Improved Sparsity Techniques for Solving Network Equations in Transient Stability Simulations

When solving network algebraic equations during power system transient stability simulations, the nonzero elements in the independent vector and the elements needed in the solution vector are determined by the location of source nodes. Different kinds of source nodes will have a different influence on the solution process of the network equations. According to these features of source nodes, sparsity techniques, more specifically, the node ordering algorithm and sparse vector method, are improved in this paper. A new heuristic ordering algorithm is proposed to enhance the efficiency of the sparse vector method by reducing the number of nodes in the factorization path set of source nodes while maintaining the sparsity of the factorized matrix. A multipath sparse vector method is proposed to avoid the unnecessary computation in the iterative solution process of the network equations, whereby the idea of the method is to form different paths for different types of source nodes. Different paths are used to solve different elements in the solution vector. The correctness and effectiveness of these improvements is proven by the simulation results of three practical power systems (up to 13 490 nodes) and six IEEE examples (up to 162 nodes).