Well-organized preconditioner for solving load flow problems by GMRES

Abstract

This paper proposes and tests strategies to accomplish high quality incomplete triangular factors (ILU) preconditioners for solve the load flow sublinear problem by GMRES. The process begins constructing the preconditioner over the reordered Jacobian matrix calculated in the first Newton iteration. If the iterative process does not start due to high inaccuracies and/or numerical stability problems emerged during the preconditioner construction, the solution process is restarted and the Jacobian matrix calculated in the first Newton iteration is preprocessed through scaling, nonsymmetric and symmetric (ordering) permutations, leading to a new and better quality preconditioner. Numerical experiments considering two Brazilian power system configurations (2256/3515 buses) operating under adverse conditions (heavy loaded) corroborate the efficiency of such strategies over the preconditioner quality improving the GMRES convergence rate. A LU preconditioner for comparison purposes is also considered.