In order to illustrate the sparsity and irregularity of the matrices
that represent the power systems networks and to provide a baseline
with which to illustrate the performance of the node-tearing algorithm
in sections 7.1 and 7.2, we
provide representations of the original matrices for the five power
systems networks in figure . These pseudo-images
illustrate the locations of the non-zero values in the matrices as
black pixels, and the matrices are symmetrical around the diagonal. A
bounding box has been placed around each sparse matrix, with the
matrix identifier located in the upper triangular portion of each
symmetric matrix.
These matrices have no fillin and are presented with the graph node identifiers as supplied in the distribution of the data --- without any additional ordering. When examining these unordered matrices, there appears to be significant differences between the power systems networks from the Boeing-Harwell series and power systems networks from the Niagara Mohawk Power Corporation. The Niagara Mohawk Power Corporation matrices have distinct block structure, while the Boeing-Harwell matrices and the EPRI matrix appear that they have been previously ordered with a minimum degree ordering. The upper left portion of these matrices appears to have fewer values in rows/columns, while the lower right hand portion of the matrices appears denser.
Figure: Pseudo-Images of Original Sparse Power Systems Matrices