Three single phase transformers are connected in delta-delta to step down a line voltage of 138 kV to 4160 V to supply power to a production plant. The plant draws 21 MW at a lagging power factor of 86 %. Calculate the apparent power furnished by the HV line. 

Problem Description:

Three single-phase transformers are connected in delta-delta to step down a line voltage of 138 kV to 4160 V to supply power to a production plant. The plant draws 21 MW at a lagging power factor of 86%. The task is to calculate the apparent power furnished by the high-voltage (HV) line.

Given Data:

• Line voltage on HV side: 138 kV
• Line voltage on LV side: 4160 V
• Real power (P): 21 MW
• Power factor (pf): 0.86 (lagging)

Solution:

The apparent power (S) is calculated using the relationship between real power (P), apparent power (S), and power factor (pf):

Formula:

S = P / pf

Step 1: Substitute the values:

P = 21 MW = 21 × 10⁶ W

pf = 0.86

S = (21 × 10⁶) / 0.86

Step 2: Perform the calculation:

S = 24.42 × 10⁶ VA

S = 24.42 MVA

Step 3: Round off the value:

The apparent power furnished by the HV line is approximately 24.4 MVA.

Final Answer:

The correct option is:

Option 1: 24.4 MVA

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: 48.8 MVA

This value is double the correct answer. It might represent a miscalculation where the power factor was mistakenly considered as 0.43 (half of 0.86). However, this does not align with the given problem statement, where the correct power factor is 0.86.

Option 3: 12.2 MVA

This value is half of the correct answer. It could result from a calculation error where the power factor was incorrectly doubled (1.72 instead of 0.86). This is not consistent with the given data and is therefore incorrect.

Option 4: 6.1 MVA

This value is significantly lower than the correct answer and could result from an error in using a much higher power factor (e.g., 3.44) or incorrectly interpreting the real power. This does not match the given data and is incorrect.

Conclusion:

The apparent power furnished by the HV line is calculated based on the real power and the power factor. Using the formula S = P / pf, the correct answer is determined to be 24.4 MVA. The other options result from potential miscalculations or incorrect assumptions about the power factor or real power.