Question

In a three-phase Y-connected system with a neutral, express the neutral current in terms of phase currents and sequence-component terms.

${\mathbf{l}}_{\mathbf{n}}$______________________________

Short answer

In a three-phase Y-connected system with a neutral, express the neutral current in terms of phase currents and sequence-component terms.

$l_n=3l_0=l_a+l_b+l_c$

Step-by-step solution

Determine the neutral current in terms of phase current.

In case of the star connected system, the neutral current is the sum of the three-phase current.

${\mathbf{l}}_{\mathbf{n}}\mathbf{=}{\mathbf{l}}_{\mathbf{a}}\mathbf{+}{\mathbf{l}}_{\mathbf{b}}\mathbf{+}{\mathbf{l}}_{\mathbf{c}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}..........\left(1\right)$

Here and are the phase currents.

Determine the neutral current in terms of sequence component.

The sequence current can be expressed as,

$$\begin{gathered} l_0=\frac{1}{3}\left(l_a+l_b+l_c\right) \\ 3l_0=l_a+l_b+l_c............\left(2\right) \\ \mathrm{From}\mathrm{equation}\left(1\right)\mathrm{and}\left(2\right). \\ {l}_n=3l_0 \\ \mathrm{Hence},\mathrm{the}\mathrm{neutral}\mathrm{current}\mathrm{in}\mathrm{terms}\mathrm{of}\mathrm{phase}\mathrm{current}\mathrm{is}{l}_a+l_b+l_c \\ \mathrm{and}\mathrm{in}\mathrm{terms}\mathrm{of}\mathrm{sequence}\mathrm{current}\mathrm{is}3{\mathrm{l}}_0. \end{gathered}$$