Let's solve the problem step by step: ### **Given:** - **Transformer T1 voltage:** 20/110 kV - **Transformer T2 voltage:** 110/13.8 kV - **Transmission line length:** 50 km - **Reactance of transmission line (XTL):** 0.5 Ω/km - **Base power (S_base):** 100 MVA --- ### **Step 1: Find the total reactance of the transmission line (XTL)** \[ X_{TL,total} = X_{TL} \times \text{length} = 0.5 \, \Omega/\text{km} \times 50 \, \text{km} = 25 \, \Omega \] --- ### **Step 2: Choose the Base Voltage** The transmission line connects the 110 kV sides of both transformers, so the base voltage should be **110 kV** (line-to-line). --- ### **Step 3: Calculate the Base Impedance** \[ Z_{base} = \frac{(V_{base})^2}{S_{base}} \] - \( V_{base} = 110 \, \text{kV} = 110,000 \, \text{V} \) - \( S_{base} = 100 \, \text{MVA} = 100,000,000 \, \text{VA} \) \[ Z_{base} = \frac{(110,000)^2}{100,000,000} \] \[ Z_{base} = \frac{12,100,000,000}{100,000,000} = 121 \, \Omega \] --- ### **Step 4: Calculate the Per Unit Value of XTL** \[ X_{TL(pu)} = \frac{X_{TL(total)}}{Z_{base}} = \frac{25}{121} = 0.206 \, \text{pu} \] --- ## **Final Answer:** \[ \boxed{X_{TL(pu)} = 0.206 \, \text{pu} \text{ (at 100 MVA base, 110 kV base voltage)}} \]