Question

At the general three-phase bus shown in Figure 9.7(a) of the text, consider a simultaneous single line-to-ground fault on phase a and line-to-line fault between phases $\mathit{b}$ and $\mathit{c}$, with no fault impedances. Obtain the sequence-network interconnection satisfying the current and voltage constraints.

Short answer

The sequential network for currents is shown below.

The sequential network for voltages is shown below.

Step-by-step solution

write the given data from the question.

The single line to ground fault on phase$a$ .

Line to line fault between phase $b$ and $c$.

Determine the sequence-network interconnection satisfying the current and voltage constraints.

The equation to calculate the sequence current is given as follows,

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

Here, role="math" localid="1655881375695" ${\mathit{I}}_{\mathbf{0}}$, $I_1$, $I_2$ are the sequence current and ${\mathit{I}}_{\mathbf{a}}\mathbf{,}{\mathit{I}}_{\mathbf{b}}\mathbf{,}{\mathit{I}}_{\mathbf{c}}$ are the phase current.

The equation to calculate the sequence voltage is given as follows,

role="math" localid="1655881512153" $\left[\begin{array}{c}{V}_0\\ V_1\\ V_2\end{array}\right]\mathbf{=}\frac{\mathbf{1}}{\mathbf{3}}\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right]\left[\begin{array}{c}{V}_a\\ V_b\\ V_c\end{array}\right]$ …… (2)

Here, ${\mathbf{V}}_{\mathbf{0}}\mathbf{,}{\mathbf{V}}_{\mathbf{1}}\mathbf{,}{\mathbf{V}}_{\mathbf{2}}$are the sequence voltages and ${\mathbf{V}}_{\mathbf{a}}\mathbf{,}{\mathbf{V}}_{\mathbf{b}}\mathbf{,}{\mathbf{V}}_{\mathbf{c}}$ are the phase voltages.

Determine the sequence-network interconnection satisfying the current and voltage constraints.

Consider the schematic diagram of the system with single line ground fault on phase$a$ and line to line fault on phase$b$ and$c$ .

The fault conditions from the above,

Calculate the relationship between sequence current and phase currents.

Substitute$-I_b$ for$I_c$ into equation (1).

The sequential network that satisfy the above equations.

Calculate the relationship between sequence voltages and phase voltages.

Substitute$V_b$ for$V_C$ into equation (2).

The sequential network that satisfy the above equations.