Let's break down the problem step by step: ### Given Data - **Line-to-line sending end voltage, \( V_{S,LL} \) = 400 kV** - **Line-to-line receiving end voltage, \( V_{R,LL} \) = 440 kV** - **Sending end per-phase current, \( I_S = 246.6 \angle 90^\circ \) A** - **Line length = 200 km** - **Frequency, \( f = 50 \) Hz** - **Three-phase transmission line** - **No load at receiving end (open-circuit load)** --- ### Step 1: Convert Line-to-Line Voltages to Phase Voltages \[ V_{S,ph} = \frac{V_{S,LL}}{\sqrt{3}} = \frac{400,000}{\sqrt{3}} = 230,940\, \text{V} \] \[ V_{R,ph} = \frac{V_{R,LL}}{\sqrt{3}} = \frac{440,000}{\sqrt{3}} = 254,034\, \text{V} \] --- ### Step 2: No Load Condition - At no load, the receiving end current is **zero**. - The **sending end current** is due to the **charging current** (shunt admittance). --- ### Step 3: Shunt Admittance Per Phase The shunt current per phase, at no load, is given by: \[ I_{S,ph} = j B V_{S,ph} \] where - \( I_{S,ph} \) is the sending end current per phase, - \( B \) is the total shunt admittance per phase, - \( V_{S,ph} \) is the sending end phase voltage. Given \( I_{S,ph} = 246.6 \angle 90^\circ \) A (which is purely reactive, as expected for a charging current). --- ### Step 4: Find Total Shunt Admittance Per Phase \[ I_{S,ph} = j B V_{S,ph} \] \[ B = \frac{I_{S,ph}}{j V_{S,ph}} \] Since \( I_{S,ph} \) is already at \( 90^\circ \), it is positive imaginary (i.e., \( j 246.6 \) A). \[ B = \frac{j 246.6}{j \cdot 230,940} \] \( j/j = 1 \) \[ B = \frac{246.6}{230,940} \] \[ B = 0.001068 \text{ S} \] or \[ B = 1.068 \times 10^{-3} \text{ S (per phase)} \] --- ### Step 5: Total Shunt Admittance for Three Phases For all three phases: \[ B_{\text{total}} = 3 \times B = 3 \times 1.068 \times 10^{-3} = 3.204 \times 10^{-3} \text{ S} \] --- ## **Final Answer** ### **The total shunt admittance of the line is:** \[ \boxed{3.20 \times 10^{-3}\ \text{S}} \] (rounded to three significant digits) --- **Summary Table:** | Quantity | Value | |-----------------------|------------------| | Per-phase shunt adm. | \(1.07\times10^{-3}\) S | | Total (3-phase) adm. | \(3.20\times10^{-3}\) S | Let me know if you need further clarification!