A four-bus power system is shown in Figure 1. Bus 1 is a slack bus the other buses are PQ buses. The initial voltages of the slack bus 1.05 p.u. The data for the buses are given in the Table 1 below. The values of the real and reactive power shown in the table are on a base of 10 MVA. The line impedances in per unit and real and reactive power in per unit are on a common base. Assume the initial value of all the voltages at buses 2, 3 and 4 to be 1.0L 0. Table 1 Bus No. V (pu) 1 1.05 234 Bus 1 GI (deg.) 0.0 Generation MW MVAR 0.0 0.0 0.0 Bus 4 0.0 0.0 0.0 MW 0 3 2 2 Bus 2 Load P= 2MW; Q=j1.5MVar MVAR 0 3 2.5 P= 3MW; Q=j3MVar 27 55 1.5 Bus 3 Type Swing Load Load Load P-2MW; Q-j2.5MVar Choose the line impedances for your calculations based on the last digit of your student number as indicated in the following table: Last Digit of Your Student Number 0-3 4-6 7-9 (a) (b) (c) (d) Z12= Z34 0.03 + 10.16 0.04 + j0.18 0.05 + j0.20 Z24 0.04 + j0.18 0.02 + j 0.2 0.03 + j0.22 Z23 0.06 +1 0.38 0.08 + j0.4 0.1 + j0.42 Create the circuit, in "PowerWorld" software. Assume a base power of 10 MVA and base voltage of 22 kV. All the field values such as voltage and phase angle at every bus and real and reactive power at both end of every line must be included in the circuit. The created circuit diagram (before simulation) must be included in your report. Simulate the circuit using Gauss-Seidel iterative method for a single iteration. Record the values of the voltage magnitudes in pu and phase angle in degrees at buses 2,3 and 4. The simulated diagram with all the field values clearly shown must be included in your report. Calculate the bus admittance matrix for the circuit using the impedance values given in the table. Printout the bus impedance matrix generated by the PowerWorld program and compare it with the bus impedance matrix calculated by you. Calculate the voltage in pu and the phase angle in degrees at the buses 2 and 3 after the first iteration using Gauss-Seidel method and compare it with the results recorded in part (b). (40 marks)