Using the bus impedance matrices determined in Problem 9.51.

Problem 9.51

Compute the \(5 \times 5\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 9.8. Use a base of 100 MVA and \(15 \mathrm{kV}\) in the zone of generator G2.

Problem 9.8

Equipment ratings for the five-bus power system shown in Figure 7.15 are given as follows:

Generator G1: \(\quad 50 \mathrm{MVA}, 12 \mathrm{kV}, \mathrm{X}_{d}^{\prime \prime}=\mathrm{X}_{2}=0.20, \mathrm{X}_{0}=0.10\) per unit 

Generator G2: \(\quad 100 \mathrm{MVA}, 15 \mathrm{kV}, \mathrm{X}_{d}^{\prime \prime}=0.2, \mathrm{X}_{2}=0.23, \mathrm{X}_{0}=0.1\) per unit 

Transformer T1: \(50 \mathrm{MVA}, 10 \mathrm{kV}\) Y/138 kV Y, X \(=0.10\) per unit 

Transformer T2: \(100 \mathrm{MVA}, 15 \mathrm{kV} \Delta / 138 \mathrm{kV} \mathrm{Y}, \mathrm{X}=0.10\) per unit 

Each 138-kV line: \(X_{1}=40\) ohms, \(X_{0}=100\) ohms 

Draw the zero-, positive-, and negative-sequence reactance diagrams using a \(100-\) MVA, \(15-\mathrm{kV}\) base in the zone of generator G2. Neglect \(\Delta-\mathrm{Y}\) transformer phase shifts.

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