Question

Question: Consider the system shown in Figure 9.18. (a) As viewed from the fault at F, determine the Thevenin equivalent of each sequence network. Neglect phase shifts. (b) Compute the fault currents for a balanced three phase fault at fault point F through three fault impedances ${\mathit{Z}}_{\mathbf{F}\mathbf{A}}\mathbf{=}{\mathit{Z}}_{\mathbf{F}\mathbf{B}}\mathbf{=}{\mathit{Z}}_{\mathbf{F}\mathbf{C}}\mathbf{=}\mathit{j}\mathbf{0}\mathbf{.}\mathbf{5}$per unit. Equipment data in per-unit on the same base are given as follows:

Synchronous generators:

$$\begin{gathered} G1 X_1=0.2 X_2=0.12 X_0=0.06 \\ G2 X_1=0.33 X_2=0.22 X_0=0.066 \end{gathered}$$

Transformers:

$$\begin{gathered} T1 X_1=X_2=X_0=0.2 \\ T2 X_1=X_2=X_0=0.225 \\ T3 X_1=X_2=X_0=0.27 \\ T4 X_1=X_2=X_0=0.16 \end{gathered}$$

Transmission lines:

$$\begin{gathered} L1 X_1=X_2=0.14 X_0=0.3 \\ L1 X_1=X_2=0.35 X_0=0.6 \end{gathered}$$

Short answer

Answer

(a) The Thevenin equivalent for positive sequence network.

The Thevenin equivalent circuit for negative sequence network.

The Thevenin equivalent for zero-sequence network.

(b) The fault current for balance three phase fault is $1.315\angle -90°\text{pu}$.

Step-by-step solution

Write the given data from the question:

Write the reactance of the generators.

For generator

The negative sequence reactance is X₂ , 0.20 the positive sequence and zero sequence reactance X₀ is 0.06.

For generator

The negative sequence reactance isX₂ , 0.33 , the positive sequence X₁ is 0.22 and zero sequence reactance X₀ is 0.066 per unit.

Write the reactance of the transformer.

For transformer

The negative sequence reactance , the positive sequence reactance and zero sequence reactance are .

For transformer

The negative sequence reactance , the positive sequence reactance and zero sequence reactance are .

For transformer

The negative sequence reactance , the positive sequence reactance and zero sequence reactance are .

For transformer

The negative sequence reactance , the positive sequence reactance and zero sequence reactance are .

Write the reactance of the transmission lines.

For line ,

The negative sequence reactance , the positive sequence reactance are and zero sequence reactance is .

For line ,

The negative sequence reactance , the positive sequence reactance are and zero sequence reactance is .

The faulty impedances,