Final answer:
To calculate the sending end current and voltage of a 220KV, 50Hz, three-phase transmission line, first determine the line's total resistance and reactance, then calculate the load current, and finally find the sending end voltage and current with the short line approximation.
Step-by-step explanation:
The student is asking to calculate the sending end current and voltage for a 220 kV, 50 Hz, three-phase transmission line using the short line model. Given the line's parameters and the fact that it delivers 300 MVA at a 0.8 lagging power factor, we first need to calculate the impedance of the line and then use it to find the sending end values. The resistance (R) of the line is 0.15 Ω/km, the inductance (L) is 1.4 mH/km, and the length of the line is 60 km.
We calculate the total resistance and reactance for the line, R=0.15Ω/km × 60 km = 9Ω and X = 2π × 50 Hz × 1.4 mH/km × 60 km. Using these values, we can form the complex impedance (Z) of the line, and from the power factor, we calculate the angle of the load impedance. After finding the load current by dividing the power by the voltage and power factor angle, we can use this current and the line impedance to find the sending end voltage using V_s = V_r + (I × Z), where V_r is the receiving end voltage. Finally, the sending end current equals the load current since it's a short line model.