A spectral divide and conquer method based preconditioner design for power flow analysis

Power system simulations, most of the time, require solution of a large sparse linear system. Traditional methods, such as LU decomposition based direct methods, are not suitable for parallelization in general. Thus, Krylov subspace based iterative methods (i.e. Conjugate Gradient, Generalized Minimal Residuals (GMRES)) can be used as very good alternatives compared to direct methods. On the other hand, Krylov based iterative solvers need a preconditioner to accelerate the convergence process. In this work we suggest a new preconditioner for GMRES, which can be used in Newton iteration of power flow analysis. The new preconditioner employs the basic spectral divide and conquer methods and invariant subspaces for clustering the eigenvalues of the Jacobean matrix appears in Newton-Raphson steps of power flow simulation.