Question

The line impedance of a three-phase transmission line is given by
\[ Z = (10 + j5)\Omega. \] For 100 MVA power delivered at 132 kV, the transmission loss is _______.

• A. 10 MW
• B. 5.74 MW
• C. 11.5 MW
• D. 1 MW

Hint:

Always use real part of impedance for calculating power loss. Use \( P = 3I^2R \) for 3-phase systems.

Answer 1

The Correct Option is B

Step 1: Use formula for power loss in a 3-phase line
\[ P_{\text{loss}} = 3I^2R \] Step 2: Calculate current from power and voltage
\[ S = \sqrt{3}VI \Rightarrow I = \frac{S}{\sqrt{3}V} = \frac{100 \times 10^6}{\sqrt{3} \times 132 \times 10^3} \approx 437.38\,\text{A} \] Step 3: Use real part of impedance (R = 10)
\[ P_{\text{loss}} = 3 \times (437.38)^2 \times 10 \approx 5.74 \times 10^6\,\text{W} = 5.74\,\text{MW} \]