Question

A Y-connected synchronous generator grounded through a neutral impedance ${\mathit{Z}}_{\mathbf{n}}$with a zero-sequence impedance ${\mathit{Z}}_{\mathbf{g}\mathbf{0}}$has zero-sequence impedance${\mathit{Z}}_{\mathbf{0}}\mathbf{=}$ ___________ in its zero-sequence network.

Short answer

The zero-sequence network is ${\mathit{Z}}_{\mathbf{0}}\mathbf{=}\mathbf{3}{\mathit{Z}}_{\mathbf{n}}\mathbf{+}{\mathit{Z}}_{\mathbf{g}\mathbf{0}}$.

Step-by-step solution

Determine the neutral current for three phase balance system.

The relationship between the neutral current and zero sequence current is given as follows.

${\mathit{I}}_{\mathbf{n}}\mathbf{=}\mathbf{3}{\mathit{I}}_{\mathbf{0}}$ …… (1)

Here,${\mathit{I}}_{\mathbf{n}}$is the neutral current and ${\mathit{I}}_{\mathbf{0}}$is the zero-sequence current.

The equation to calculate voltage drop across the impedance of the neutral is given as follows.

${\mathit{V}}_{\mathbf{n}}\mathbf{=}{\mathit{Z}}_{\mathbf{n}}{\mathit{I}}_{\mathbf{n}}$ …… (2)

Determine the zero-sequence impedance.

Calculate the voltage drop across the neutral impedance of the generator.

Substitute $\mathbf{3}{\mathit{I}}_{\mathbf{0}}$for ${\mathit{I}}_{\mathbf{n}}$into equation (2).

${\mathit{V}}_{\mathbf{n}}\mathbf{=}{\mathit{Z}}_{\mathbf{n}}\left(3I_0\right)$

${\mathit{V}}_{\mathbf{n}}\mathbf{=}{\mathit{Z}}_{\mathbf{n}}{\mathbf{I}}_{\mathbf{0}}$

The neutral impedance and zero sequence impedance connects in the series, that means the current will also the same in the series connection.

${\mathit{V}}_{\mathbf{n}}\mathbf{=}\left(I_0\right)\left(3Z_n\right)$

The neutral impedance $\mathbf{3}{\mathit{Z}}_{\mathbf{n}}$is connected in the series with the zero-sequence network.

Calculate the zero-sequence network.

${\mathit{Z}}_{\mathbf{0}}\mathbf{=}\mathbf{3}{\mathit{Z}}_{\mathbf{n}}\mathbf{+}{\mathit{Z}}_{\mathbf{g}\mathbf{0}}$

Hence, the zero-sequence network is$\mathbf{3}{\mathit{Z}}_{\mathbf{n}}\mathbf{+}{\mathit{Z}}_{\mathbf{g}\mathbf{0}}$.