A general algorithm for building Z-matrix based on transitional matrices

A general and procedural algorithm for Z-matrix building is proposed in this paper. This algorithm can be accomplished by an improved search technique to choose the tree branch set (TS) and link branch set (LS) and is easily implemented for a network containing the controlled sources. The look-up table saved during the search process of TS is fully utilized to reduce the computational amount when formulating the transitional matrix M_IB. During the construction of another transitional matrix M_BV, the applications of different kinds of controlled sources are discussed thoroughly considering the characteristics of the current-controlled sources and voltage- controlled sources, respectively. With these two matrices, the relationships between the bus current injections, branch currents and bus voltages can easily be found. Numerical example shows that the proposed method is very effective and suitable to be used for the analysis of large-scale power systems.