Critical evaluation of direct and iterative methods for solving Ax=b systems in power flow calculations and contingency analysis

Studies comparing the performance of direct and iterative solvers of Ax=b systems have been performed. By direct methods we mean sparsity preserving Gaussian elimination based approaches, whereas by iterative methods we mean pre-conditioned conjugate gradient methods such as the ones based on incomplete factorization of matrix A (e.g., incomplete Cholesky and K₀ pre-conditioners). A new ordering scheme has been developed which decreases the number of iterations required by iterative methods to reach convergence and an alternative conditioning approach is suggested in connection with the contingency screening problem. Tests have been performed with networks varying from 14 to 1663 buses, including base-case and contingency cases