Computation-free preconditioners for the parallel solution of power system problems

Abstract

Solution of a set of linear equations A x = b is a recurrent problem in power system analysis. Because of computational dependencies, direct methods have proven of limited value in both parallel and highly vectorized computing environments. The preconditioned conjugate gradient method has been suggested as a better alternative to direct methods. The preconditioning step itself is not particularly well suited to parallel processing. Partitioned inverse representations of A are better suited to high performance computation. However, obtaining the partitioned inverse matrices can be expensive. This paper describes two techniques for preconditioning based on the partitioned inverses where the preconditioner matrix is obtained directly from an incomplete factorization without the need for additional numerical computation. Experiments indicate a 50% reduction in solution time in a uarallel environment.

A Review of High-Performance Computing and Parallel Techniques Applied to Power Systems Optimization

“…Most sequential algorithms are LU-based direct solvers as they do not suffer from ill-conditioning. However, Iterative solvers such as the Conjugate Gradient method, which have been around since the 90s [119], are re-gaining traction for their scalability and parallel computing advancement.…”

A sparsity-preserving spectral preconditioner for power flow analysis

“…For large and sparse systems, Krylov subspace methods (conjugate gradient, GMRES, etc.) have advantages over direct methods in terms of better parallelism and less memory requirement [7,8]. However, in most cases, a preconditioner is essential for accelerating the convergence rate of Krylov subspace-based iterative methods [9,10].…”

Nonlinear microwave simulation techniques

“…where linear and nonlinear functions, the Jacobian matrix will have many zero elements (sparse matrix) [27][28][29]. This will enable the straightforward application of sparse-matrix techniques for linear-system solution, such as preconditioned Krylov subspace methods [27][28][29].…”

“…This will enable the straightforward application of sparse-matrix techniques for linear-system solution, such as preconditioned Krylov subspace methods [27][28][29].…”