Three 15 kva single phase transformers are connected delta wye the primary voltage is 480 what is the primary phase current?

To determine the primary phase current of a delta-wye connected transformer system, follow these steps:

### Given:
- **Transformer rating** = 15 kVA (each transformer)
- **Number of transformers** = 3
- **Primary voltage** (delta connection) = 480 V

### Step 1: Calculate the total apparent power (S)
Since there are three transformers, the total apparent power \( S_{\text{total}} \) is the sum of the power of each transformer:
\[
S_{\text{total}} = 3 \times 15 \text{ kVA} = 45 \text{ kVA}
\]

### Step 2: Calculate the line current in the primary (delta side)
In a delta connection, the line current (\( I_{\text{L}} \)) is related to the phase current (\( I_{\text{ph}} \)) by the formula:
\[
I_{\text{L}} = \sqrt{3} \times I_{\text{ph}}
\]

The phase current is found using the apparent power formula:
\[
S_{\text{total}} = \sqrt{3} \times V_{\text{L}} \times I_{\text{L}}
\]
Where:
- \( S_{\text{total}} \) is the total apparent power (45 kVA).
- \( V_{\text{L}} \) is the line voltage (480 V).

Rearranging to solve for \( I_{\text{L}} \):
\[
I_{\text{L}} = \frac{S_{\text{total}}}{\sqrt{3} \times V_{\text{L}}}
\]

Substitute the values:
\[
I_{\text{L}} = \frac{45,000}{\sqrt{3} \times 480} = \frac{45,000}{831.6}
\]
\[
I_{\text{L}} \approx 54.12 \, \text{A}
\]

### Final Answer:
The primary line current is approximately **54.12 A**.

Would you like any additional details or clarification?

### Related Questions:
1. How does the wye connection on the secondary side affect the current?
2. What would the secondary line current be if the secondary voltage is known?
3. How does the phase current compare between delta and wye connections?
4. What happens if the load on the transformer increases?
5. How does the power factor affect the primary current calculation?

**Tip:** In a delta-wye transformer, the line voltage on the primary (delta) side is equal to the phase voltage, while on the secondary (wye) side, the line voltage is \(\sqrt{3}\) times the phase voltage.

Learn how to calculate the primary phase current for three 15 kVA single-phase transformers connected in delta-wye configuration with a primary voltage of 480V. This guide covers transformer theory, key formulas, and step-by-step solutions. Ideal for undergraduate electrical engineering students.

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