
分类号:TM712;TM721.3 文献标识码:A
文章编号:1004-9649(2007)11-0025-08
Applying complex network theory to analyze mechanism of cascading large blackouts failure
DING Dao-qi
作者简介:丁道齐(1938-),男,江苏扬州人,国电通信中心前主任,高级工程师(教授级),从事电力系统运行、电力系统自动化及电力系统通信的技术管理工作.E-mail:dingdaoqi@vip.sina.com
作者单位:丁道齐(国电通信中心,北京,100761)
参考文献:
[1]U.S.-Canada Power System Outage Task Force.Final report on the August 14th blackout in the United States and Canada:causes and recommendations[EB/OL].http://www.nerc.com/.2004.
[2]何大愚.一年以后对美加"8.14"大停电事故的反思[J].电网技术,2004,28(21):1-5.HE Da-yu.Rethinking over' 8.14' US-Canada blackout after one year[J].Power System Technology,2004,28 (21):1-5.
[3]WATTS D J,STROGATZ S H.Collective dynamics of 'small-world'networks[J].Nature,1998,393 (6684):440-442.
[4]BARABáSI A L,ALBERT R.Emergence of scaling in random networks[J].Science,1999,286:509-512.
[5]CARRERAS B A,NEWMAN D E,DOBSON I,et al.Initial evidence for self-organized criticality in electric power blackouts[EB/OL].http://eceserv0.ece.wisc.edu/~dobson/PAPERS/carrerasHICSS00.pdf.
[6]CHEN J,THORP J S,PARASHAR M.Analysis of electric power system disturbance data[C]//Thirty-fourth Hawaii International Conference on System Sciences.Maui,Hawaii,2001:738-744.
[7]CARRERAS B A,NEWMAN D E,DOBSON I,et al.Evidence for self organized criticality in electric power system blackouts[C]//Thirtyfourth Hawaii International Conference on System Sciences.Maui,Hawaii,2001:705-709.
[8]鲁宗相.电网复杂性及大停电事故的可靠性研究[J].电力系统自动化,2005,29(12):93-97.LU Zong-xiang.Survery of the research on the complexity of power grids and reliability analysis of blackouts[J].Automation of Electric Power Systems,2005,29 (12):93-97.
[9]周涛,傅忠谦,牛永伟,等.复杂网络上传播动力学研究综述[J].自然科学进展,2005,15(5):513-518.ZHOU Tao,FU Zhong-qian,NIU Yong-wei,et al.Spreading dynamics research overview on the Complex Networks,Progress in Natural Science,2005,15(5):513-518.
[10]周涛,周佩玲,刘隽,等.规则网络上的耗散级联动力学[J].复杂系统与复杂性科学,2005,2(1):18-23.ZHOU Tao,ZHOU Pei-ling,LIU Jun,et al.Dissipation cascading dynamics on regular networks[J].Complex Systems and Complexity Science,2005,2 (1):18-23.
[11]柏文洁,汪秉宏,周涛.从复杂网络的观点看大停电事故[J].复杂系统与复杂性科学,2005,2(3):29-37.BAI Wen-jie,WANG Bing-hong,ZHOU Tao.Brief review of blackouts on electric power grids in viewpoint of complex networks[J].Complex Systems and Complexity Science,2005,2 (3):29-37.
[12]丁明,韩平平.基于复杂系统理论的电网连锁故障研究[J].合肥工业大学学报:自然科学版,2005,28(9):1047-1052.DING Ming,HAN Ping-ping.Research on power system cascading failure with complex system theory[J].Journal of Hefei University of Technology:Natural Science,2005,28 (9):1047-1052.
[13]曹一家,刘美君,丁理杰,等.大电网安全性评估的系统复杂性理论研究[J].电力系统及其自动化学报,2007,19(1):1-8.CAO Yi-jia,LIU Mei-jun,DING Li-jie,et al.Research on system complexity theory for security evaluation of large power grids[J].Proceedings of the CSU-EPSA,2007,19 (1):1-8.
[14]邓慧琼,艾欣,赵亮.电网连锁故障分析方法评述[J].现代电力,2006,23(6):10-20.DENG Hui-qiong,AI Xin,ZHAO Liang.Comment on analysis method of cascading outages in power grid[J].Modern Electric Power,2006,23 (6):10-20.
[15]BARABáSI A-L.Emergence of scaling in complex networks.In:Bornholdt S,Schuster H G (Eds.).Handbook of graphs and networks:from the genome to the Internet[M].Berlin:Wiley-VCH,2002.
[16]Albert R,Barabási A-L.Statistical mechanics of complex networks[J].Reviews of Modern Physics,2002,74:47-97.
[17]BARABáSI A-L,BONABEAU E.Scale-free networks[J].Scientific American,2003 (5):50-59.
[18]胡海波,王林.幂律分布研究简史[J].物理,2005,34(12):889-896.HU Hai-bo WANG Lin.A brief research history of power law distributions[J].Physics,2005,34(12):889-896.
[19]COHEN R,HAVLIN S.Scale-free networks are ultra small[J].Physical Review Letters,2003,90 (5):058701.
[20]ZHOU T,WANG B H,HUI P M,et al.Topological properties of integer networks[J].arXiv:cond-mat / 0405258,2004.
[21]孟仲伟,鲁宗相,宋靖雁.中美电网的小世界拓扑模型比较分析[J].电力系统自动化,2004,28(15):21-24,29.MENG Zhong-wei,LU Zong-xiang,SONG Jing-yan.Comparison analysis of the small-world topological model of Chinese and American power grids[J].Automation of Electric Power Systems,2004,28 (15):21-24,29.
[22]CARRERAS B A,NEWMAN D E,DOBSON I,et al.Evidence for self-organized criticality in a time series of electric power system blackouts[J].IEEE Trans.Circuits and System,2004,51 (9):1733-1740.
[23]DOBSON I,CARRERAS B A,LYNCH V E,et al.An initial model for complex dynamics in electric power system blackouts[C]//Proceedings of 34th Hawaii International Conference on System Sciences.Maui,Hawaii.January,2001,710-718.
[24]CRUCITTI R,LATORA V,MARCHIORi M.A topological analysis of the Italian electric power grid[J].Physics A,2004,338 (1):92-97.
[25]SURDUTOVICH G,CORTEZ C,VITILINA R,et al.Dynamics of"Small World" networks and vulnerability of the electric power grid[C]//Ⅷ Symposium of Specialists in Electric Operational and Expansion Planning,Brazil,May,2002.
[26]陈洁,许田,何大韧.中国电力网的复杂网络共性[J].科技导报,2004(4):11-14.CHEN J,XU T,HE D R.Universal properties of China's power grid as a complex network[J].Science and Technology Review,2004(4):11-14.
[27]XU T,CHEN J,HE Y,et al.Complex network properties of Chinese power grid[J].International Journal of Modern Physics B,2004,18(17-19):2599-2603.
[28]FAIRLEY P.The unruly power grid[J].Spectrum,IEEE,2004,8(21):22-24.
[29]ZHOU T,WANG B H.Catastrophes in scale-free networks[J].Chinese Physics Letters,2005,22 (5):1072-1075.
[30]NEWMAN D E,CARRERAS B A,LYNCH V E,et al.The impact of various upgrade strategies on the long-term dynamics and robustness of the transmission grid[C]//Pittsburgh PA:Electricity Transmission in Deregulated Markets,Conference at Carnegie-Mellon University,2004.
[31]ALBERT R,ALBERT I,NAKARADO G L.Structural vulnerability of the North American power grid[J].Physical Review E,2004,69(2):025103.
[32]MOTTER A E,LAI Y C.Cascade-based attacks on complex networks[J].Physical Review E,2002,66 (6):065102.
[33]MOTTER A E.Cascade control and defense in complex networks[J].Physical Review Letters,2004,93 (9):098701.
[34]LAI Y C,MOTTER A,NISHIKAWA T,et al.Complex networks:dynamics and security[J].Pramana Journal of Physics,2005,64 (4):483-502.
[35]BAK P,TANG C,WIESENFELD K.Self-organized criticality:an explanation of the 1/f noise[J].Physical Review Letters,1987,59:381-384.
[36]曹一家,江全元,丁理杰.电力系统大停电的自组织临界现象[J].电网技术,2005,29(15):1-5.CAO Yi-jia,JIANG Quan-yuan,DING Li-Jie.Self-organized criticality phenomenon for power system blackouts[J].Power System Technology,2005,29(15):1-5.
[37]于群,郭剑波.我国电力系统停电事故自组织临界性的研究[J].电网技术,2006,30(6):1-5.YU Qun,GUO Jian-bo.Study on self-organized criticality of power system blackouts in China[J].Power System Technology,2006,30(6):1-5.
[38]汪小帆,李翔,陈关荣.复杂网络理论及其应用[M].北京:清华大学出版社,2006.WANG Xiao-fan,LI Xiang,CHEN Guan-yong.The complicated network theories and its application[M].Beijing:Tsinghua University Press,2006.
[39]CARRERAS B A,LYNCH V E,DOBSON I,et al.Critical points and transition in an electric power transmission model for cascading failure blackouts[J].Chaos,2002,12 (4):985-993.
[40]DOBSON I,CARRERAS B A,NEWMAN D E.A branching process approximation to cascading load-dependent system failure[C]//Proceeding of 37th Hawaii International Conference on System Sciences (HICSS'04)-Track 2-Volume 2.Jan.2004:20055.3.
[41]GOH K I,LEE D S,KAHNG B,et al.Sandpile on scale-free networks[J].Physical Review Letters,2003,91 (14):8701-8704.
[42]WANG Xiao-fan,CHEN Guan-yong.Pinning control of scale-free dynamical networks[J].Physics A,2002,310:521-531.
[43]LI Xiang,WANG Xiao-fan,CHEN Guan-rong.Pinning a complex dynamical networks to its equilibrium[J].IEEE Trans.on Circuits and Systems-Ⅰ,2004,51:2074-2087. |