基于图论的智能电网最优孤岛划分模型和算法
|
摘要
孤岛运行(或独立子系统运行)是互联电网和含分布式发电(DG)配电系统的一类特殊运行方式。对于前者而言,及时地将系统解列成多个能够稳定运行的孤岛系统可以避免局部事故扩散引发大面积停电甚至系统崩溃;对于后者而言,灵活、优化的孤岛运行方式可以提高配电系统供电可靠性,充分发挥分布式能源的潜力。针对当前电力系统最优孤岛划分方面研究的不足,以图论中的相关理论为研究工具,本文对智能输电网最优主动解列断面选择和智能配电网最优孤岛划分的模型和算法进行了深入和全面的研究,相关研究内容及成果如下:
第一,首次建立了一类全新的图论问题——含连通图约束的背包问题(CGKP)并提出了其有效近似算法。本文引入了与图连通性相关的四个新的节点集合,研究了新节点集合的性质和搜索方法;以此为基础,通过对求解含图约束背包问题(GKP)的近似算法进行扩展,提出了求解CGKP的有效近似算法。
第二,建立了大电网最优主动解列断面选择问题的完整数学模型,并提出了“搜索+调整”的两阶段求解方法。本文将完整主动解列数学模型分解成图的最优平衡分割和基于优化潮流的调整两个子问题,并利用CGKP近似算法和电网优化调节措施分两个阶段相继求解这两个子问题从而得到最终的系统解列方案。
第三,通过引入电气距离测度改进基于CGKP的图平衡分割子问题的求解方法。该方法将与某一同调发电机群电气距离明显更近的负荷节点优先划入到同一孤岛而显著减少CGKP算法的搜索空间,也使得解列之后孤岛结构更加合理。
第四,提出了基于主从问题交替优化的最优主动解列断面选择方法。该方法将“搜索+调整”策略中相继独立求解的图最优平衡分割问题和最优潮流问题分别设置为主问题和从问题,利用从问题的优化结果调整主问题模型中的参数及求解过程,从而通过多次交替迭代得到整体上更为优化的主动解列方案。
第五,提出了含DG配电系统最优孤岛划分新模型,并利用“搜索+调整”策略进行求解。该策略首先基于动态规划算法和分枝定界算法通过求解包含多个树背包问题(TKP)的孤岛建立和孤岛合并问题而得到初始孤岛组成,然后通过可行性校验和调节得到最终孤岛划分方案。在此基础上,深入研究和比较了基于动态规划算法及分枝定界算法的孤岛划分策略的优缺点及适用条件。
第六,基于简化等效网络,提出了利用蒙特卡罗序贯仿真法对含风力/光伏发电等DG电源的配电系统可靠性进行评估的新方法。该方法利用简化网络得到区域元件故障影响表,然后基于序贯蒙特卡罗仿真方法对DG的随机功率输出、设备运行/故障状态,以及负荷的随机容量对系统可靠性的影响进行了分析及计算。相关分析结果有力证实了智能配网最优孤岛划分研究的现实意义。
Island operation(or independent sub-system operation)is a special operation mode for interconnected transmission power system and distribution power system integrated with distributed generation (DG). Many blackouts or even system collapse caused by a local disturbance would have been avoided if the interconnected transmission power system is safely and quickly split into several islands in time. For the distribution power system, its supply reliability can be not only improved through flexible and optimum island operation, but also the usage of DG can be taken fully advantage of. To focus on the deficit and difficulty existed in current study on the optimum island partition of power system, with the related theories of graph theory to be tools, the model and algorithm for optimum controlled separation surface searching of smart transmission system and optimum island partition of smart distribution system has been thoroughly studied in this thesis, and many satisfactory achievements have been obtained. The main achievements and research contents are listed in the following. First, a new graph theory problem--connected graph constrained knapsack problem (CGKP) is built, and an efficient approximation algorithm is proposed to solve the CGKP. In this thesis, four node sets related to graph connectivity are first introduced. The characteristics of the sets are studied, also the searching methods of the sets are proposed. Based on those study achievements on the characteristics and searching algorithms of the new node sets, an approximation algorithm for CGKP is presented by the extension of the approximation algorithm of graph constrained knapsack problem (GKP). Second, the mathematic model of the optimum controlled separation surface searching
problem of interconnected transmission power system is constructed, and a two-stage strategy of“searching and regulation”is designed to solve this problem. The model is decomposed into an optimum balance graph partition sub-problem and a regulation sub-problem based on optimal power flow. These two sub-problems are successively solved by the CGKP approximation algorithm and optimal regulation measure based on the solution of optimal power flow to acquire a final controlled separation surface. Third, electrical distance constraint is proposed to improve the CGKP-based method of the optimum balance graph partition sub-problem. The load nodes which are closer to a specific coherence generator group are preferentially allocated to the island containing the specific coherence generator group by the improved method, so that the searching space of the CGKP approximation algorithm is reduced evidently. At the same time, the configuration of the sub-system obtained is also more reasonable. Fourth, an optimum controlled partition method based on the alternate optimization of the master problem and sub-problem is proposed. The optimum balance graph partition sub-problem and optimal power flow sub-problem which are successively solved in the“searching and regulation”strategy are set to be master problem and sub-problem, respectively. The result fed by the sub-problem is used to adjust the parameters and solving process of the master problem. Therefore, a more optimal controlled separation scheme will be obtained by repeating the alternate optimization of the master problem and sub-problem for several times.
Fifth, in this thesis, a novel optimum island partition model is presented for the distribution system integrated with DG, and the“search and regulation”strategy is applied to solve this problem. Initial optimum island partition scheme is gained through island partition procedures including multiple tree knapsack problems (TKP) and island combination procedures based on dynamic programming algorithm and branch and bound algorithm. The final island partition scheme is obtained after feasibility checking and adjustment. Furthermore, through the comparison of the optimum island partition strategies based on dynamic programming algorithm and branch and bound algorithm, application scopes of those two methods are shown. Last, a new reliability evaluation method using the Monte Carlo time sequential simulation for the distribution system with DG including wind power and photovoltaic power generation system and etc. is presented based on the simplified equivalent network The zone element failure effect table is obtained only at the simplified network; then, the impact of the DGs’stochastic power output, running/failure statuses of the devices and the stochastic capacity of the loads on the distribution system reliability are analyzed and calculated by the Monte Carlo time sequential simulation. The results of samples demonstrate the validity of the method proposed, fourthly, it also strongly proofs the practical significance of the optimum island study on the smart distribution system.
第一,首次建立了一类全新的图论问题——含连通图约束的背包问题(CGKP)并提出了其有效近似算法。本文引入了与图连通性相关的四个新的节点集合,研究了新节点集合的性质和搜索方法;以此为基础,通过对求解含图约束背包问题(GKP)的近似算法进行扩展,提出了求解CGKP的有效近似算法。
第二,建立了大电网最优主动解列断面选择问题的完整数学模型,并提出了“搜索+调整”的两阶段求解方法。本文将完整主动解列数学模型分解成图的最优平衡分割和基于优化潮流的调整两个子问题,并利用CGKP近似算法和电网优化调节措施分两个阶段相继求解这两个子问题从而得到最终的系统解列方案。
第三,通过引入电气距离测度改进基于CGKP的图平衡分割子问题的求解方法。该方法将与某一同调发电机群电气距离明显更近的负荷节点优先划入到同一孤岛而显著减少CGKP算法的搜索空间,也使得解列之后孤岛结构更加合理。
第四,提出了基于主从问题交替优化的最优主动解列断面选择方法。该方法将“搜索+调整”策略中相继独立求解的图最优平衡分割问题和最优潮流问题分别设置为主问题和从问题,利用从问题的优化结果调整主问题模型中的参数及求解过程,从而通过多次交替迭代得到整体上更为优化的主动解列方案。
第五,提出了含DG配电系统最优孤岛划分新模型,并利用“搜索+调整”策略进行求解。该策略首先基于动态规划算法和分枝定界算法通过求解包含多个树背包问题(TKP)的孤岛建立和孤岛合并问题而得到初始孤岛组成,然后通过可行性校验和调节得到最终孤岛划分方案。在此基础上,深入研究和比较了基于动态规划算法及分枝定界算法的孤岛划分策略的优缺点及适用条件。
第六,基于简化等效网络,提出了利用蒙特卡罗序贯仿真法对含风力/光伏发电等DG电源的配电系统可靠性进行评估的新方法。该方法利用简化网络得到区域元件故障影响表,然后基于序贯蒙特卡罗仿真方法对DG的随机功率输出、设备运行/故障状态,以及负荷的随机容量对系统可靠性的影响进行了分析及计算。相关分析结果有力证实了智能配网最优孤岛划分研究的现实意义。
Island operation(or independent sub-system operation)is a special operation mode for interconnected transmission power system and distribution power system integrated with distributed generation (DG). Many blackouts or even system collapse caused by a local disturbance would have been avoided if the interconnected transmission power system is safely and quickly split into several islands in time. For the distribution power system, its supply reliability can be not only improved through flexible and optimum island operation, but also the usage of DG can be taken fully advantage of. To focus on the deficit and difficulty existed in current study on the optimum island partition of power system, with the related theories of graph theory to be tools, the model and algorithm for optimum controlled separation surface searching of smart transmission system and optimum island partition of smart distribution system has been thoroughly studied in this thesis, and many satisfactory achievements have been obtained. The main achievements and research contents are listed in the following. First, a new graph theory problem--connected graph constrained knapsack problem (CGKP) is built, and an efficient approximation algorithm is proposed to solve the CGKP. In this thesis, four node sets related to graph connectivity are first introduced. The characteristics of the sets are studied, also the searching methods of the sets are proposed. Based on those study achievements on the characteristics and searching algorithms of the new node sets, an approximation algorithm for CGKP is presented by the extension of the approximation algorithm of graph constrained knapsack problem (GKP). Second, the mathematic model of the optimum controlled separation surface searching
problem of interconnected transmission power system is constructed, and a two-stage strategy of“searching and regulation”is designed to solve this problem. The model is decomposed into an optimum balance graph partition sub-problem and a regulation sub-problem based on optimal power flow. These two sub-problems are successively solved by the CGKP approximation algorithm and optimal regulation measure based on the solution of optimal power flow to acquire a final controlled separation surface. Third, electrical distance constraint is proposed to improve the CGKP-based method of the optimum balance graph partition sub-problem. The load nodes which are closer to a specific coherence generator group are preferentially allocated to the island containing the specific coherence generator group by the improved method, so that the searching space of the CGKP approximation algorithm is reduced evidently. At the same time, the configuration of the sub-system obtained is also more reasonable. Fourth, an optimum controlled partition method based on the alternate optimization of the master problem and sub-problem is proposed. The optimum balance graph partition sub-problem and optimal power flow sub-problem which are successively solved in the“searching and regulation”strategy are set to be master problem and sub-problem, respectively. The result fed by the sub-problem is used to adjust the parameters and solving process of the master problem. Therefore, a more optimal controlled separation scheme will be obtained by repeating the alternate optimization of the master problem and sub-problem for several times.
Fifth, in this thesis, a novel optimum island partition model is presented for the distribution system integrated with DG, and the“search and regulation”strategy is applied to solve this problem. Initial optimum island partition scheme is gained through island partition procedures including multiple tree knapsack problems (TKP) and island combination procedures based on dynamic programming algorithm and branch and bound algorithm. The final island partition scheme is obtained after feasibility checking and adjustment. Furthermore, through the comparison of the optimum island partition strategies based on dynamic programming algorithm and branch and bound algorithm, application scopes of those two methods are shown. Last, a new reliability evaluation method using the Monte Carlo time sequential simulation for the distribution system with DG including wind power and photovoltaic power generation system and etc. is presented based on the simplified equivalent network The zone element failure effect table is obtained only at the simplified network; then, the impact of the DGs’stochastic power output, running/failure statuses of the devices and the stochastic capacity of the loads on the distribution system reliability are analyzed and calculated by the Monte Carlo time sequential simulation. The results of samples demonstrate the validity of the method proposed, fourthly, it also strongly proofs the practical significance of the optimum island study on the smart distribution system.
引文
[1] Li H, Rosenwald Gary W, Jung Juhwan, Liu Chen-Ching, Strategic Power Infrastructure Defense, Proceedings of The IEEE, 2005, 93(5): 918~933
[2] Taylor C W, Erickson D C, Recording and analyzing the July 2 cascading outage [Western USA power system], IEEE Computer Applications in Power, 1997, 10(1): 26~30
[3]薛禹胜,综合防御由偶然事故演化为电力灾害——北美“8.14”大停电的警示,电力系统自动化,2003,27(18): 1~6
[4]胡学浩,美加联合电网大面积停电事故的反思和启示,电网技术,2003,27(9):2~6
[5] Senroy N, Heydt G T, Vittal V, Decision tree assisted controlled islanding, IEEE Transactions on Power Systems, 2006,21(4): 1790~1797
[6] Senroy N, Heydt G T, Timing of a controlled islanding strategy, Transmission and Distribution Conference and Exhibition, 2005/2006 IEEE PES, 2006, 1460~1466
[7] Nilanjan Senroy, Gerald T Heydt, A Conceptual Framework for the Controlled Islanding of Interconnected Power Systems, IEEE Transactions On Power Systems, 2006, 21(2):1005~1006
[8] K Rajamani, U K Hambarde, Islanding and load shedding schemes for captive power plants, IEEE Transactions on Power Delivery, 1999, 14(3): 805~809
[9] IEEE-SA Standards Board, 1547 IEEE standard for interconnecting distributed resources into electric power systems, NY, USA: The Institute of Electrical and Electronic Engineers,Inc,2003
[10] P P Barker, R W De Mello, Determining the impact of distributed generation on power systems I: Radial distribution systems, IEEE Power Engineering Society Summer Meeting, 2000, 3: 1645~1656
[11] Neto A C, da Silva M G, Rodrigues A B, Impact of Distributed Generation on Reliability Evaluation of Radial Distribution Systems Under Network Constraints, International Conference on Probabilistic Methods Applied to Power Systems, 2006, 1~6
[12] Burgio A, Menniti D, Pinnarelli A, Sorrentino N, The reliability studies of a novel integrated configuration for micro-grids, Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, 2008, 2634~2639
[13]袁季修,防御大停电的广域保护好紧急控制,北京:中国电力出版社,2006
[14]张保全,张毅刚,刘海涛,基于本地量大振荡解列装置原理研究,中国电机工程学报,2001,21(12):67~72
[15]张保全,加强继电保护与紧急控制系统的研究提高互联电网安全防御能力,中国电机工程学报,2004,24(7):1~6
[16]王达,薛禹胜,Q H WU,等,故障解列与失步解列的协调优化,电力系统自动化,2009,33(14): 1~7
[17]高鹏,王健全,甘德强,等,电力系统失步解列综述,电力系统自动化,2005,29(19):90~96
[18] B A Archer, J B Davies, System islanding considerations for improving power system restoration at Manitoba Hydro, IEEE Canadian Conference on Electrical and Computer Engineering, 2002, 1: 60~65
[19] K Rajamani, U K Hambarde, Islanding and load shedding schemes for captive power plants, IEEE Transactions on Power Delivery, 1999, 14(3): 805~809
[20] S Agematsu, S Imai, R Tsukui, H Watanabe, T Nakamura, T Matsushima, Islanding protection system with active and reactive power balancing control for Tokyo metropolitan power system and actual operational experiences, 7th IEE International Conference on Developments in Power System Protection, 2001, 351~354
[21] Kai Sun, Da-Zhong Zheng, Qiang Lu, Splitting strategies for islanding operation of large-scale power systems using OBDD-based methods, IEEE transactions on power systems, 2003, 18(2): 912~923
[22] Qianchuan Zhao, Kai Sun, Da-Zhong Zheng, Jin Ma, Qiang Lu, A study of system splitting strategies for island operation of power system: a two-phase method based on OBDDs, IEEE transactions on power systems, 2003, 18(4): 1556~1565
[23] Kai Sun, Da-Zhong Zheng, Qiang Lu, A simulation study of OBDD-based proper splitting strategies for power systems under consideration of transient stability, IEEE transactions on power systems, 2005, 20(1): 1151~1159
[24] Sun K,Zheng D Z, Lu Q, Searching for feasible splitting strategies of controlled system islanding, Generation, Transmission and Distribution, IEE Proceedings, 2006, 153(1): 89~98
[25] Peiravi A, Ildarabadi R, A fast Algorithm for intentional islanding of power systems using the multilevel Kernel K-Means Approach, Journal of Applied Sciences, 2009, 9(12): 2247~2255
[26] Peiravi A, Ildarabadi R, Complexities of using graph partitioning in modern scientific problems and application to power system islanding, Journal of American Science, 2009, 5(5):1~12
[27] Xu G, Vittal V, Slow coherency based cutset determination algorithm for large power systems, IEEE Transactions on power systems, 2010, 25(2): 877~844
[28] Li J, Liu C C, Power Systems reconfiguration based on multilevel graph partitioning, IEEE Bucharest power Tech. Conference, 2009, pp5
[29] Li J, Liu C C. Schneider K P, Controlled Partitioning of Power network considering real and reactive power balance, IEEE Transactions on Smart grid, 2010, 1(3): 261~269
[30] Sen A, Ghosh P, Vittal V, Yang B, A new min-cut problem with application to electric power network partitioning, European Transactions on Electrical Power, 2009, 19: 778~797
[31] Pothen A, Simon H D, Liou K P, Partitioning Sparse Matrixes with Eigenvectors of Graphs, SIAM Journal on Matrix Analysis and Applications, 1990, 11 (3): 430~452
[32] Yang H, Wang G F, Efficient network flow based on min-cut, balanced partitioning, IEEE Transactions on Computer-Aided Design, 1996, 15(2): 1533~1540
[33] Dhillon I S, Guan Y, Kulis B, Weighted graph cuts without eigenvectors: a multilevel approach, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(11): 1944~1957
[34]段振国,高曙,杨以涵,卢强,基于图论理论的电力系统解列策略生成方法,中国电力,1988, 31(3): 7~9
[35] You H, Vittal V, Wang X, Slow coherency based islanding, IEEE Transactions on power systems, 2004, 19(1): 483~491
[36] Wang Xiaoming, Vittal Vijay, System islanding using minimal cutsets with minimum net flow, Proceeding of IEEE Power Systems Conference and Exposition, New York, 2004
[37] Wang X, Vittal V, Heydt G T, Tracing Generator Coherency Indices Using the Continuation Method: A Novel Approach, IEEE Transactions on Power Systems, 2005,20(3):1510~1518
[38]乔颖,沈沉,卢强,大电网解列决策空间筛选及快速搜索方法,中国电机工程学报,2008, 28(22):23~28
[39] Najafi S, Hosseinian S H, Abedi M, Proper Splitting of Interconnected Power System, IEEJ Transactions on Electrical and Electronic Engineering,2010, 5:211~220
[40]刘源祺,刘玉田,基于调度分区的电力系统解列割集搜索算法,电力系统自动化, 2008,32(11):20~24
[41] C G Wang, B H Zhang, Z G Hao, and etc,, A Novel Real-Time Searching Method for Power System Splitting Boundary, IEEE Transactions on Power Systems, 2010, 25(4): 1902~1909
[42] Ming Jin, Tarlochan S Sidhu, Kai Sun, A New System Splitting Scheme Based on the Unified Stability Control Framework, IEEE Transactions on Power Systems, 2007, 22(1): 433~441
[43] Guler T,Gross G, Detection of island formation and identification of causal factors under multiple line outages, IEEE Transactions on Power Systems, 2007,22(2) :483~491
[44] Caldon R, Stocco A, Turri R, Feasible of adaptive intentional islanding operation of electric utility systems with distributed generation, Electrical Power System Reserch, 2008, 78(12): 2017~2023
[45]易新,陆于平,分布式发电条件下的配电网孤岛划分算法,电网技术, 2006, 30(7): 49~54
[46]丁磊,潘贞存,丛伟,基于有根树的分布式发电孤岛搜索,中国电机工程学报, 2008, 28(25): 62~67
[47] Mao Yiming, Miu K N, Switch placement to improve system reliability for radial distribution system with distributed generation, IEEE Transactions on Power Systems, 2003, 18(4): 1346~1352
[48] Traca de Almeida A, Martins, A, Jesus H, Climaco J, Source reliability in a combined wind-solar-hydro system, IEEE Transactions on Power Apparatus and system, 1983, 102(6): 1515~1520
[49] R Billinton, L Gan, Wind power modeling and application in generating adequacy assessment, IEEE Conference onCommunications Computers and Power in the Modern Environment , 1993, 100~106
[50] Karaki S H, Chedid R B, Ramadan R, Probabilistic performance assessment of autonomous solar-wind energy conversion systems, IEEE Transaction on Energy Conversion, 1999, 14(3):766~772
[51]刘传铨,张焰,计及分布式电源的配电网供电可靠性,电力系统自动化,31(22):46~48
[52] Hegezy Y G, Chikhani A Y, Intention islanding of distributed generation for reliability enhancement, IEEE Power Engineering Society General Meeting, 2003: 208~213
[53] Wang Guoquan, Liu Zongqi, Liu Nian et al, Reliability evaluation of distribution system with distribution generation based on islanding algorithm, Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, 2008,: 2697~2700
[54] Wang P, Billinton R, Time-sequential simulation technique for rural distribution system reliability cost/worth evaluation including wind generation as alternative supply, IEE Proceedings on Generation, Transmission and Distribution, 2001, 148(4): 355~360
[55] Maliki Guindo, Wang Chengshan, Reliability analysis on the integration of wind/PV hybrid distributed generation in distribution system, Automation of Electric Power System, 2005, 29(23): 33~38
[56] Duttagupta S S, Singh C, A reliability assessment methodology for distribution system with distributed generation, IEEE Power Engineering Society General Meeting, 2006: 1~7
[57]别朝红,王锡凡,配电系统的可靠性分析,中国电力,1997,30(5): 10~11
[58] Lagonotte P, Sabonnadiere J C, Leost J Y, Paul J P,Structural analysis of the electrical system: application to secondary voltage control in France, IEEE Transaction on Power System, 1989, 4(2):479~485
[59]李运坤,吕飞鹏,蒋科,陈新,胡亚平,基于最短电气距离的运行方式组合方法,电力系统保护与控制,2010,38(15):24~27
[60]曹一家,陈晓刚,孙可,基于复杂网络理论的大型电力系统脆弱线路辨识,电力自动化设备,2006, 26(12):1~5
[61] Duan Gang, Yu Yixin, Power distribution system optimization by an algorithm for capacitated Steiner tree problems with complex-flows and arbitrary cost functions, Electrical power and energy systems, 2003, 25: 515~523
[62]余贻鑫,段刚,基于最短路算法和遗传算法的配电网络重构,中国电机工程学报,2000,20(9):44~49
[63]吕飞鹏,米麟书,姜可薰,环网方向保护配合最小断点集的神经计算方法,中国电机工程学报, 1997,17(3): 184~189
[64]王英英,罗毅,涂光瑜,刘沛,采用图论的电网连锁故障模式搜索方法,高电压技术, 2010, 36(2): 401~405
[65]梅义,丘东元,张波,基于深度优先搜索的潜在电路计算机辅助分析法,中国电机工程学报, 2008,28(24):75~81
[66]周德才,张保会,姚峰,王立永,邹本国,赵义术,基于图论的输电断面快速搜索,中国电机工程学报, 2006,26(12):32~38
[67]楼世博,金晓龙,李鸿祥,图论及其应用,北京,人民邮电出版社,1982,
[68]屈婉玲,耿素云,张立昂,离散数学,北京,清华大学出版社, 2005
[69]堵丁柱,葛可一,王洁,计算复杂性导论,北京,高等教育出版社, 2002.
[70]谢政,网络算法与复杂性理论,北京,国防科技大学出版社,2003
[71]王红梅,胡明,王涛,数据结构(C++版),北京,清华大学出版社,2005
[72] Min M, Du H W, Jia X H, Improving construction for connected dominating set with Steiner tree in wireless sensor networks, Journal of global optimization, 2006, 35(11): 111~119
[73] Das B, Bharghavan V, Routing in ad hoc networks using minimum connected dominating sets
[74] Garey M R, Johnson D S, Computers and intractability: A guide to the theory of NP-completeness, San Francisco, W. H. Freeman, 1979
[75] Sivakumar R, Das B, Bharghavan V, An improved spine-based infrastructure for routing in Ad Hoc networks, IEEE Symposium on computers and communications, 1998
[76] Wu J, Li H, On calculating connected dominating set for efficient routing in Ad Hoc wireless networks, The 3rd international workshop on discrete algorithm and methods for mobile computing and communications,, 1999:7~14
[77] Ruan L, Du H, Jia X, Wu W, Li Y, Ko K-I, A greedy approximation for minimum connected dominating sets, Theoretical computer science, 2004, 329: 325~330
[78] Storer J A, Constructing full spanning trees for cubic graphs, Information Processing Letters, 1981, 31:8~11
[79] Ravi R, Lu, Approximating maximum leaf spanning trees in almost linear time, Journal of algorithms, 1998, 29(1): 132~141
[80] Solis-Oba R, 2-Approximation Algorithm for Finding a Spanning Tree with Maximum Number of Leaves, ESA’98, 1998, 1461: 441~452
[81] Guha S, Khuller S, Approximation algorithms for connected dominating sets, Algorithmica, 1998, 20: 374~387
[82] Klein P N, Ravi R, A nearly best-possible approximation algorithm for node-weighted Steiner trees, J, Algorithms, 1995, 19(1): 104~114
[83] Guha S, Khuller S, Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets, Information and Computation, 1999, 150(1): 57~74
[84] Robins G, Zelikovsky A, Improved Steiner tree approximation in graphs, Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms, 2000
[85] Chen Donghui, Du Dingzhu Hu Xiao Dong, etc, Approximations for Steiner trees with minimum number of Steiner points, Theoretical Computer Science, 2001, 262: 83~99
[86] R C Prim, Shortest connection networks and some generalizations. Bell System Technical Journal, 1957, 36: 1389–1401
[87] Dijkstra E W, A note on two problem in connexion with graphs, Numerische Mathematik, 1959, 1:269~271
[88]姚恩瑜,何勇,陈仕平,数学规划与组合优化,浙江:浙江大学出版社,2001
[89] G Borradaile, B Heeringa, and G T Wilfong, Approximation Algorithms for Constrained Knapsack Problems, CoRR, 2009, abs/0910.0777
[90] Johnson D S, Niemi K A, On Knapsacks, Partitions and A New Dynamic Programming Technique for Trees, Mathematics of Operations Research, 1983, 8(1): 1~14
[91] J A Lukes, Efficient algorithm for the partitioning of trees, IBM Journal of Research and Development, 1974, 18:214–224
[92] D Bienstock, A lot-sizing problem on trees, related to network design, Mathmaticas of Operations Research, 1993, 18: 402–422
[93] Y Pochet, L A Wolsey, Lot-sizing constant batches: Formulation and valid inequalities, Mathmaticas of Operations Research, 1993, 18: 767–785
[94] Cho G, Shaw D X, A depth-tirst dynamic programming algorithm for the tree knapsack problem, Informs Journal on Computing, 1997, 9(4): 431~438
[95] Shaw D X, Cho G, The Critical-Item, Upper Bounds, and a Branch-and-Bound Algorithm for the Tree Knapsack Problem, Network, 1998: 205~216
[96] Cho G, Shaw D X, An efficient algorithm for a capacitated subtree of a tree problem in local access telecommunication networks, Computers & Operations Research, 1997, 24(8): 737~748
[97] Merwe van der D J, Hattingh J M, Tree knapsack approaches for local access network design. European Journal of Operational Research, 2006, 174: 1968~1978,
[98] IBM ILOG CPLEX Optimizer, http://www-01.ibm.com/software/integration/ optimization/cplex-optimizer/
[99] Baran M E,Wu F F, Optimal capacitor placement on radial distribution systems. IEEE Transactions Power Delivery, 1989, 4(1): 725~734
[100] Kersting W H,Phillips W H,Doyle R Clay, Distribution feeder Reliability Studies, IEEE Transactions on Industry Application, 1999, 32(2):319~323
[101]林济铿,王旭东,基于网络化简的计及开关故障配电网可靠性评估,电力系统自动化,2009, 33(9): 32~36
[102] Abouzahr I, Ramakumar R, An approach to assess the performance of utility-interactive wind electric conversion systems, IEEE Transactions on Energy Conversion, 1991, 6(4): 627~638
[103] Jatzeck, B M, Robinson A M, WATSUN-PV 4.0 Modifications to Include Wind Turbine Generations, AC Load Shedding, and Operation with Zero-capacity Diesel Generator, IEEE Canadian Conference on Electrical and Computer Engineering, 1996, 2: 655~658
[104] HOMER. The Optimization Model for Distributed Power. http://www.nrel.gov/homer/.
[105] PVSYST 3.3 Software for Photovoltaic Systems. http://www.pvsyst.com.
[106]陆志峰,周家启,计及开关和母线故障的配电系统可靠性评估,电网技术,2002,26(4):26~29
[107] Billinton R, Johnnavithula S, A test system for teaching overall power system reliability assessment, IEEE Transactions on Power System, 1996, 11(4): 1670~1676
[108] All R N,Billinton R,Sjarief I,et al, A reliability test system for educational purpose-basic distribution system data and results, IEEE Transactions on Power System, 1991, 6(2): 813~730
[109] IEEE Reliability Test System, IEEE Transactions on Power Apparatus and Systems, 1979, 98(6): 2047~2054
[2] Taylor C W, Erickson D C, Recording and analyzing the July 2 cascading outage [Western USA power system], IEEE Computer Applications in Power, 1997, 10(1): 26~30
[3]薛禹胜,综合防御由偶然事故演化为电力灾害——北美“8.14”大停电的警示,电力系统自动化,2003,27(18): 1~6
[4]胡学浩,美加联合电网大面积停电事故的反思和启示,电网技术,2003,27(9):2~6
[5] Senroy N, Heydt G T, Vittal V, Decision tree assisted controlled islanding, IEEE Transactions on Power Systems, 2006,21(4): 1790~1797
[6] Senroy N, Heydt G T, Timing of a controlled islanding strategy, Transmission and Distribution Conference and Exhibition, 2005/2006 IEEE PES, 2006, 1460~1466
[7] Nilanjan Senroy, Gerald T Heydt, A Conceptual Framework for the Controlled Islanding of Interconnected Power Systems, IEEE Transactions On Power Systems, 2006, 21(2):1005~1006
[8] K Rajamani, U K Hambarde, Islanding and load shedding schemes for captive power plants, IEEE Transactions on Power Delivery, 1999, 14(3): 805~809
[9] IEEE-SA Standards Board, 1547 IEEE standard for interconnecting distributed resources into electric power systems, NY, USA: The Institute of Electrical and Electronic Engineers,Inc,2003
[10] P P Barker, R W De Mello, Determining the impact of distributed generation on power systems I: Radial distribution systems, IEEE Power Engineering Society Summer Meeting, 2000, 3: 1645~1656
[11] Neto A C, da Silva M G, Rodrigues A B, Impact of Distributed Generation on Reliability Evaluation of Radial Distribution Systems Under Network Constraints, International Conference on Probabilistic Methods Applied to Power Systems, 2006, 1~6
[12] Burgio A, Menniti D, Pinnarelli A, Sorrentino N, The reliability studies of a novel integrated configuration for micro-grids, Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, 2008, 2634~2639
[13]袁季修,防御大停电的广域保护好紧急控制,北京:中国电力出版社,2006
[14]张保全,张毅刚,刘海涛,基于本地量大振荡解列装置原理研究,中国电机工程学报,2001,21(12):67~72
[15]张保全,加强继电保护与紧急控制系统的研究提高互联电网安全防御能力,中国电机工程学报,2004,24(7):1~6
[16]王达,薛禹胜,Q H WU,等,故障解列与失步解列的协调优化,电力系统自动化,2009,33(14): 1~7
[17]高鹏,王健全,甘德强,等,电力系统失步解列综述,电力系统自动化,2005,29(19):90~96
[18] B A Archer, J B Davies, System islanding considerations for improving power system restoration at Manitoba Hydro, IEEE Canadian Conference on Electrical and Computer Engineering, 2002, 1: 60~65
[19] K Rajamani, U K Hambarde, Islanding and load shedding schemes for captive power plants, IEEE Transactions on Power Delivery, 1999, 14(3): 805~809
[20] S Agematsu, S Imai, R Tsukui, H Watanabe, T Nakamura, T Matsushima, Islanding protection system with active and reactive power balancing control for Tokyo metropolitan power system and actual operational experiences, 7th IEE International Conference on Developments in Power System Protection, 2001, 351~354
[21] Kai Sun, Da-Zhong Zheng, Qiang Lu, Splitting strategies for islanding operation of large-scale power systems using OBDD-based methods, IEEE transactions on power systems, 2003, 18(2): 912~923
[22] Qianchuan Zhao, Kai Sun, Da-Zhong Zheng, Jin Ma, Qiang Lu, A study of system splitting strategies for island operation of power system: a two-phase method based on OBDDs, IEEE transactions on power systems, 2003, 18(4): 1556~1565
[23] Kai Sun, Da-Zhong Zheng, Qiang Lu, A simulation study of OBDD-based proper splitting strategies for power systems under consideration of transient stability, IEEE transactions on power systems, 2005, 20(1): 1151~1159
[24] Sun K,Zheng D Z, Lu Q, Searching for feasible splitting strategies of controlled system islanding, Generation, Transmission and Distribution, IEE Proceedings, 2006, 153(1): 89~98
[25] Peiravi A, Ildarabadi R, A fast Algorithm for intentional islanding of power systems using the multilevel Kernel K-Means Approach, Journal of Applied Sciences, 2009, 9(12): 2247~2255
[26] Peiravi A, Ildarabadi R, Complexities of using graph partitioning in modern scientific problems and application to power system islanding, Journal of American Science, 2009, 5(5):1~12
[27] Xu G, Vittal V, Slow coherency based cutset determination algorithm for large power systems, IEEE Transactions on power systems, 2010, 25(2): 877~844
[28] Li J, Liu C C, Power Systems reconfiguration based on multilevel graph partitioning, IEEE Bucharest power Tech. Conference, 2009, pp5
[29] Li J, Liu C C. Schneider K P, Controlled Partitioning of Power network considering real and reactive power balance, IEEE Transactions on Smart grid, 2010, 1(3): 261~269
[30] Sen A, Ghosh P, Vittal V, Yang B, A new min-cut problem with application to electric power network partitioning, European Transactions on Electrical Power, 2009, 19: 778~797
[31] Pothen A, Simon H D, Liou K P, Partitioning Sparse Matrixes with Eigenvectors of Graphs, SIAM Journal on Matrix Analysis and Applications, 1990, 11 (3): 430~452
[32] Yang H, Wang G F, Efficient network flow based on min-cut, balanced partitioning, IEEE Transactions on Computer-Aided Design, 1996, 15(2): 1533~1540
[33] Dhillon I S, Guan Y, Kulis B, Weighted graph cuts without eigenvectors: a multilevel approach, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(11): 1944~1957
[34]段振国,高曙,杨以涵,卢强,基于图论理论的电力系统解列策略生成方法,中国电力,1988, 31(3): 7~9
[35] You H, Vittal V, Wang X, Slow coherency based islanding, IEEE Transactions on power systems, 2004, 19(1): 483~491
[36] Wang Xiaoming, Vittal Vijay, System islanding using minimal cutsets with minimum net flow, Proceeding of IEEE Power Systems Conference and Exposition, New York, 2004
[37] Wang X, Vittal V, Heydt G T, Tracing Generator Coherency Indices Using the Continuation Method: A Novel Approach, IEEE Transactions on Power Systems, 2005,20(3):1510~1518
[38]乔颖,沈沉,卢强,大电网解列决策空间筛选及快速搜索方法,中国电机工程学报,2008, 28(22):23~28
[39] Najafi S, Hosseinian S H, Abedi M, Proper Splitting of Interconnected Power System, IEEJ Transactions on Electrical and Electronic Engineering,2010, 5:211~220
[40]刘源祺,刘玉田,基于调度分区的电力系统解列割集搜索算法,电力系统自动化, 2008,32(11):20~24
[41] C G Wang, B H Zhang, Z G Hao, and etc,, A Novel Real-Time Searching Method for Power System Splitting Boundary, IEEE Transactions on Power Systems, 2010, 25(4): 1902~1909
[42] Ming Jin, Tarlochan S Sidhu, Kai Sun, A New System Splitting Scheme Based on the Unified Stability Control Framework, IEEE Transactions on Power Systems, 2007, 22(1): 433~441
[43] Guler T,Gross G, Detection of island formation and identification of causal factors under multiple line outages, IEEE Transactions on Power Systems, 2007,22(2) :483~491
[44] Caldon R, Stocco A, Turri R, Feasible of adaptive intentional islanding operation of electric utility systems with distributed generation, Electrical Power System Reserch, 2008, 78(12): 2017~2023
[45]易新,陆于平,分布式发电条件下的配电网孤岛划分算法,电网技术, 2006, 30(7): 49~54
[46]丁磊,潘贞存,丛伟,基于有根树的分布式发电孤岛搜索,中国电机工程学报, 2008, 28(25): 62~67
[47] Mao Yiming, Miu K N, Switch placement to improve system reliability for radial distribution system with distributed generation, IEEE Transactions on Power Systems, 2003, 18(4): 1346~1352
[48] Traca de Almeida A, Martins, A, Jesus H, Climaco J, Source reliability in a combined wind-solar-hydro system, IEEE Transactions on Power Apparatus and system, 1983, 102(6): 1515~1520
[49] R Billinton, L Gan, Wind power modeling and application in generating adequacy assessment, IEEE Conference onCommunications Computers and Power in the Modern Environment , 1993, 100~106
[50] Karaki S H, Chedid R B, Ramadan R, Probabilistic performance assessment of autonomous solar-wind energy conversion systems, IEEE Transaction on Energy Conversion, 1999, 14(3):766~772
[51]刘传铨,张焰,计及分布式电源的配电网供电可靠性,电力系统自动化,31(22):46~48
[52] Hegezy Y G, Chikhani A Y, Intention islanding of distributed generation for reliability enhancement, IEEE Power Engineering Society General Meeting, 2003: 208~213
[53] Wang Guoquan, Liu Zongqi, Liu Nian et al, Reliability evaluation of distribution system with distribution generation based on islanding algorithm, Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, 2008,: 2697~2700
[54] Wang P, Billinton R, Time-sequential simulation technique for rural distribution system reliability cost/worth evaluation including wind generation as alternative supply, IEE Proceedings on Generation, Transmission and Distribution, 2001, 148(4): 355~360
[55] Maliki Guindo, Wang Chengshan, Reliability analysis on the integration of wind/PV hybrid distributed generation in distribution system, Automation of Electric Power System, 2005, 29(23): 33~38
[56] Duttagupta S S, Singh C, A reliability assessment methodology for distribution system with distributed generation, IEEE Power Engineering Society General Meeting, 2006: 1~7
[57]别朝红,王锡凡,配电系统的可靠性分析,中国电力,1997,30(5): 10~11
[58] Lagonotte P, Sabonnadiere J C, Leost J Y, Paul J P,Structural analysis of the electrical system: application to secondary voltage control in France, IEEE Transaction on Power System, 1989, 4(2):479~485
[59]李运坤,吕飞鹏,蒋科,陈新,胡亚平,基于最短电气距离的运行方式组合方法,电力系统保护与控制,2010,38(15):24~27
[60]曹一家,陈晓刚,孙可,基于复杂网络理论的大型电力系统脆弱线路辨识,电力自动化设备,2006, 26(12):1~5
[61] Duan Gang, Yu Yixin, Power distribution system optimization by an algorithm for capacitated Steiner tree problems with complex-flows and arbitrary cost functions, Electrical power and energy systems, 2003, 25: 515~523
[62]余贻鑫,段刚,基于最短路算法和遗传算法的配电网络重构,中国电机工程学报,2000,20(9):44~49
[63]吕飞鹏,米麟书,姜可薰,环网方向保护配合最小断点集的神经计算方法,中国电机工程学报, 1997,17(3): 184~189
[64]王英英,罗毅,涂光瑜,刘沛,采用图论的电网连锁故障模式搜索方法,高电压技术, 2010, 36(2): 401~405
[65]梅义,丘东元,张波,基于深度优先搜索的潜在电路计算机辅助分析法,中国电机工程学报, 2008,28(24):75~81
[66]周德才,张保会,姚峰,王立永,邹本国,赵义术,基于图论的输电断面快速搜索,中国电机工程学报, 2006,26(12):32~38
[67]楼世博,金晓龙,李鸿祥,图论及其应用,北京,人民邮电出版社,1982,
[68]屈婉玲,耿素云,张立昂,离散数学,北京,清华大学出版社, 2005
[69]堵丁柱,葛可一,王洁,计算复杂性导论,北京,高等教育出版社, 2002.
[70]谢政,网络算法与复杂性理论,北京,国防科技大学出版社,2003
[71]王红梅,胡明,王涛,数据结构(C++版),北京,清华大学出版社,2005
[72] Min M, Du H W, Jia X H, Improving construction for connected dominating set with Steiner tree in wireless sensor networks, Journal of global optimization, 2006, 35(11): 111~119
[73] Das B, Bharghavan V, Routing in ad hoc networks using minimum connected dominating sets
[74] Garey M R, Johnson D S, Computers and intractability: A guide to the theory of NP-completeness, San Francisco, W. H. Freeman, 1979
[75] Sivakumar R, Das B, Bharghavan V, An improved spine-based infrastructure for routing in Ad Hoc networks, IEEE Symposium on computers and communications, 1998
[76] Wu J, Li H, On calculating connected dominating set for efficient routing in Ad Hoc wireless networks, The 3rd international workshop on discrete algorithm and methods for mobile computing and communications,, 1999:7~14
[77] Ruan L, Du H, Jia X, Wu W, Li Y, Ko K-I, A greedy approximation for minimum connected dominating sets, Theoretical computer science, 2004, 329: 325~330
[78] Storer J A, Constructing full spanning trees for cubic graphs, Information Processing Letters, 1981, 31:8~11
[79] Ravi R, Lu, Approximating maximum leaf spanning trees in almost linear time, Journal of algorithms, 1998, 29(1): 132~141
[80] Solis-Oba R, 2-Approximation Algorithm for Finding a Spanning Tree with Maximum Number of Leaves, ESA’98, 1998, 1461: 441~452
[81] Guha S, Khuller S, Approximation algorithms for connected dominating sets, Algorithmica, 1998, 20: 374~387
[82] Klein P N, Ravi R, A nearly best-possible approximation algorithm for node-weighted Steiner trees, J, Algorithms, 1995, 19(1): 104~114
[83] Guha S, Khuller S, Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets, Information and Computation, 1999, 150(1): 57~74
[84] Robins G, Zelikovsky A, Improved Steiner tree approximation in graphs, Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms, 2000
[85] Chen Donghui, Du Dingzhu Hu Xiao Dong, etc, Approximations for Steiner trees with minimum number of Steiner points, Theoretical Computer Science, 2001, 262: 83~99
[86] R C Prim, Shortest connection networks and some generalizations. Bell System Technical Journal, 1957, 36: 1389–1401
[87] Dijkstra E W, A note on two problem in connexion with graphs, Numerische Mathematik, 1959, 1:269~271
[88]姚恩瑜,何勇,陈仕平,数学规划与组合优化,浙江:浙江大学出版社,2001
[89] G Borradaile, B Heeringa, and G T Wilfong, Approximation Algorithms for Constrained Knapsack Problems, CoRR, 2009, abs/0910.0777
[90] Johnson D S, Niemi K A, On Knapsacks, Partitions and A New Dynamic Programming Technique for Trees, Mathematics of Operations Research, 1983, 8(1): 1~14
[91] J A Lukes, Efficient algorithm for the partitioning of trees, IBM Journal of Research and Development, 1974, 18:214–224
[92] D Bienstock, A lot-sizing problem on trees, related to network design, Mathmaticas of Operations Research, 1993, 18: 402–422
[93] Y Pochet, L A Wolsey, Lot-sizing constant batches: Formulation and valid inequalities, Mathmaticas of Operations Research, 1993, 18: 767–785
[94] Cho G, Shaw D X, A depth-tirst dynamic programming algorithm for the tree knapsack problem, Informs Journal on Computing, 1997, 9(4): 431~438
[95] Shaw D X, Cho G, The Critical-Item, Upper Bounds, and a Branch-and-Bound Algorithm for the Tree Knapsack Problem, Network, 1998: 205~216
[96] Cho G, Shaw D X, An efficient algorithm for a capacitated subtree of a tree problem in local access telecommunication networks, Computers & Operations Research, 1997, 24(8): 737~748
[97] Merwe van der D J, Hattingh J M, Tree knapsack approaches for local access network design. European Journal of Operational Research, 2006, 174: 1968~1978,
[98] IBM ILOG CPLEX Optimizer, http://www-01.ibm.com/software/integration/ optimization/cplex-optimizer/
[99] Baran M E,Wu F F, Optimal capacitor placement on radial distribution systems. IEEE Transactions Power Delivery, 1989, 4(1): 725~734
[100] Kersting W H,Phillips W H,Doyle R Clay, Distribution feeder Reliability Studies, IEEE Transactions on Industry Application, 1999, 32(2):319~323
[101]林济铿,王旭东,基于网络化简的计及开关故障配电网可靠性评估,电力系统自动化,2009, 33(9): 32~36
[102] Abouzahr I, Ramakumar R, An approach to assess the performance of utility-interactive wind electric conversion systems, IEEE Transactions on Energy Conversion, 1991, 6(4): 627~638
[103] Jatzeck, B M, Robinson A M, WATSUN-PV 4.0 Modifications to Include Wind Turbine Generations, AC Load Shedding, and Operation with Zero-capacity Diesel Generator, IEEE Canadian Conference on Electrical and Computer Engineering, 1996, 2: 655~658
[104] HOMER. The Optimization Model for Distributed Power. http://www.nrel.gov/homer/.
[105] PVSYST 3.3 Software for Photovoltaic Systems. http://www.pvsyst.com.
[106]陆志峰,周家启,计及开关和母线故障的配电系统可靠性评估,电网技术,2002,26(4):26~29
[107] Billinton R, Johnnavithula S, A test system for teaching overall power system reliability assessment, IEEE Transactions on Power System, 1996, 11(4): 1670~1676
[108] All R N,Billinton R,Sjarief I,et al, A reliability test system for educational purpose-basic distribution system data and results, IEEE Transactions on Power System, 1991, 6(2): 813~730
[109] IEEE Reliability Test System, IEEE Transactions on Power Apparatus and Systems, 1979, 98(6): 2047~2054
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |