Question

A 220V/22kV three-phase transformer is connected in star/delta. The protective transformers on the 220V side have a current ratio of 400/5. Calculate the CT ratio on the 22kV side.

Answer 1

To calculate the Current Transformer (CT) ratio on the high-voltage (22kV) side, you need to use the transformation ratios and the CT ratio on the low-voltage (220V) side. Here's a step-by-step approach:

### 1. **Determine the Transformation Ratio of the Transformer**

The transformation ratio of the three-phase transformer is given by the voltage ratio:
\[ \text{Transformation Ratio} = \frac{\text{High-Voltage Side Voltage}}{\text{Low-Voltage Side Voltage}} \]

Given:
- High-Voltage Side Voltage = 22 kV
- Low-Voltage Side Voltage = 220 V

So,
\[ \text{Transformation Ratio} = \frac{22,000 \text{ V}}{220 \text{ V}} = 100 \]

### 2. **CT Ratio on the Low-Voltage Side**

The CT ratio on the 220V side is given as 400/5. This means that for every 400 A of primary current, the CT provides 5 A of secondary current.

### 3. **Calculate the CT Ratio on the High-Voltage Side**

To find the CT ratio on the high-voltage side, you need to adjust the ratio according to the transformer’s voltage ratio. The CT ratio on the high-voltage side should be scaled by the same factor as the transformer’s voltage ratio.

The CT ratio on the high-voltage side (22kV) can be calculated using the following formula:
\[ \text{CT Ratio on HV Side} = \text{CT Ratio on LV Side} \times \text{Transformation Ratio} \]

Substitute the given values:
\[ \text{CT Ratio on HV Side} = \frac{400}{5} \times 100 \]

\[ \text{CT Ratio on HV Side} = 80 \times 100 \]

\[ \text{CT Ratio on HV Side} = 8000 \]

### **Conclusion**

The CT ratio on the 22kV side of the transformer is **8000/5**.

Answer 2

To calculate the Current Transformer (CT) ratio on the 22kV side of a three-phase transformer, you need to consider the relationship between the line currents on both sides of the transformer and the connection types (Star/Delta in this case).

### Step 1: Understand the Transformer Connections

- **Primary Side (220V):** Star (Y) connection.
- **Secondary Side (22kV):** Delta (Δ) connection.

### Step 2: Determine the Line Current Ratio
The line current ratio between the primary and secondary sides of the transformer can be found using the voltage transformation ratio. For a star-delta connected transformer, the line voltage ratio is:

\[
\text{Voltage Ratio} = \frac{V_{\text{secondary}}}{V_{\text{primary}}} = \frac{22\,\text{kV}}{220\,\text{V}} = \frac{22000\,\text{V}}{220\,\text{V}} = 100
\]

For a star-delta transformer, the line current ratio is the inverse of the voltage ratio:

\[
\text{Current Ratio} = \frac{1}{\text{Voltage Ratio}} = \frac{1}{100} = 0.01
\]

### Step 3: Apply the Current Ratio to the CT Ratio

On the 220V side, the CT ratio is given as 400/5.

This means the actual line current on the 220V side is \(I_{L1} = 400 \times \frac{5}{400} = 5\,\text{A}\).

The corresponding line current on the 22kV side is:

\[
I_{L2} = I_{L1} \times \frac{1}{\text{Current Ratio}} = 5\,\text{A} \times 100 = 500\,\text{A}
\]

### Step 4: Determine the CT Ratio on the 22kV Side

To have the same secondary current (5 A) on the 22kV side, the CT ratio should be:

\[
\text{CT Ratio on 22kV Side} = \frac{500\,\text{A}}{5\,\text{A}} = 100/1
\]

Therefore, the CT ratio on the 22kV side should be **100/1**.