For the system of Problem 9.11, compute the fault current and voltages at the fault for the following faults at point \(\mathrm{F}\) :

(a) a bolted single line-to-ground fault;

(b) a line-to-line fault through a fault impedance \(Z_{\mathrm{F}}=j 0.05 \) per unit;

(c) a double line-to-ground fault from phase B to C to ground, where phase \(\mathrm{B}\) has a fault impedance \(Z_{\mathrm{F}}=j 0.05 \) per unit, phase \(\mathrm{C}\) also has a fault impedance \(Z_{\mathrm{F}}=j 0.05 \) per unit, and the common line-to-ground fault impedance is \(Z_{\mathrm{G}}=j 0.033 \) per unit.

Problem 9.11

Consider the system shown in Figure 9.18.

Synchronous generators:

G1 \(\mathrm{X}_{1}=0.2\)

\(\mathrm{X}_{2}=0.12\)

\(\mathrm{X}_{0}=0.06\)

G2 \(\quad \mathrm{X}_{1}=0.33\)

\(\mathrm{X}_{2}=0.22\)

\(\mathrm{X}_{0}=0.066\)

Transformers:

T1 \(\quad \mathrm{X}_{1}=\mathrm{X}_{2}=\mathrm{X}_{0}=0.2\)

T2 \(\quad \mathrm{X}_{1}=\mathrm{X}_{2}=\mathrm{X}_{0}=0.225\)

T3 \(\quad \mathrm{X}_{1}=\mathrm{X}_{2}=\mathrm{X}_{0}=0.27\)

T4 \(\quad \mathrm{X}_{1}=\mathrm{X}_{2}=\mathrm{X}_{0}=0.16\)

Transmission lines:

\(\begin{array}{lll}\text { L1 } & \mathrm{X}_{1}=\mathrm{X}_{2}=0.14 & \mathrm{X}_{0}=0.3 \\ \text { L1 } & \mathrm{X}_{1}=\mathrm{X}_{2}=0.35 & \mathrm{X}_{0}=0.6\end{array}\)

Figure 9.18

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