Question

With symmetrical components, the conversion from phase to sequence components decouples the networks and the resulting KVL equations.

(a) True (b) False

Short answer

Answer

The correct option is (a): True.

Step-by-step solution

Write the relationship for voltage and current between the sequence component and phase.

The relationship between the phase and sequence component of the current is given as follows.

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

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

The relationship between the phase and sequence component of the voltage is given as follows.

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

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

Determine the conversion from phase to sequence components decouples the networks and the resulting KVL equations.

When phase component is converted to sequence component, three sequence components is obtained which are drawn from different plane.

Therefore, the conversion from phase to sequence components decouples the networks and the resulting KVL equations occurs with symmetrical component.

Therefore, the correct option is True.