The oneline diagram of the system is shown in Fig. E5-1. The data for the components in the system are given in per unit in Tables E6-1,2 and 3. The base values are Shase-100 MVA, Vbase-15 kV at bus 1. The ratings of the devices are: Generator Gl: Generator G2: Transformer T1: Transformer T2: 400 MVA, 15 kV 800 MVA, 15 kV 400 MVA, 15 A/345 Y kV 800 MVA, 345 Y/15 A kV Lengths of transmission lines: L1=200 mi, L2=100 mi, L3-50 mi. G1 D ΤΙ + L3 L2 LI 800 MW 280 Mvar FIGURE E5-1 Θ 白白 TABLE E5-1 Bus input data T2 ww ㅁ 80 MW AMV ○ 3 V 8 PG QG PL QL QCmax Qomin Bus Type p.u degrees p.u. p.u. p.u. p.u. p.u. p.u. 1 Swing 1.0 0 - - 0 0 2 Load - - 0 0 8.0 2.8 - Voltage- 3 1.05 - 5.2 - 0.8 0.4 4.0 -2.4 controlled 4 Load 0 5 Load - - 0 00 0 0 0 0 0 0 TABLE E5-2 Line input data R X G B Maximum MVA Bus-to-bus p.u. p.u. p.u. p.u. p.u. 2-4 0.009 0.1 0 1.72 12.0 2-5 0.0045 0.050 0 0.88 12.0 4-5 0.00225 0.025 0 0.44 12.0 TABLE E5-3 Transformer input data R X Ge Bm Maximum MVA Bus-to-bus p.u. p.u. p.u. p.u. p.u. 1-5 0.0015 0.02 0 1.72 6.0 2-5 0.00075 0.01 0 0.88 10.0 (a) Calculate Ybus for the system using the data in the tables. (b) Using the initial values given in Table 1, perform one Gauss-Seidel iteration for bus 2 and 3 voltages V2(1) and V3(1). Note that bus 3 is a voltage-controlled bus. Therefore, correction must be applied to the magnitude of V3(1) to force it to have the specified value (||=1.05). (c) In the Newton-Raphson method, calculate the initial power mismatches at all the buses 2-5. Also, calculate the Jacobian matrix elements of the partition J11. (NOTE: a power mismatch at a bus "k" is defined as AP(n) = P(1), where P is the scheduled real power and P(n) is the power calculated from the power flow equation after iteration n.