Question

In terms of sequence components of phase given by ${\mathbf{V}}_{\mathbf{ao}}\mathbf{=}{\mathbf{V}}_{\mathbf{O}}$, ${\mathbf{V}}_{\mathbf{a}\mathbf{1}}\mathbf{=}{\mathbf{V}}_{\mathbf{1}}$, and ${\mathbf{V}}_{\mathbf{a}\mathbf{2}}\mathbf{=}{\mathbf{V}}_{\mathbf{2}}$ , give expressions for the phase voltages ${\mathbf{V}}_{\mathbf{a}\mathbf{}\mathbf{,}}{\mathbf{V}}_{\mathbf{b}\mathbf{}\mathbf{,}}$and ${\mathbf{V}}_{\mathbf{c}}$. ${\mathbf{V}}_{\mathbf{a}}$ _______________; ${\mathbf{V}}_{\mathbf{b}}$_______________;${\mathbf{V}}_{\mathbf{c}}$ _______________

Short answer

In terms of sequence components of phase given by ${\mathrm{V}}_{\mathrm{ao}}={\mathrm{V}}_{\mathrm{O}}$ , ${\mathrm{V}}_{\mathrm{a}1}={\mathrm{V}}_1$, and ${\mathrm{V}}_{\mathrm{a}2}={\mathrm{V}}_2$ , give expressions for the phase voltages ${\mathrm{V}}_{\mathrm{a},}{\mathrm{V}}_{\mathrm{b},}$ and ${\mathrm{V}}_{\mathrm{c}}$${\mathrm{V}}_{\mathrm{a}}={\mathrm{V}}_{\mathrm{O}}+{\mathrm{V}}_1+{\mathrm{V}}_{2,}{\mathrm{V}}_{\mathrm{b}}={\mathrm{V}}_{\mathrm{O}}+{\mathrm{a}}^2{\mathrm{V}}_1+{\mathrm{aV}}_{2,}{\mathrm{V}}_{\mathrm{c}}={\mathrm{V}}_{\mathrm{O}}+{\mathrm{aV}}_1+{\mathrm{a}}^2{\mathrm{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:

$$\begin{gathered} {\mathrm{V}}_{\mathrm{a}}={\mathrm{V}}_{\mathrm{a}0}+{\mathrm{V}}_{\mathrm{a}}1+{\mathrm{V}}_{\mathrm{a}}2 \\ {\mathrm{V}}_{\mathrm{b}}={\mathrm{V}}_{\mathrm{a}0}+{\mathrm{a}}^2{\mathrm{V}}_{\mathrm{a}1}+{\mathrm{aV}}_{\mathrm{a}2} \\ {\mathrm{V}}_{\mathrm{c}}={\mathrm{V}}_{\mathrm{a}0}+{\mathrm{aV}}_{\mathrm{a}1}+{\mathrm{a}}^2{\mathrm{V}}_{\mathrm{a}2} \end{gathered}$$

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

Consider the below variables,

$$\begin{gathered} {\mathrm{V}}_{\mathrm{a}0}={\mathrm{V}}_0 \\ {\mathrm{V}}_{\mathrm{a}1}={\mathrm{V}}_1 \\ {\mathrm{V}}_{\mathrm{a}2}={\mathrm{V}}_2 \end{gathered}$$

Then the phase voltages become:

$$\begin{gathered} {\mathrm{V}}_{\mathrm{a}}={\mathrm{V}}_0+{\mathrm{V}}_1+{\mathrm{V}}_2 \\ {\mathrm{V}}_{\mathrm{b}}={\mathrm{V}}_0+{\mathrm{a}}^2{\mathrm{V}}_1+{\mathrm{aV}}_2 \\ {\mathrm{V}}_{\mathrm{c}}={\mathrm{V}}_0+{\mathrm{aV}}_1+{\mathrm{a}}^2{\mathrm{V}}_2 \end{gathered}$$