Parallel computing of sparse linear systems using matrix condensation algorithm

Abstract

Solving sparse systems of linear equations permeates power system analysis. Newton-Raphson, decoupled, and fast decoupled algorithms all require the repeated solution of sparse systems of linear equations in order to capture the steady state operational conditions of the studied power system. Solving these systems of equations is usually done with LU factorization which has an order of complexity O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ), where n represents the number of equations in the system. The Chio's matrix condensation algorithm is an alternative approach, which in general has a complexity of O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ). However, it has a straightforward formulation that can be easily implemented in a parallel computing architecture to reach a potential speedup by N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Previous research has not investigated the application of the matrix condensation algorithm under sparse matrix, which is typical for power system analysis. This paper proposes a parallel solution of sparse linear systems using matrix condensation algorithm and realistic test data from power flow analysis. Different sparse matrix techniques are discussed, and a reordering scheme is applied to further improve the efficiency for solving the sparse linear system.