Question

In a balanced Y-connected system, what is the zero-sequence component of the line currents?

Short answer

The zero-sequence component of the line current is zero.

Step-by-step solution

Determine the formula to calculate the zero-sequence component of the line currents.

The equation for zero sequence current in balance three phase system is given as follows.

${\mathbf{l}}_{\mathbf{0}}\mathbf{=}\frac{{\mathbf{l}}_{\mathbf{n}}}{\mathbf{3}}$ …… (1)

Here ${\mathrm{l}}_{\mathrm{n}}$is the neutral current.

The neutral current in three phase system is given as follows.

${\mathbf{l}}_{\mathbf{n}}\mathbf{=}{\mathbf{l}}_{\mathbf{a}}\mathbf{+}{\mathbf{l}}_{\mathbf{b}}\mathbf{+}{\mathbf{l}}_{\mathbf{c}}$

Here $l_a,l_b\mathrm{and}{l}_c$are the phase currents.

Calculate the zero-sequence component of the line current.

The zero-sequence current can be expression as,

Substitute $l_a+l_b+l_c\mathrm{for}{l}_n$into equation (1).

$l_o=\frac{l_a+l_b+l_c}{3}$ .........(2)

According to the Kirchhoff’s law, in case of three phase star connected system the sum of all currents is equal to zero.

$l_a+l_b+l_c=0$

Calculate zero sequence current.

Substitute 0 for $l_a+l_b+l_c$into equation (2).

$$\begin{gathered} l_o=\frac{0}{3} \\ {l}_o=0A \end{gathered}$$

Hence, the zero-sequence component of the line current is zero.