(Solved): Figure 1 shows the one-line diagram of a simple three-bus power system with generators at buses 1 ...

Figure 1 shows the one-line diagram of a simple three-bus power system with generators at buses 1 and 3. The magnitude of voltage at bus 1 is adjusted to \( 1.05 \) pu. Voltage magnitude at bus 3 is fixed at \( 1.04 \) pu with a real power generation of 200 MW. A load consisting of \( 400 \mathrm{MW} \) and \( 250 \mathrm{Mvar} \) is taken from bus 2 . Line impedances are marked in per unit on a 100 MVA base and the line charging susceptance's are neglected. (a) Determine the bus admittance matrix-Y of the system shown in Figure \( 1 . \) Determine the Bus susceptance matrices B' and B" for this power system. (4 Marks) Page 2 of 7 Semester One Examinations, 2022 ELEC4310 Power Systems Analysis (b) Determine the Values of \( \mathrm{V}_{2} \angle \delta_{2} \) and \( \angle \delta_{3} \) using Decouple Load flow algorithm after the first iteration. (5 Marks) Where the elements of the Jacobian matrix with the initial estimate are given below. \[ \mathrm{J}=\left|\begin{array}{ccc} 54.28 & -33.28 & 24.86 \\ -33.28 & 66.04 & -16.64 \\ -27.14 & 16.64 & 49.72 \end{array}\right| \] (c) Determine the Values of \( \mathrm{V}_{2} \angle \delta_{2} \) and \( \angle \delta_{3} \) using Fast Decouple load flow algorithm after the first iteration. (4 Marks) (d) Calculate \( P_{1} \) and \( Q_{1} \), with the bus voltage solutions obtained from (b). (2 Marks)