基于偶图分解的电压控制区域划分
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摘要
随着电网规模的不断扩大以及电力系统的不断发展,为提高供电的电能质量和电力系统的可靠性,对电力系统电压控制的要求也在不断提高。针对电网电压无功问题具有区域性的特点,分层分区的三层电压控制模式已成为现阶段主流的电压控制模式,对二级电压控制中存在问题的研究也日益成为广大电力工作者关注的热点问题之一。二级电压控制的基本思想是对电网划分成多个电压无功联系较为紧密、彼此近似解耦的电压控制区域,因此电压控制区域的划分成为二级电压控制最重要的问题之一,直接关系到三层电压控制模式的有效性。
通过深入研究前人电压控制分区方法以及各种图论社团检测方法,推导了两个基于牛顿-拉夫逊法潮流方程雅克比矩阵的灵敏度矩阵作为划分和子区校验的依据。通过对图论社团检测的定义、方法的深入研究分析,将偶图的概念引入到电压控制中,选择效果较好的偶图分解算法来实现无功电压分区的划分,并对具体应用过程中存在的问题进行了讨论,提出了完整的基于偶图分解的电压控制分区算法,在IEEE39节点和山东聊城电网上进行了算例分析,算例分析的结果表明了该算法的合理性和有效性。
With the continuous expansion of the grid size and the continuous development of the power system, to improve the quality of power supply and power system reliability, the requirements of power system voltage control are also continuously improved. For the regional characteristics of the grid voltage and reactive power problem, the three-level voltage control mode is extensively used; the study of control problems in secondary control mode has also increasingly become focus of the majority of electricity researchers. Basic idea of secondary voltage control is to divide the power network into several voltage control areas (VCA) where the voltage and reactive power are more closely connected within same area and approximately decoupled between these areas. So the VCA partition is one of the most important problems and directly related to the effectiveness of the three-level voltage control mode.
Through in-depth study on voltage control area partition and community detection in graph theory, two sensitivity matrixes based on Jacobin matrix is introduced to the presented VCA partition algorithm. Based on thorough analysis on the definitions and methods of community detection, the bipartite graph model is used to describe power network and bipartite decomposition is applied to the voltage reactive power partition. The problems in the actual realization are discussed and a complete bipartite graph decomposition voltage control partitioning algorithm is proposed in this paper. The algorithm is tested on the IEEE39benchmark and Liaocheng grid and proved to be effective according to the results of example analysis.
通过深入研究前人电压控制分区方法以及各种图论社团检测方法,推导了两个基于牛顿-拉夫逊法潮流方程雅克比矩阵的灵敏度矩阵作为划分和子区校验的依据。通过对图论社团检测的定义、方法的深入研究分析,将偶图的概念引入到电压控制中,选择效果较好的偶图分解算法来实现无功电压分区的划分,并对具体应用过程中存在的问题进行了讨论,提出了完整的基于偶图分解的电压控制分区算法,在IEEE39节点和山东聊城电网上进行了算例分析,算例分析的结果表明了该算法的合理性和有效性。
With the continuous expansion of the grid size and the continuous development of the power system, to improve the quality of power supply and power system reliability, the requirements of power system voltage control are also continuously improved. For the regional characteristics of the grid voltage and reactive power problem, the three-level voltage control mode is extensively used; the study of control problems in secondary control mode has also increasingly become focus of the majority of electricity researchers. Basic idea of secondary voltage control is to divide the power network into several voltage control areas (VCA) where the voltage and reactive power are more closely connected within same area and approximately decoupled between these areas. So the VCA partition is one of the most important problems and directly related to the effectiveness of the three-level voltage control mode.
Through in-depth study on voltage control area partition and community detection in graph theory, two sensitivity matrixes based on Jacobin matrix is introduced to the presented VCA partition algorithm. Based on thorough analysis on the definitions and methods of community detection, the bipartite graph model is used to describe power network and bipartite decomposition is applied to the voltage reactive power partition. The problems in the actual realization are discussed and a complete bipartite graph decomposition voltage control partitioning algorithm is proposed in this paper. The algorithm is tested on the IEEE39benchmark and Liaocheng grid and proved to be effective according to the results of example analysis.
引文
[1]余贻鑫,王成山.电力系统稳定性理论与方法[M].北京：科学出版社,1999
[2]余贻鑫,陈礼义.电力系统的安全性和稳定性[M].北京：科学出版社,1988
[3]王梅义,吴竞昌,蒙定中.大电网系统技术(第二版)[M].北京：中国电力出版社,1995
[4]袁季修.电力系统安全稳定控制[M].北京：中国电力出版社,1996
[5]周双喜,朱凌志,郭锡玖等.电力系统电压稳定性及其控制[M].北京：中国电力出版社,2004
[6]陆安定,胡康银,曹士杰等.功率因数与无功补偿[M].上海：上海科学普及出版社,2004
[7]王锡凡,方万良,杜正春.现代电力系统分析[M].北京：科学出版社,2003
[8]汤涌,仲悟之.电力系统电压稳定机理研究[J].电网技术,2010,34(4)：23-29
[9]陈珩.电力系统稳态分析(第三版)[M].北京：中国电力出版社,2007
[10]李鹏,郝治国,张保会等.一种防止电压失稳的切负荷控制方法[J].电网技术,2011,35(3)：32-37
[11]王菲,余贻鑫,刘艳丽.基于安全域的电网最小切负荷计算方法[J].中国电机工程学报,2010,30(13)：28-33
[12]刘水平,刘明波,谢敏.基于轨迹灵敏度的电力系统模型预测切负荷控制方法[J].中国电机工程学报,2010,30(34)：28-35
[13]郭庆来,张伯明,孙宏斌等.电网无功电压控制模式的演化分析[J].清华大学学报(自然科学版),2008,48(1)：16-19
[14]Paul J P, Leost Y L, Tesseron L M. Survey of the secondary voltage control in France:Present realization and investigations[J]. IEEE Transactions on Power Systems,1987,2(2):505-512
[15]郭庆来,孙宏斌,张伯明等.协调二级电压控制的研究[J].电力系统自动化,2005,29(23)：19-24
[16]刘水平,刘明波,谢敏.应用MPC和轨迹灵敏度技术实现最优协调电压控制[J].电力系统保护与预测,2011,39(1)：1-6
[17]吕岩岩.基于分区控制的电力系统电压稳定性研究[D].杭州：浙江大学,2006
[18]汤涌,贺仁睦,鞠平等.电力受端系统的动态特性及安全性评价的基础研究[M].北京：清华大学出版社,2009
[19]陈静,基于区域平衡的电力系统电压/无功管理[D].大连：大连理工大学,2008
[20]LAGONOTTE P, SABONNADEERE J C, LEOST J C et al. Structural Analysis of the Electrical System:Application to Secondary Voltage Control in France[J]. IEEE Trans on Power Systems,1989,4(2):479-486
[21]LAGONOTTEP. Probabilistic Approach of Voltage Control Based on Structural Aspect of Power Systems[J]. Abidjan.1991:208-213
[22]郭庆来,孙宏斌,张伯明等.基于无功源控制空间聚类分析的无功电压分区[J].电力系统自动化,2005,29(10)：36-40
[23]张伯明,陈寿孙,严正.高等电力网络分析(第二版)[M].北京：清华大学出版社,2007
[24]赵晋泉,刘傅成,邓勇等.基于映射分区的无功电压控制分区算法[J].电力系统自动化,2010,34(7)：36-39
[25]倪向萍,阮前途,梅生伟等.基于复杂网络理论的无功分区算法及其在上海电网中的应用[J].电网技术,2007,31(9)：6-12
[26]刘大鹏,唐国庆,陈珩.基于tabu搜索的电压控制分区[J].电力系统自动化,2002,26(6)：18-22
[27]熊虎岗,程浩忠,孔涛.基于免疫-中心点聚类算法的无功电压控制分区[J].电力系统自动化,2007,31(2)：22-26
[28]杨秀媛,董征,唐宝等.基于模糊聚类分析的无功电压控制分区[J].中国电机工程学报,2006,26(22)：6-9
[29]SCHLUETER R A, HU I, CHANG MW, et al. Methods for determining proximity to voltage collapse [J]. IEEE Trans on Power Systems,1991,6(1):285
[30]LIE T, SCHLUETER R A, RUSCHE P A, et al. Method of identifying weak transmission network stability boundaries[J]. IEEE Trans on Power Systems, 1993,8(1):293-301
[31]冯光明,陆超,黄志刚等.基于雅可比矩阵的电压控制区域划分的改进[J].电力系统自动化,2007,31(12)：7-11
[32]范磊,陈珩.二级电压控制研究(一)[J].电力系统自动化,2000,24(12)：20-24
[33]黄伟.基于电压控制区的主导节点电压校正方法[D].南京：河海大学,2004
[34]张忠静,陈刚,关仲等.基于阀值搜索和动态分散的电压/无功分区算法[J].重庆大学学报(自然科学版),2006,29(12)：52-55
[35]Yakout Mansour, Wilsun Xu. SVC placement using critical modes of voltage instability[J]. IEEE Trans on Power Systems,1994,9(2)
[36]Venkataramana Ajjarapu, Colin Christy. The continuation power flow-a tool forsteady state voltage stability analysis [J]. IEEE Trans on Power Systems, 1992,7(1):416-423
[37]Ismail Musirin, Titik Khawa Abdul Rahman. Voltage stability based weak area clustering technique in power system. National Power & Energy Conference (PEC on)2004 Proceedings, Kuala Lumpur, Malaysia
[38]魏震波,刘俊勇,程飞.利用社区挖掘的快速无功电压分区方法[J].中国电机工程学报,2011,31(31)：166-172
[39]李文君,鲍海.基于矩阵叠加定理的电压/无功控制分区方法[C].中国高等学校电力系统及其自动化专业第二十四届学术年会论文集
[40]Santo Fortunato. Community detection in graphs [J]. Physics Reports,2010,486: 75-174
[41]魏芳.基于图挖掘的网络社团结构发现[D].上海：复旦大学,2008
[42]G Parlla, I Derenyi, I Farkas, et al. Uncovering the overlapping community structure of complex networks in nature and society [J]. Nature,2005, 435:814-818
[43]F Radicchi, C Castellano, F Cecconi, et al. Defining and identifying communities in networks. Proceedings of the National Academy of Science of the USA(PNAS),2004,101(9):2658-2663
[44]M E J Newman, M Girvan. Finding and evaluating community structure in networks[J]. Physical Review E,2004,69(2):026113
[45]官山,何大韧,朱陈平.跨越多个实际科学领域的合作网络与合作-竞争网络[J].力学进展,2008,38(6)：827-834
[46]Michael J. Barber. Modularity and community detection in bipartite networks[J], http://arXiv.org
[47]Xin Liu, Tsuyoshi Murata. Community Detection in Large-scale Bipartite Networks[J]. Information and Media Technologies,2010:5(1):184-192
[48]Stanislav Busygin, Oleg Prokopyev, Panos M. Pardalos.Biclustering in data mining [J]. Computers & Operations Research,2008,35:2964-2987
[49]方鸽飞,刘君华,吕岩岩.基于树形分布的电压控制分区[J].电力系统及其自动化学报,2007,19(1)：83-86
[50]孔万增,孙志海,杨灿等.基于本征间隙与正交特征向量的自动谱聚类[J].电子学报,2010,8(8)：1880-1885
[2]余贻鑫,陈礼义.电力系统的安全性和稳定性[M].北京：科学出版社,1988
[3]王梅义,吴竞昌,蒙定中.大电网系统技术(第二版)[M].北京：中国电力出版社,1995
[4]袁季修.电力系统安全稳定控制[M].北京：中国电力出版社,1996
[5]周双喜,朱凌志,郭锡玖等.电力系统电压稳定性及其控制[M].北京：中国电力出版社,2004
[6]陆安定,胡康银,曹士杰等.功率因数与无功补偿[M].上海：上海科学普及出版社,2004
[7]王锡凡,方万良,杜正春.现代电力系统分析[M].北京：科学出版社,2003
[8]汤涌,仲悟之.电力系统电压稳定机理研究[J].电网技术,2010,34(4)：23-29
[9]陈珩.电力系统稳态分析(第三版)[M].北京：中国电力出版社,2007
[10]李鹏,郝治国,张保会等.一种防止电压失稳的切负荷控制方法[J].电网技术,2011,35(3)：32-37
[11]王菲,余贻鑫,刘艳丽.基于安全域的电网最小切负荷计算方法[J].中国电机工程学报,2010,30(13)：28-33
[12]刘水平,刘明波,谢敏.基于轨迹灵敏度的电力系统模型预测切负荷控制方法[J].中国电机工程学报,2010,30(34)：28-35
[13]郭庆来,张伯明,孙宏斌等.电网无功电压控制模式的演化分析[J].清华大学学报(自然科学版),2008,48(1)：16-19
[14]Paul J P, Leost Y L, Tesseron L M. Survey of the secondary voltage control in France:Present realization and investigations[J]. IEEE Transactions on Power Systems,1987,2(2):505-512
[15]郭庆来,孙宏斌,张伯明等.协调二级电压控制的研究[J].电力系统自动化,2005,29(23)：19-24
[16]刘水平,刘明波,谢敏.应用MPC和轨迹灵敏度技术实现最优协调电压控制[J].电力系统保护与预测,2011,39(1)：1-6
[17]吕岩岩.基于分区控制的电力系统电压稳定性研究[D].杭州：浙江大学,2006
[18]汤涌,贺仁睦,鞠平等.电力受端系统的动态特性及安全性评价的基础研究[M].北京：清华大学出版社,2009
[19]陈静,基于区域平衡的电力系统电压/无功管理[D].大连：大连理工大学,2008
[20]LAGONOTTE P, SABONNADEERE J C, LEOST J C et al. Structural Analysis of the Electrical System:Application to Secondary Voltage Control in France[J]. IEEE Trans on Power Systems,1989,4(2):479-486
[21]LAGONOTTEP. Probabilistic Approach of Voltage Control Based on Structural Aspect of Power Systems[J]. Abidjan.1991:208-213
[22]郭庆来,孙宏斌,张伯明等.基于无功源控制空间聚类分析的无功电压分区[J].电力系统自动化,2005,29(10)：36-40
[23]张伯明,陈寿孙,严正.高等电力网络分析(第二版)[M].北京：清华大学出版社,2007
[24]赵晋泉,刘傅成,邓勇等.基于映射分区的无功电压控制分区算法[J].电力系统自动化,2010,34(7)：36-39
[25]倪向萍,阮前途,梅生伟等.基于复杂网络理论的无功分区算法及其在上海电网中的应用[J].电网技术,2007,31(9)：6-12
[26]刘大鹏,唐国庆,陈珩.基于tabu搜索的电压控制分区[J].电力系统自动化,2002,26(6)：18-22
[27]熊虎岗,程浩忠,孔涛.基于免疫-中心点聚类算法的无功电压控制分区[J].电力系统自动化,2007,31(2)：22-26
[28]杨秀媛,董征,唐宝等.基于模糊聚类分析的无功电压控制分区[J].中国电机工程学报,2006,26(22)：6-9
[29]SCHLUETER R A, HU I, CHANG MW, et al. Methods for determining proximity to voltage collapse [J]. IEEE Trans on Power Systems,1991,6(1):285
[30]LIE T, SCHLUETER R A, RUSCHE P A, et al. Method of identifying weak transmission network stability boundaries[J]. IEEE Trans on Power Systems, 1993,8(1):293-301
[31]冯光明,陆超,黄志刚等.基于雅可比矩阵的电压控制区域划分的改进[J].电力系统自动化,2007,31(12)：7-11
[32]范磊,陈珩.二级电压控制研究(一)[J].电力系统自动化,2000,24(12)：20-24
[33]黄伟.基于电压控制区的主导节点电压校正方法[D].南京：河海大学,2004
[34]张忠静,陈刚,关仲等.基于阀值搜索和动态分散的电压/无功分区算法[J].重庆大学学报(自然科学版),2006,29(12)：52-55
[35]Yakout Mansour, Wilsun Xu. SVC placement using critical modes of voltage instability[J]. IEEE Trans on Power Systems,1994,9(2)
[36]Venkataramana Ajjarapu, Colin Christy. The continuation power flow-a tool forsteady state voltage stability analysis [J]. IEEE Trans on Power Systems, 1992,7(1):416-423
[37]Ismail Musirin, Titik Khawa Abdul Rahman. Voltage stability based weak area clustering technique in power system. National Power & Energy Conference (PEC on)2004 Proceedings, Kuala Lumpur, Malaysia
[38]魏震波,刘俊勇,程飞.利用社区挖掘的快速无功电压分区方法[J].中国电机工程学报,2011,31(31)：166-172
[39]李文君,鲍海.基于矩阵叠加定理的电压/无功控制分区方法[C].中国高等学校电力系统及其自动化专业第二十四届学术年会论文集
[40]Santo Fortunato. Community detection in graphs [J]. Physics Reports,2010,486: 75-174
[41]魏芳.基于图挖掘的网络社团结构发现[D].上海：复旦大学,2008
[42]G Parlla, I Derenyi, I Farkas, et al. Uncovering the overlapping community structure of complex networks in nature and society [J]. Nature,2005, 435:814-818
[43]F Radicchi, C Castellano, F Cecconi, et al. Defining and identifying communities in networks. Proceedings of the National Academy of Science of the USA(PNAS),2004,101(9):2658-2663
[44]M E J Newman, M Girvan. Finding and evaluating community structure in networks[J]. Physical Review E,2004,69(2):026113
[45]官山,何大韧,朱陈平.跨越多个实际科学领域的合作网络与合作-竞争网络[J].力学进展,2008,38(6)：827-834
[46]Michael J. Barber. Modularity and community detection in bipartite networks[J], http://arXiv.org
[47]Xin Liu, Tsuyoshi Murata. Community Detection in Large-scale Bipartite Networks[J]. Information and Media Technologies,2010:5(1):184-192
[48]Stanislav Busygin, Oleg Prokopyev, Panos M. Pardalos.Biclustering in data mining [J]. Computers & Operations Research,2008,35:2964-2987
[49]方鸽飞,刘君华,吕岩岩.基于树形分布的电压控制分区[J].电力系统及其自动化学报,2007,19(1)：83-86
[50]孔万增,孙志海,杨灿等.基于本征间隙与正交特征向量的自动谱聚类[J].电子学报,2010,8(8)：1880-1885