Critical investigation of preconditioned GMRES via incomplete LU factorization applied to power flow simulation

For solving the power flow sublinear problem efficiently by the GMRES preconditioned via incomplete LU factorization (ILU), this paper investigates causes associated to the preconditioner low quality and proposes a method to improve it and the GMRES convergence rate as well. The goal is provide a well-organized ILU-GMRES for solving linear systems of difficult solution comprising ill-conditioned coefficient matrices, normally associated to heavy load power systems. The investigations reveal that a dropping rule for nonzero elements (fill-ins) based on a relative tolerance may introduce large errors during the preconditioner construction, lowering its quality and the GMRES performance. Based on that, it is proposed a fill-in dropping rule making use of two criteria; one based on the resulting error and the other based on a relative tolerance, applied to the preconditioner lower (L) and upper (U) triangular matrices, respectively. Ordering schemes are also considered. Numerical experiments taking into account different power system configurations operating under heavy load conditions corroborate the efficiency of such strategies.

► Power flow sublinear problem is solved by ILU-GMRES efficiently.
► Fill-in dropping rule based on the resulting error attenuates ILU drawbacks.
► Minimum degree ordering drops a large amount of fill-in increasing ILU quality.
► Difficulties associated to heavy load scenarios are overcome.