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 Sbase=100 MVA, Vbase 15 kV at bus 1. The ratings of the devices are: Generator Gl: 400 MVA, 15 kV 800 MVA, 15 kV Generator G2: Transformer T1: 400 MVA, 15 A/345 Y kV Transformer T2: 800 MVA, 345 Y/15 A kV Lengths of transmission lines: L1=200 mi, L2=100 mi, L3-50 mi. T1 ° ㅁㅁ L3 L2 Ll 800 MW 280 Mvar FIGURE E5-1 ㅁㅁ T2 TABLE E5-1 Bus input data 80 MW V 8 Po QG PL QL Bus Туре QCmax QGmin 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 0 0 0 0 5 Load 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 B 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) = Pack - Pai(n), where P is the scheduled real power and P(n) is the power calculated from the power flow equation after iteration n.