Question

In an unbalanced three-phase system, line-to-neutral voltage ______ have a zero-sequence component, whereas line-to-line voltages __________ have a zero-sequence component.

Short answer

In an unbalanced three-phase system, line-to-neutral voltage may have a zero-sequence component, whereas line-to-line voltages never have a zero-sequence component.

Step-by-step solution

Determine formula to calculate the zero-sequence current.

The equation for zero sequence current is given as follows.

${\mathit{V}}_{\mathbf{0}}\mathbf{=}\frac{{\mathbf{V}}_{\mathbf{a}}\mathbf{+}{\mathbf{V}}_{\mathbf{b}}\mathbf{+}{\mathbf{V}}_{\mathbf{c}}}{\mathbf{3}}............\left(1\right)$

Here ${\mathbf{V}}_{\mathbf{a}}\mathbf{,}{\mathbf{V}}_{\mathbf{b}\mathbf{}}\mathbf{and}\mathbf{}{\mathbf{V}}_{\mathbf{c}}$ are the line to neutral voltages.

Determine line to neutral ad line to line voltages have zero sequence component?

Consider the values for the line-to-neutral voltages.

$$\begin{gathered} V_a=10\angle 0^{0}V \\ {V}_b=20\angle {120}^{0}V \\ {V}_c=20\angle -{120}^{0}V \end{gathered}$$

Calculate the zero-sequence current.

From the above, the line to neutral voltage have zero-sequence component and in case of the line-to-line voltage the sum of voltages always equal to zero. Therefore, line to line voltages never have zero sequence component.

Hence, for unbalanced system, the line to neutral may have the zero-sequence current but line-to-line voltage never have zero sequence component.

Hence