Question

In terms of sequence components of phase given by,, and, give expressions for the phase voltages,, and._______________;_______________;_______________

Short answer

In terms of sequence components of phase given by $V_{a0}=V_0$, $V_{a1}=V_1$, and $V_{a2}=V_2$, give expressions for the phase voltages $V_a$, $V_b$, and $V_c$. $V_a=V_0+V_1+V_2$; $V_b=V_0+a^2{V}_1+a{V}_2$; $V_c=V_0+a{V}_1+a^2{V}_2$.

Step-by-step solution

Sequence Components

There are three-phases of symmetrical component power system which are resolved into three sets of sequence components such as: Positive-sequence, Negative-sequence and Zero-sequence component.

Determine the answer

Sequence components of phase voltages are:

$$\begin{gathered} V_a=V_{a0}+V_{a1}+V_{a2} \\ {V}_b=V_{a0}+a^2{V}_{a1}+a{V}_{a2} \\ {V}_c=V_{a0}+a{V}_{a1}+a^2{V}_{a2} \end{gathered}$$

Here, $V_a$, $V_b$, and $V_c$are the phase voltages and $V_{a0}$, $V_{a1}$, and $V_{a2}$are sequence components.

Consider the below variables,

$$\begin{gathered} V_{a0}=V_0 \\ {V}_{a1}=V_1 \\ {V}_{a2}=V_2 \end{gathered}$$

Then the phase voltages become:

$$\begin{gathered} V_a=V_0+V_1+V_2 \\ {V}_b=V_0+a^2{V}_1+a{V}_2 \\ {V}_c=V_0+a{V}_1+a^2{V}_2 \end{gathered}$$