Determination Of Network Topology By Matrix Partial Multiplication

With the development of power system, demands on the management level and management means of the energy management system (EMS) have been increasing. Power system network topology analysis module is the basis of the power management system which accomplishes various analysis and computing such as dynamic coloring, state estimation, load forecasting, optimal power flow and fault calculation. Network topology analysis determines the electrical connectivity of power system according to switch status and ultimately determines the electrical island.Based on the study of the algorithm by multiplying the adjacency matrix repeatedly, according to the characteristics of connectivity matrix, this thesis presents a new network topology analysis method named determination of network topology by matrix partial multiplication. Study found that the calculation of the connectivity matrix in one row is independent of that of other rows. Therefore, when calculating the elements of connectivity matrix, it can determine part of nodes of some connected graph through its first row elements. Thus the elements calculation of some rows which correspond to those nodes can be exempted.Further study found that the elements of rows belong to the same connected graph in the full connectivity matrix are exactly the same. So combing this feature with the calculation of connectivity matrix row elements is independent of each other to come up a new algorithm. The algorithm can get all nodes’connection between each other by just calculate the elements of the first row of each connected graph. Because this algorithm is improved on the basis of determination of network topology by matrix partial multiplication, and the connectivity matrix is not stored by the full connectivity matrix but generated a temporary array directly when it is needed. Using the sparse matrix techniques to store the adjacency matrix, the algorithm implementation no longer contains the matrix multiplication, so the algorithm is named vector method network topology analysis.Reducing matrix’s computation and storage is the most effective way to increase the speed of matrix method network topology. Both the two algorithms presented in this thesis are based on the algorithm by multiplying the adjacency matrix repeatedly, and make reducing matrix’s computation and storage space as its goal. They adopted sparse matrix techniques, optimal numbering and connectivity matrix elements immediately updating measures which greatly increased the speed of network topology. A practical network is analyzed by the proposed algorithms in this thesis, and the results prove the effectiveness and validity of the proposed algorithms. So it is suitable for network topology analysis of large-scale power system.