Abstract:The current of current-controlled current source (CCCS) branch is controlled by the current of another branch, which makes it difficult to build the node impedances matrix (Z-matrix). To solve this problem, a novel algorithm for building Z-matrix is put forward. The relationships between the current injection, node voltage, branch current and branch voltage are lucubrated to in this paper. Three transitional matrices are introduced: branch current vs. current injection matrix MIJ, node voltage vs. branch voltage matrix MVU and node voltage vs. branch current matrix MVI. These three matrices cooperating to the kron reduction methods made it to build Z-matrix. This algorithm can easily deal with large networks containing CCCS branches. The main structure of the algorithm is illustrated with the help of a 7-bus system and is validated by several IEEE testing systems. The results show that this algorithm is effective. So it will be a new sustaining tool for further research by using Z-matrix.
冯天民, 刘宝柱, 鲍海. 一类含CCCS网络形成节点阻抗矩阵的新算法[J]. 电工技术学报, 2009, 24(2): 139-143.
Feng Tianmin, Liu Baozhu, Bao Hai. A Novel Algorithm for Building Z-Matrix of Electric Power Network Including CCCS. Transactions of China Electrotechnical Society, 2009, 24(2): 139-143.
[1] Peterson W L, Makram E B, Bakdwin T L. A generalized PC based bus impedance matrix building algorithm[C]. IEEE Proceedings of Energy and Information Technologies in the Southeast, 1989, 2: 432-436. [2] 王艳松, 何新霞. 基于网络模型的节点阻抗矩阵的新算法[J]. 石油大学学报, 2000, 24(3):98-99. [3] 曹国臣, 武晓梅, 宋家骅, 等. 一种基于分解协调法的电力系统故障计算方法[J]. 中国电机工程学报, 1999, 1(19): 14-18. [4] Reitan D K, Kruempel K C. Modification of the bus impedance matrix for system changes involving mutual couplings[C]. Proceedings of the IEEE, 1969: 1432-1433. [5] 卢斌先, 王泽忠. 外场激励下多导体传输线响应的节点导纳分析法[J]. 电工技术学报, 2007, 22(10): 145-149. [6] Shipley R B, Sato N, Coleman D W, et al. Direct calculation of power system stability using the impedance matrix[J]. IEEE Transaction on Power Apparatus and Systems, 1966, 85(7): 777-782. [7] Elham B Makram, Katherine P Thornton, Homer E Brown. Selection of lines to be switched to eliminate overloaded lines using a Z-matrix method[J]. IEEE Transactions on Power Systems, 1989, 4(2): 653-657. [8] 罗庆跃, 李晓明, 佘国鸿, 等. 零阻抗支路在短路故障计算机分析中的应用[J]. 电工技术学报, 2005, 20(4): 107-110. [9] Daniel K, Reitan. A new method using the bus- impedance matrix model for short-circuit calculations[C]. Proceedings of the IEEE, 1980, 68(8): 1027-1030. [10] 李伟, 鲍海, 傅吉悦, 等. 基于功率分量理论的网损分摊问题[J]. 中国电机工程学报, 2005, 25(25): 157-160. [11] 郭文勇, 赵彩宏, 肖立业. 超导储能用电流调节器充放电数学模型及其控制系统[J]. 电工技术学报, 2007, 22(10): 117-122. [12] Mehul Desai, Peter Aronhime. Node expansion theo- rem for controlled sources[C]. Circuits and Systems, 1993, Proceedings of the 36th Midwest Symposium, 1993: 1204-1207. [13] Tetsuo Nishi, Leono Chua. Uniqueness of solution for nonlinear resistive circuits containing CCCS’s or VCVS’s whose controlling coefficients are finite[J]. IEEE Transactions on Circuits and Systems, 1986, 33(4): 381-396. [14] 张丽红. 含受控源电路节点矩阵分析的研究[J]. 太原理工大学学报, 2004, 35(4): 470-472. [15] Seth Chailcen, Narendran P. The all-minors VCCS matrix tree theorem, half-resistors and applications in symbolic simulation[C]. Circuits and Systems, 1995. ISCAS’95, 1995 IEEE International Symposium, 1995, 2: 1239-1242. [16] 陈珩. 电力系统稳态分析[M]. 2版. 北京:中国电力出版社, 1995. [17] Whei Minlin, Yuh Sheng, et al. A new building algorithm for Z-matrix[C]. IEEE Power System Technology, Proceedings Power International Conference, 2000, 20(4): 1041-1046. [18] Teng J H, Su Y S, et al. Decomposition approach and analysis for a Z-matrix building process[C]. IEE Proc. Gener. Transm. Distrib., 2004, 151(5): 638-643. [19] 乐全明, 郁惟镛, 杜俊红. 一种形成节点阻抗矩阵的改进算法[J]. 中国电机工程学报, 2005, 25(2):34-39. [20] 吕飞鹏, 王强, 张军文, 等. 修正节点阻抗矩阵元素的递归算法[J]. 继电器, 2000, 28(10): 19-20. 作者简介: 冯天民 男, 1983年生, 硕士研究生, 研究方向为电力系统运行、分析与控制。刘宝柱 男, 1974年生, 博士, 讲师, 主要从事电力系统运行、分析与控制的研究工作。