Question

Question:Repeat Problem 9.28 for the two-conductors-open fault shown in Figure 9.21(b). The fault conditions in the phase domain are ${}_{\mathrm{b}}={\mathrm{I}}_{\mathrm{b}\text{'}}={\mathrm{I}}_{\mathrm{c}}={\mathrm{I}}_{\mathrm{c}\text{'}}=0and{\mathrm{V}}_{\mathrm{aa}\text{'}}=0$

figure 9.21

Short answer

Answer

The sequence fault condition is:

$$\begin{gathered} {V_{aa}}^{\text{'}}=\left({V_{00}}^{\text{'}}+{V_{11}}^{\text{'}}+{V_{22}}^{\text{'}}\right) \\ =0 \end{gathered}$$

The sequence connection is,

Step-by-step solution

Write the given data from the question.

The I₀ is the zero sequence current.

The I₁ is the positive sequence current.

The I₂ is the negative sequence current.

The ,I_a I_b and I_c are phase currents.

The V_bb is voltage b-b^' between terminals and Vcc is voltage c-c^' between terminals.

Determine the formula of fault condition in sequence domain.

Write the formula of fault condition in sequence domain.

$\left[\begin{array}{c}{I}_0\\ I_1\\ I_2\end{array}\right]\mathbf{=}\frac{\mathbf{1}}{\mathbf{3}}\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a^2& a\end{array}\right]\left[\begin{array}{c}{I}_a\\ I_b\\ I_c\end{array}\right]$ …… (1)

Here, I_a,I_b and I_care phase currents.

Determine the fault condition in sequence domain where phases and and between andare short circuit and phases and is open circuit.

Determine the fault condition in the given phase domain is,

I_b =0 …… (2)

I_a =0 …… (3)

Determine the fault condition in the given sequence domain by using equation (2) and (3).

Substitute 0 forI_b and 0 for I_c into equation (1).

$$\begin{gathered} \left[\begin{array}{c}{\mathrm{I}}_0\\ {\mathrm{I}}_1\\ {\mathrm{I}}_2\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& {\mathrm{a}}^2& \mathrm{a}\\ 1& {\mathrm{a}}^2& \mathrm{a}\end{array}\right]\left[\begin{array}{c}{\mathrm{I}}_{\mathrm{a}}\\ 0\\ 0\end{array}\right] \\ =\left[\begin{array}{c}\frac{{\mathrm{I}}_{\mathrm{a}}}{3}\\ \frac{{\mathrm{I}}_{\mathrm{a}}}{3}\\ \frac{{\mathrm{I}}_{\mathrm{a}}}{3}\end{array}\right] \end{gathered}$$

Hence,

$$\begin{gathered} I_0=I_1 \\ =I_2 \end{gathered}$$

Similarly,

$$\begin{gathered} {I\text{'}}_0={I\text{'}}_1 \\ ={I\text{'}}_2 \end{gathered}$$

Since, all the sequence currents are equal. Therefore, the sum of the sequence voltage is zero.

$$\begin{gathered} {V_{aa}}^{\text{'}}=\left({V_{00}}^{\text{'}}+{V_{11}}^{\text{'}}+{V_{22}}^{\text{'}}\right) \\ =0 \end{gathered}$$

Hence, the requiredfault condition in sequence domain.

$$\begin{gathered} {V_{aa}}^{\text{'}}=\left({V_{00}}^{\text{'}}+{V_{11}}^{\text{'}}+{V_{22}}^{\text{'}}\right) \\ =0 \end{gathered}$$

Draw the diagram of interconnection sequence network is shown in figure 1.