基于最大流算法的复杂电力网络脆弱性分析
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摘要
结合电力网络的电气特征,提出一种基于复杂网络理论和网络最大流算法得到定位电力网络关键线路的方法。首先,通过计算电力网络导纳矩阵,对连接线赋予相应权重;然后,基于网络最大流算法算出连接线最大流量,并综合导纳及线路最大流量值作为识别关键线路新的状态指标。最后,对IEEE 39节点系统和IEEE 118节点系统进行仿真分析。结果表明,该系统对随机攻击具有较强的鲁棒性,随机选择和移除元件对系统效率几乎没有影响,但对有高中心性指数的线路蓄意攻击后,网络效率急剧下降,IEEE 39系统约下降了60%,IEEE 118系统约下降了40%。
Combined with the electrical characteristics of power network, a method has thus been proposed based on complex network theory and network maximum flow algorithm to locate the key lines of power network.Firstly, by calculating the power network admittance matrix, the connecting lines are assigned with corresponding weights. Then, based on the maximum flow algorithm of the network, the maximum flow of the connecting line can be worked out, with a synthesis of the admittance and maximum flow of the line as new state indicators for identifying key lines. Finally, the simulation analysis has been carried out of the 39-node system and 118-node system of the IEEE.The results show that the system has strong robustness to random attacks, with the efficiency of the system almost unaffected by the random selection and removal of components, while the efficiency of the network decreases sharply with deliberate attacks on lines with high centrality index, with a decrease by about 60% the efficiency of the IEEE 39 system and a decrease by about 40% the efficiency of the IEEE 118 system.
Combined with the electrical characteristics of power network, a method has thus been proposed based on complex network theory and network maximum flow algorithm to locate the key lines of power network.Firstly, by calculating the power network admittance matrix, the connecting lines are assigned with corresponding weights. Then, based on the maximum flow algorithm of the network, the maximum flow of the connecting line can be worked out, with a synthesis of the admittance and maximum flow of the line as new state indicators for identifying key lines. Finally, the simulation analysis has been carried out of the 39-node system and 118-node system of the IEEE.The results show that the system has strong robustness to random attacks, with the efficiency of the system almost unaffected by the random selection and removal of components, while the efficiency of the network decreases sharply with deliberate attacks on lines with high centrality index, with a decrease by about 60% the efficiency of the IEEE 39 system and a decrease by about 40% the efficiency of the IEEE 118 system.
引文
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[2]DING M,HAN P.Reliability Assessment to LargeScale Power Grid Based on Small-World Topological Model[C]//International Conference on Power System Technology.[S.l.]:IEEE,2007:1-5.
[3]ZHAO H S,ZHANG C,REN H.Power Transmission Network Vulnerable Region Identifying Based on Complex Network Theory[C]//International Conference on Electric Utility Deregulation&Restructuring&Power Technologies.[S.l.]:IEEE,2008:1082-1085.
[4]魏震波,苟竞.复杂网络理论在电网分析中的应用与探讨[J].电网技术,2015,39(1):279-287.WEI Zhenbo,GOU Jing.An Overview on Application of Complex Network Theory in Power System Analysis[J].Power System Technology,2015,39(1):279-287.
[5]刘耀年,术茜,康科飞,等.基于电抗加权介数指标的电网脆弱线路识别[J].电力系统保护与控制,2011,39(23):89-92.LIU Yaonian,ZHU Xi,KANG Kefei,et al.Identification of Vulnerable Lines in Power Grid Based on Reactive Weighted Median Index[J].Power System Protection and Control,2011,39(23):89-92.
[6]陈晓刚,孙可,曹一家.基于复杂网络理论的大电网结构脆弱性分析[J].电工技术学报,2007,22(10):138-144.CHEN Xiaogang,SUN Ke,CAO Yijia.Vulnerability Analysis of Large Power Grid Structure Based on Complex Network Theory[J].Transactions of China Electrotechnical Society,2007,22(10):138-144.
[7]蔡泽祥,王星华,任晓娜,等.复杂网络理论及其在电力系统中的应用研究综述[J].电网技术,2012,36(11):114-121.CAI Zexiang,WANG Xinghua,REN Xiaona,et al.AReview of Complex Network Theory and Its Application in Power Systems[J].Power System Technology,2012,36(11):114-121.
[8]WATTS D J.Small Worlds:The Dynamics of Networks Between Order and Randomness[J].Physics Today,2002,31(4):74-75.
[9]严子恒.最小割最大流算法的研究与应用[D].南京:南京邮电大学,2016.YAN Ziheng.Research and Application of Minimum Cut Maximum Flow Algorithm[D].Nanjing:Nanjing University of Posts and Telecommunications,2016.
[10]BOETTCHER S,MERTENS S.Analysis of the Karmarkar-Karp Differencing Algorithm[J].European Physical Journal B,2008,65(1):131-140.
[11]GOLDBERG A V,TARJAN R E.A New Approach to the Maximum Flow Problem[J].Journal of the ACM,1988,35(4):921-940.
[12]AHUJA R K,ORLIN J B.A Fast and Simple Algorithm for the Maximum Flow Problem[J].Operations Research,1989,37:748-759.
[13]杜政均.一种新的最大流算法的研究[D].成都:电子科技大学,2015.DU Zhengjun.Research on a New Maximum Flow Algorithm[D].Chengdu:University of Electronic Science and Technology of China,2015.