Question

A 60-Hz, three-phase transmission line is 100 miles long. It has a total series impedance of 35 + j140 Ω and a shunt admittance of 930 x 10-6 at phase angle of 90⁰ S. It delivers 40 MW at 220 KV at 0.95 power factor lagging.

a. Determine the voltage, current, and power factor at the sending end of the line.

Answer 1

The question is about determining the sending-end electrical parameters of a three-phase transmission line given the receiving-end load and line constants using power system analysis techniques.

Step-by-step explanation:

TTo determine the voltage, current, and power factor at the sending end of the line, we can use the information provided. The power delivered is 40 MW at 220 KV and a power factor of 0.95 lagging. We can start by calculating the apparent power delivered using the formula S = P / power factor. In this case, S = 40 MW / 0.95 = 42.11 MVA. The sending end voltage can be calculated using the formula S = V * I, where V is the voltage and I is the current. Rearranging the formula, we get V = S / I. Substituting the values, V = 42.11 MVA / (220 KV * sqrt(3)) = 115.08 kV. Finally, the current can be calculated using the formula I = S / (V * sqrt(3)). Substituting the values, I = 42.11 MVA / (115.08 kV * sqrt(3)) = 197.89 A.

Therefore, the voltage at the sending end is 115.08 kV, the current at the sending end is 197.89 A, and the power factor at the sending end is 0.95 lagging..