Question

For a balanced-Y impedance load with per-phase impedance of ZY and a neutral impedance Zn, the zero-sequence voltage ${\mathit{V}}_{\mathbf{0}}\mathbf{=}{\mathit{I}}_{\mathbf{0}}{\mathit{Z}}_{\mathbf{0}}$, where ${\mathit{Z}}_{\mathbf{0}}$ ___________.

Short answer

The zero-sequence impedance is ${\mathit{Z}}_{\mathbf{0}}\mathbf{=}\left(Z_y+3Z_n\right)$.

Step-by-step solution

Determine the formulas to calculate the zero-sequence impedance.

The relationship between the sequence voltage, sequence impedance and sequence current is given as follows.

$$\begin{gathered} {\mathit{V}}_{\mathbf{s}}\mathbf{=}{\mathit{Z}}_{\mathbf{s}}{\mathit{I}}_{\mathbf{s}} \\ \left[\begin{array}{c}{V}_0\\ V_1\\ V_2\end{array}\right]\mathbf{=}\left[\begin{array}{ccc}{Z}_y+3Z_n& 0& 0\\ 0& Z_y& 0\\ 0& 0& Z_y\end{array}\right]\left[\begin{array}{c}{I}_0\\ I_1\\ I_2\end{array}\right] \end{gathered}$$ …… (1)

Here, ${\mathit{V}}_{\mathbf{0}}$, ${\mathit{V}}_{\mathbf{1}}$and localid="1654160813285" ${\mathit{V}}_{\mathbf{2}}$are the sequence voltages, ${\mathit{I}}_{\mathbf{0}}$, ${\mathit{I}}_{\mathbf{1}}$and ${\mathit{I}}_{\mathbf{2}}$are the sequence currents.

Calculate the zero-sequence impedance.

From the equation (1), the relationship between the zero-sequence voltage current and impedance is given as follows.

${\mathit{V}}_{\mathbf{0}}\mathbf{=}\left(Z_y+3Z_n\right){\mathit{I}}_{\mathbf{0}}$

Substitute ${\mathit{Z}}_{\mathbf{0}}{\mathit{I}}_{\mathbf{0}}$for ${\mathit{V}}_{\mathbf{0}}$into above equation.

width="140" height="25" role="math">Z0I0=(Zy+3Zn)I0

${\mathit{Z}}_{\mathbf{0}}\mathbf{=}\left(Z_y+3Z_n\right)$

Hence, the zero-sequence impedance is $\left(Z_y+3Z_n\right)$.