一种形成节点阻抗矩阵的改进算法

AN IMPROVED NOVEL ALGORITHM FOR BUILDING Z-MATRIX

文中根据节点注入电流与支路电流以及支路电流与节点电压之间的拓扑关系，分别定义了节点注入电流对支路电流矩阵MI，J和支路电流对节点电压矩阵MI，V，并解释了其物理意义；借用稀疏矩阵求逆的前推回推算法，提出了一种能够快速形成大规模电网节点阻抗矩阵的改进新方法。该算法能统一处理互感和无互感线路、单连通树支集的特定网络以及树枝集中有分支的通用电网络。在考虑支路间存在任意互感的前提下，详细推导了2个过度矩阵以及节点阻抗矩阵的形成过程；2个构造矩阵能有效地反映电网支路发生短路故障或系统切除负荷的紧急事故前、后网络参量的变化。该算法具有占用内存少，计算速度快的特点。最后通过算例验证和比较了该方法的实用性和高效性。

According to the relations of branch current vs. current injection and branch current vs. bus voltage, matrixes Mi,J and MI,V are respectively defined for the first time, and their physical meanings are depicted from the point of view of power system in this paper. An improved new viewpoint to building Z-matrix of large-scale power network is put forward considered the back/forward method used in inversing sparse matrix. The algorithm can deal with mutual inductance or non mutual inductance network and especial 'a stroke' tree set network or general offset-trees network. The building processes about matrixes MI,J, MI,V and Z-matrix are particularly expatiated considering mutual inductances among any branches group. The two developed matrixes can reflect the changes of parameters in networks after any fault or contingency of cutting load and so on happened. The algorithm has the characteristic of less memory and rapid calculating. A lot of examples show that the improved novel algorithm is effective and universal.