Question

Two 11 KV, three-phase 2500 KVA generators having reactance of 12% operate in parallel. The generators supply power to a transmission line through a 6000 KVA transformer of ratio 11/22 KV and having leakage reactance of 4%. Calculate fault KVA on H.T. side of transformer.

Answer 1

To calculate the fault KVA on the high-tension (H.T.) side of the transformer, we first need to determine the equivalent reactance of the system, which includes the reactance of both generators and the transformer.

### Step 1: Calculate the generator reactance
The two generators are in parallel. Since they have the same rating, we can consider their equivalent reactance using the formula for parallel reactances:

\[
\frac{1}{X_{eq}} = \frac{1}{X_1} + \frac{1}{X_2}
\]

Where:
- \(X_1 = X_2 = 0.12 \times 2500 \, \text{KVA} = 0.12 \times 2500 = 300 \, \text{KVA} \)

So,

\[
\frac{1}{X_{eq}} = \frac{1}{300} + \frac{1}{300} = \frac{2}{300} \Rightarrow X_{eq} = \frac{300}{2} = 150 \, \text{KVA}
\]

### Step 2: Calculate the transformer reactance on the H.T. side
The leakage reactance of the transformer is given as 4%. To convert this to per unit (p.u.) on the H.T. side (22 kV), we first need to determine the base MVA on the H.T. side.

The transformer's rating is 6000 KVA (or 6 MVA), and its H.T. voltage is 22 kV.

\[
X_{T} = 0.04 \times 6000 \, \text{KVA} = 240 \, \text{KVA}
\]

### Step 3: Convert all reactances to the same base
The H.T. side of the transformer has a base of 6000 KVA. We will convert the reactance of the generators from 2500 KVA to 6000 KVA base using the following formula:

\[
X_{base\_6000} = X_{base\_2500} \times \left(\frac{S_{base\_2500}}{S_{base\_6000}}\right)
\]

Where:
- \(S_{base\_2500} = 2500 \, \text{KVA}\)
- \(S_{base\_6000} = 6000 \, \text{KVA}\)

So, converting \(X_{eq}\):

\[
X_{eq\_6000} = 150 \times \left(\frac{2500}{6000}\right) = 150 \times \frac{5}{12} = 62.5 \, \text{KVA}
\]

### Step 4: Total reactance on the H.T. side
Now we can sum the reactances to find the total reactance on the H.T. side:

\[
X_{total} = X_{eq\_6000} + X_{T} = 62.5 + 240 = 302.5 \, \text{KVA}
\]

### Step 5: Calculate fault KVA
The fault KVA can be calculated using the formula:

\[
\text{Fault KVA} = \frac{V^2}{X}
\]

Where \(V\) is the line-to-line voltage on the H.T. side of the transformer (22 kV), converted to the appropriate units:

\[
\text{Fault KVA} = \frac{(22 \times 1000)^2}{302.5}
\]

Calculating it:

\[
\text{Fault KVA} = \frac{48400000}{302.5} \approx 160000 \, \text{KVA}
\]

### Final Result
Thus, the fault KVA on the H.T. side of the transformer is approximately **160,000 KVA**.

Answer 2

To calculate the fault KVA on the high-tension (H.T.) side of the transformer, we can use the following steps:

### Step 1: Convert Generator Reactance to Common Base
First, we need to find the equivalent reactance of the two generators operating in parallel, converted to a common base. The base values for this calculation are:

- Base Power (\( S_{\text{base}} \)) = 2500 KVA (since both generators are identical)
- Base Voltage (\( V_{\text{base}} \)) = 11 KV (same as the generator voltage)

The reactance of each generator is given as 12%. This can be expressed as:

\[
X_{\text{generator}} = 0.12 \times \frac{S_{\text{base}}}{S_{\text{generator}}}
\]

Since both generators are in parallel, their equivalent reactance \( X_{\text{eq}} \) is:

\[
\frac{1}{X_{\text{eq}}} = \frac{1}{X_{\text{generator1}}} + \frac{1}{X_{\text{generator2}}}
\]

But because the generators are identical, \( X_{\text{eq}} = \frac{X_{\text{generator}}}{2} \).

So,

\[
X_{\text{eq}} = \frac{0.12 \times 2500}{2500 \times 2} = \frac{0.12}{2} = 0.06 \text{ pu on 2500 KVA base}
\]

### Step 2: Convert Transformer Reactance to Generator Base
The transformer reactance is 4% on a 6000 KVA base. We need to convert it to the generator base (2500 KVA). The conversion is:

\[
X_{\text{transformer}} = X_{\text{transformer\_per\_unit}} \times \frac{S_{\text{base (generator)}}}{S_{\text{base (transformer)}}}
\]

\[
X_{\text{transformer}} = 0.04 \times \frac{2500}{6000} = 0.01667 \text{ pu on 2500 KVA base}
\]

### Step 3: Calculate Total Reactance
The total reactance on the generator base side is the sum of the equivalent generator reactance and the transformer reactance:

\[
X_{\text{total}} = X_{\text{eq}} + X_{\text{transformer}}
\]

\[
X_{\text{total}} = 0.06 + 0.01667 = 0.07667 \text{ pu on 2500 KVA base}
\]

### Step 4: Calculate Fault KVA on the Transformer H.T. Side
Finally, the fault KVA on the H.T. side of the transformer can be calculated using the formula:

\[
\text{Fault KVA} = \frac{S_{\text{base}}}{X_{\text{total}}}
\]

Substitute the values:

\[
\text{Fault KVA} = \frac{2500}{0.07667} \approx 32610 \text{ KVA}
\]

So, the fault KVA on the H.T. side of the transformer is approximately **32,610 KVA**.