Question

A three-phase transformer having a line voltage ratio of 0.4 kV/11kV is connected Star/Delta and protective transformers on the 0.4 kV side have a current ratio of 500/5. Calculate the ratio of the protective transformers on the 11 kV side. Draw a neat circuit diagram and indicate the given values at appropriate places.

Answer 1

To solve this problem, we need to find the current ratio for the protective transformers on the 11 kV side of a star-delta connected three-phase transformer. Let's break down the steps to calculate this:

### Given Data
1. **Transformer Line Voltage Ratio:** \( V_{primary} / V_{secondary} = 0.4 \text{ kV} / 11 \text{ kV} \)
2. **Connection:** Star (Y) / Delta (Δ)
3. **Protective Transformer (CT) Ratio on 0.4 kV Side:** 500/5
4. **Find:** Ratio of protective transformers (CTs) on the 11 kV side.

### Step-by-Step Solution

#### 1. Transformer Voltage Ratio
The line voltage ratio of the transformer is:
\[
\frac{V_{L1}}{V_{L2}} = \frac{0.4 \text{ kV}}{11 \text{ kV}}
\]

#### 2. Determine the Current Ratio on the Transformer
For a star-delta transformer:
- Primary side (0.4 kV) is Star-connected
- Secondary side (11 kV) is Delta-connected

**Primary Side (Star) Line Current (\(I_{L1}\)):**
\[
I_{L1} = I_{ph1}
\]

**Secondary Side (Delta) Line Current (\(I_{L2}\)):**
\[
I_{L2} = I_{ph2} \times \sqrt{3}
\]

The power relationship (assuming ideal transformer):
\[
V_{L1} \times I_{L1} = V_{L2} \times I_{L2}
\]

Using the line voltage ratio:
\[
0.4 \times I_{L1} = 11 \times I_{L2}
\]

\[
I_{L1} = \frac{11}{0.4} \times I_{L2}
\]

\[
I_{L1} = 27.5 \times I_{L2}
\]

The current ratio of the transformer:
\[
\frac{I_{L1}}{I_{L2}} = 27.5
\]

#### 3. Protective Transformer (CT) Ratios
- **CT Ratio on the 0.4 kV side:** 500/5 = 100:1

Since the CT is on the primary side (0.4 kV side):
- The current on the 0.4 kV side is 500 A (before the CT).
- The corresponding secondary side (11 kV side) current can be calculated using the transformer current ratio.

Since the transformer current ratio is \( 27.5:1 \), if the current on the 0.4 kV side (primary) is 500 A:
\[
I_{secondary} = \frac{500}{27.5} \approx 18.18 \, \text{A}
\]

Now, we need the CT ratio for this current on the 11 kV side:
- Assume the CT secondary current for protection is also 5 A (standard practice).

So the CT ratio on the 11 kV side:
\[
\frac{18.18}{5} \approx 3.636
\]

To simplify into a standard CT ratio, the closest ratio is:
\[
4:1
\]

### Final CT Ratio on 11 kV Side
The CT ratio on the 11 kV side should be **20/5**, or approximately **4:1**.

### Circuit Diagram
Here's a description of the circuit diagram for the given system:

1. **Transformer:**
   - The primary side (0.4 kV) is star-connected (Y).
   - The secondary side (11 kV) is delta-connected (Δ).

2. **Protective Transformers:**
   - On the 0.4 kV side, current transformers (CTs) with a ratio of 500/5 (100:1).
   - On the 11 kV side, current transformers (CTs) with a ratio of 20/5 (4:1).

3. **Connections:**
   - The CTs on the 0.4 kV side are connected to measure the primary current.
   - The CTs on the 11 kV side are connected to measure the secondary current.

### Textual Representation of the Diagram
```
             0.4 kV Side (Star)                       11 kV Side (Delta)
             -------------------                       ----------------
           |--------CT 500/5--------|                |--------CT 20/5--------|
           |                        |                |                       |
        Phase A   Phase B   Phase C                 Phase A   Phase B   Phase C
           |        |         |                       |         |         |
        -------   -------   -------                -------   -------   -------
       |  Y   | |  Y   | |  Y   |                 | Δ  |   | Δ  |   | Δ  |
        -------   -------   -------                -------   -------   -------
            |       |        |                       |         |         |
           ---------------------------------         --------------------------------
                 Three-Phase Transformer
                    (0.4 kV / 11 kV)
```

### Summary
- The primary current (0.4 kV side) of 500 A steps down to around 18.18 A on the secondary (11 kV) side.
- The CT ratio on the primary (0.4 kV) side is 500/5 (100:1).
- The CT ratio on the secondary (11 kV) side is approximately 20/5 (4:1).

Answer 2

To solve the problem, let's break it down into a series of steps:

1. **Understanding the Transformer Setup:**

   You have a three-phase transformer with a line voltage ratio of \(0.4 \text{ kV} / 11 \text{ kV}\). This means that the primary side (high voltage side) has a voltage of 11 kV and the secondary side (low voltage side) has a voltage of 0.4 kV.

   The transformer is connected in a star (Y) configuration on the primary side (11 kV) and in a delta (Δ) configuration on the secondary side (0.4 kV).

   Protective transformers are used to step down the current to a safer level for measuring or for protection purposes. The current ratio for the protective transformers on the 0.4 kV side is given as \(500 / 5\).

2. **Calculating the Protective Transformer Ratio on the 11 kV Side:**

   **a. Find the Current Ratio for the 0.4 kV Side:**

   The current ratio of the protective transformers on the 0.4 kV side is \(500 / 5 = 100\). This means that the primary current of the protective transformer is 100 times the secondary current.

   **b. Calculate the Current Ratio for the 11 kV Side:**

   The current ratio of a transformer is inversely proportional to the voltage ratio. To find the current ratio for the protective transformers on the 11 kV side, use the voltage ratio of the main transformer.

   The voltage ratio of the main transformer is \(11 \text{ kV} / 0.4 \text{ kV}\). To convert this to the current ratio, take the inverse of this voltage ratio.

   \[
   \text{Current Ratio on the 11 kV Side} = \frac{0.4 \text{ kV}}{11 \text{ kV}} \times \text{Current Ratio on the 0.4 kV Side}
   \]

   \[
   \text{Current Ratio on the 11 kV Side} = \frac{0.4}{11} \times 100
   \]

   \[
   \text{Current Ratio on the 11 kV Side} = \frac{40}{11} \approx 3.64
   \]

   Thus, the current ratio for the protective transformers on the 11 kV side is approximately 3.64.

3. **Drawing the Circuit Diagram:**

   Here’s a simplified version of the circuit diagram:

   ```
   [ 11 kV Side ]                         [ 0.4 kV Side ]
   -----------------               -------------------
   |                   |                |                   |
   |     Primary      |               |     Secondary   |
   |     Transformer |  ---|  |-------> |      Transformer |
   |     (Star)       |               |      (Delta)         |
   |                   |                |                   |
   -----------------               -------------------

   ```

   **Indicate the Given Values:**

   - **Primary Transformer (Star Connection):** 11 kV
   - **Secondary Transformer (Delta Connection):** 0.4 kV
   - **Protective Transformer Current Ratio (0.4 kV Side):** 500 / 5 = 100
   - **Calculated Protective Transformer Current Ratio (11 kV Side):** ≈ 3.64

This diagram represents a simplified view of how the transformers and their connections might look. In practice, there would be additional elements like circuit breakers, fuses, and other protection devices, but this is the core setup.