Parallel algorithms for direct solution of large sparse power system matrix equations

A coarse-grain parallel implementation is presented of LU factorisation, forward and backward substitution for solving large, sparse linear sets of algebraic equations arising from network analysis. A block solution approach was chosen instead of the usual element-wise method, to reduce communication overhead and consequently to obtain a better performance of the parallel implementation. An inverse-based technique was used to further improve the overall efficiency of repeated solutions. Data exchanges among processors are kept to the minimum in the factorisation and solution phases. This method has been successfully applied to a realistic UK 811-busbar power system network with up to 16 processors. Results are presented with detailed information on computation and communication.