Iterative solver techniques in large scale power system computation

The solution of large sparse linear systems forms the core of power system computations whether it is power flow, state estimation or security assessment (static or dynamic). There is a continuous need to speed-up this process by improved numerical algorithms. Iterative solver techniques based on the Krylov subspace projection method offer an attractive alternative to the traditional LU factorization methods because of the ease of parallelization and/or vectorization. In this paper we review the efforts since the late 80's in applying these techniques to power system problems.

[1]  A. Bose,et al.  A highly parallel method for transient stability analysis , 1989, Conference Papers Power Industry Computer Application Conference.

[2]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[3]  Adam Semlyen Fundamental concepts of a Krylov subspace power flow methodology , 1996 .

[4]  Anjan Bose,et al.  Bottlenecks in parallel algorithms for power system stability analysis , 1993 .

[5]  H. Chiang,et al.  Solving the nonlinear power flow equations with an inexact Newton method using GMRES , 1998 .

[6]  P. W. Sauer,et al.  Conjugate Gradient Approach to Parallel Processing in Dynamic Simulation of Power Systems , 1992, 1992 American Control Conference.

[7]  I. C. Decker,et al.  Parallel implementation of a power system dynamic simulation methodology using the conjugate gradient method , 1991 .

[8]  T. Manteuffel An incomplete factorization technique for positive definite linear systems , 1980 .

[9]  R. Bacher,et al.  Application of non-stationary iterative methods to an exact Newton-Raphson solution process for power flow equations , 1996 .

[10]  J. W. Walker,et al.  Direct solutions of sparse network equations by optimally ordered triangular factorization , 1967 .

[11]  Jack J. Dongarra,et al.  Solving linear systems on vector and shared memory computers , 1990 .

[12]  Fernando Alvarado,et al.  Parallel Solution of Transient Problems by Trapezoidal Integration , 1979, IEEE Transactions on Power Apparatus and Systems.

[13]  J. Meijerink,et al.  An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix , 1977 .

[14]  S. McFee,et al.  On the application of a pre-conditioned conjugate gradient algorithm to power network analysis , 1993 .

[15]  O. Alsac,et al.  Fast Decoupled Load Flow , 1974 .

[16]  F. Alvarado,et al.  Toward improved uses of the conjugate gradient method for power system applications , 1997 .

[17]  J. Nieplocha,et al.  Iterative methods for the WLS state estimation on RISC, vector, and parallel computers , 1993 .