ΜF/km per phase. The resistance is negligible. Assuming the voltage at the sending end of the line is 400 kV, determine:

a) The receiving end voltage when the line is delivering 800 MW.

b) The maximum power that can be transmitted through the line without exceeding a voltage drop of 10% of the sending end voltage.

c) The surge impedance of the line.

d) The capacitance reactance of the line per phase.

a) The receiving end voltage can be determined using the formula:

V_R = V_S - I_L Z_L - I_C Z_C

where V_S is the sending end voltage, I_L is the line current, Z_L is the line impedance, I_C is the capacitive current, and Z_C is the capacitive reactance.

First, we need to calculate the line impedance and capacitive reactance per phase:

Z_L = jωL = j2πfL = j2π50(0.97×10^-3)×300 = j138.6 Ω

Z_C = 1/jωC = -j1/(2πfC) = -j1/(2π50×0.0115×10^-6) = -j123.2 Ω

Next, we can calculate the line current:

I = P/(√3 V_S cos φ) = 800×10^6/(√3×400×10^3×1) = 1547.7 A

where cos φ = 1 (assuming unity power factor).

Finally, we can calculate the receiving end voltage:

V_R = 400×10^3 - j138.6×1547.7 - j123.2×1547.7 = 346.3∠-13.3° kV

Therefore, the receiving end voltage is 346.3 kV at an angle of -13.3° with respect to the sending end voltage.

b) The maximum power that can be transmitted through the line without exceeding a voltage drop of 10% of the sending end voltage can be determined using the formula:

P_max = 3 V_S^2/(2Z_L) (1 - V_R/V_S)

where V_R is the receiving end voltage and V_S is the sending end voltage.

We can rearrange this formula to solve for V_R:

V_R = V_S (1 - 2P_max Z_L/(3V_S^2))

Substituting the given values, we get:

V_R = 400×10^3 (1 - 2×P_max×138.6/(3×(400×10^3)^2))

When the voltage drop is 10% of the sending end voltage, V_R/V_S = 0.9. Solving for P_max, we get:

P_max = 3×(400×10^3)^2×(1 - 0.9)/(2×138.6×0.9) = 1600 MW

Therefore, the maximum power that can be transmitted through the line without exceeding a voltage drop of 10% of the sending end voltage is 1600 MW.

c) The surge impedance of the line can be calculated using the formula:

Z_0 = √(Z_L/Z_C) = √(j138.6/-j123.2)