Efficient storage scheme and algorithms for W-matrix vector multiplication on vector computers

The W-matrix method has been proposed in many literatures to exploit parallelism in the solution of many power system problems. This paper presents a storage scheme for storing the sparse W-matrix in solving linear equations on vector computers. Based on the proposed storage scheme, several efficient algorithms have been developed to perform the W-matrix vector multiplication for finding linear system solutions. In this paper, attention is given to the issues of vector length, data movement between vector registers and memory, and the vector stride. The proposed storage scheme and algorithms are tested on Convex 3840 and Alliant FX/80 vector machines. It is shown that a speedup of two to four times is obtainable as compared to traditional scalar operation. The proposed storage scheme and algorithms can be applied to power system problems that require repeat solutions of linear system, such as load flow, contingency analysis, fast decoupled state estimation and short circuit calculations