Using the compact storage technique described in Section 6.8, determine the vectors DIAG, OFFDIAG, COL, and ROW for the following matrix:

\[\mathbf{S}=\left[\begin{array}{cccccc}17 & -9.1 & 0 & 0 & -2.1 & -7.1 \\-9.1 & 25 & -8.1 & -1.1 & -6.1 & 0 \\0 & -8.1 & 9 & 0 & 0 & 0 \\0 & -1.1 & 0 & 2 & 0 & 0 \\-2.1 & -6.1 & 0 & 0 & 14 & -5.1 \\-7.1 & 0 & 0 & 0 & -5.1 & 15\end{array}\right]\]

Data From Section 6.8:-

Transcribed Image Text:

A typical power system has an average of fewer than three lines connected to each bus. As such, each row of Yus has an average of fewer than four non- zero elements, one off-diagonal for each line and the diagonal. Such a matrix, which has only a few nonzero elements, is said to be sparse. Newton-Raphson power-flow programs employ sparse matrix techniques to reduce computer storage and time requirements [2]. These techniques include compact storage of You and J(i) and reordering of buses to avoid fill-in of J (i) during Gauss elimination steps. Consider the following matrix: 1.0 -1.1-2.1 -3.1" -4.1 2.0 0 -5.1 S= -6.1 0 3.0 0 -7.1 00 4.0 (6.8.1) One method for compact storage of S consists of the following four vectors: DIAG [1.0 2.0 3.0 4.0] (6.8.2) OFFDIAG [-1.1-2.1 -3.1 -4.1 -5.1 -6.1 -7.1] (6.8.3) COL 2 3 4 1411] = ROW [3 2 1 1] (6.8.4) (6.8.5) DIAG contains the ordered diagonal elements and OFFDIAG contains the nonzero off-diagonal elements of S. COL contains the column number of each off-diagonal element. For example, the fourth element in COL is 1, in- dicating that the fourth element of OFFDIAG, -4.1, is located in column I. ROW indicates the number of off-diagonal elements in each row of S. For example, the first element of ROW is 3, indicating the first three elements of OFFDIAG, -1.1, -2.1, and -3.1, are located in the first row. The second element of ROW is 2, indicating the next two elements of OFFDIAG, -4.1 and -5.1, are located in the second row. The S matrix can be completely re- constructed from these four vectors. Note that the dimension of DIAG and