Consider the six-bus power system shown in Figure 11.29, where all data are given in per-unit on a common system base. All resistances as well as transmission-line capacitances are neglected.

(a) Determine the \(6 \times 6\) per-unit bus admittance matrix \(\boldsymbol{Y}_{\text {bus }}\) suitable for a power-flow computer program.

(b) Determine the per-unit admittance matrices \(\boldsymbol{Y}_{11}, \boldsymbol{Y}_{12}\), and \(\boldsymbol{Y}_{22}\) given in (11.5.5), which are suitable for a transient stability study.

 Figure 11.29

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3 Q = 2.0 B13 X1 = 0.20 H. = 25.0 B31 B11 ine 3 X = 0.10 B12 line 5. X = 0.025 632 P = 3.0 X3 = 0.10 H = 3.0 line X = 0.05 B51 P = 1.0 G 0 = 0.3 B61 6 B52 B53 B62 line 4 X = 0.025 Qu - 0.9 I'ne 6 X, = 0.05 B22 X = 0.10 11,= 6.C B41 B21 line 2 X = 0.10 2 B23 342 4 P = 2.0