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A new preconditioner design based on spectral division for power flow analysis

Manguoğlu, Murat
Solution of large sparse linear systems is the most lime consuming part in many power system simulations. Direct solvers based on LU factorization, although robust, are known to have limited satiability on parallel platforms. Thus. Krylov subspace based iterative methods (i.e. Conjugate Gradient method, Generalized Minimal Residuals (GMRES) method) can be used as alternatives. To achieve competitive performance and robustness, however, the Krylov subspace methods need a suitable preconditioner. In this work we propose a new preconditioner iterative methods, which can be used in Newton-Raphson process of power flow analysis. The suggested preconditioner employs the basic spectral divide and conquer methods and invariant subspaces for clustering the eigenvalues of the Jacobian matrix appearing in Newton-Raphson steps of power flow simulation. To obtain the preconditioner, we use Matrix Sign Function (MSF) and to obtain the MSF itself we use Sparse Approximate Inverse (SPAI) algorithm with Newton iteration. We compare the convergence characteristics of our preconditioner against the well-known black-box preconditioners such as incomplete-LU and SPAI.