Question

Question:Determine the CT ratios for differential protection of a three-phase,$\Delta --\mathbf{Y}$ connected,10-MVA,33:11 KV , transformer, such that the circulating current in the transformer D does not exceed 5A .

Short answer

Answer

The value of the CT ratio for the differential protection of a three phase is .

Step-by-step solution

Write the given data from the question

Consider the value of base MVA is 10 .

Consider the value of three-phase voltage ratio is 33;11 KV.

Consider circulating current is 5 A.

Determine the formula of CT ratio for the differential protection of a three phase.

Write the formula ofCT ratio on HV side is,

${\left(\mathbf{CT}\mathbf{ratio}\right)}_{\mathbf{HV}}=\frac{{\mathbf{I}}_{\mathbf{2}}}{\mathbf{5}}$ …… (1)

Here, I₁ is line current of secondary side.

Write the formula of CT ratio on LV side is,

${\left(\mathbf{CT}\mathbf{ratio}\right)}_{\mathbf{LV}}=\frac{{\mathbf{I}}_{\mathbf{1}}}{\mathbf{5}}$ …… (2)

Here, I₂ is line current of primary side.

 Determine the value of CT ratio for the differential protection of a three phase.

Determine the line current in the primary side (delta side).

$$\begin{gathered} I_1=\frac{10\times {10}^6}{\sqrt{3}\left(33\times {10}^3\right)} \\ =174.95\text{A} \end{gathered}$$

Determine the line current in the secondary side (star side).

$$\begin{gathered} I_2=\frac{10\times {10}^6}{\sqrt{3}\left(11\times {10}^3\right)} \\ =524.86\text{A} \end{gathered}$$

Therefore, the HV side is connected in delta, so the CTs on HV side are connected in star.

Determine the circulating current should not exceed. So, the CT ratio on HV side.

Substitute 524.86 for I₂ into equation (1).

$$\begin{gathered} {\left(\text{CT}\text{ratio}\right)}_{\text{HV}}=\frac{524.86}{5} \\ =104.97 \end{gathered}$$

Similarly, the CT ratio on LV side.

Substitute $174.95\sqrt{3}$For $I_1$ into equation (2).

$$\begin{gathered} {\left(\text{CT} \text{ratio}\right)}_{\text{LV}}=\frac{174.95\sqrt{3}}{5} \\ =60.6 \end{gathered}$$

Therefore,the value of the CT ratio for the differential protection of a three phase is 60.6 .