Question

1 A 138kV,3ϕ, short transmission lone has a perphase impedance of (2+j4)Ω. If the ine supplies a 25 mW load at 0.8PF lagging : Calaulata (a) The sending end voltage and P.F (B) The efficiency of transinission.

Answer 1

To calculate the sending end voltage and power factor, you need to calculate the complex power at the load and the sending end. The efficiency of transmission can be calculated by finding the power input and power loss in the transmission line.

Step-by-step explanation:

(a) To calculate the sending end voltage and power factor:

1. Calculate the complex power at the load using the formula: complex power = active power + j * reactive power. In this case, the active power is 25 mW (given) and reactive power can be found using the formula: reactive power = apparent power * sin(arccos(power factor)). So, reactive power = 25 mW * sin(arccos(0.8)) = 20 mVar.
2. Now, calculate the complex power at the sending end using the formula: complex power = complex power at the load + (3 * per phase impedance).
3. The sending end voltage can be calculated using the formula: sending end voltage = square root of (complex power / (3 * complex conjugate of line current)).
4. The power factor can be found by calculating the angle between the complex power and the complex conjugate of line current.

(b) To calculate the efficiency of transmission:

1. First, calculate the power input to the transmission line using the formula: power input = square root of (3) * line voltage * line current * power factor.
2. Next, calculate the power loss in the transmission line using the formula: power loss = power input - active power at the load.
3. Finally, the efficiency of transmission can be calculated using the formula: efficiency = (active power at the load) / power input.