Preconditioning Complex-Symmetric Layered Systems Arising in Electrical Power Modeling (Extended Abstract)

Abstract

We consider the problem of solving linear systems arising in AC electrical power networks. These linear systems are complex and symmetric (but not self-adjoint). They can be highly ill-conditioned when a network with faults (short ciruits or open circuits) is modeled. We address this illconditioning by rewriting the system in an augmented layered format. Even in this format, convergence is still slow because the spectrum of a graph adjacency matrix is spread out. We address this second kind of ill-conditioning by extending the support-tree preconditioner of Gremban, Miller and Zagha to handle layered linear systems. Preliminary computational experiments using preconditioned QMR are reported