[Electrical Engineering] Three-phase transmission line problem

[MrPacane]

Homework Statement

A three-phase line delivers 3600 kW at its receiving end at a lagging power factor of 0.85. The line resistance and reactance are 5 Ohms and 8 Ohms per phase respectively. Given that the sending end line voltage is 33kV, you are asked to determine the receiving end line voltage.

Homework Equations

Z = R + jX
z = 90 - arctan(X/R)

p.f. = P/√(P²+Q²)

P2 = Active power at the receiving end = 3600 kW
Q2 = Reactive power at the receiving end = 2231.08 kVAR (found using the equation above)

P2 = E1*E2*sin(z+d)/Z - (E2/Z)^2*R
Q2 = E1*E2*cos(z+d)/Z - (E2/Z)^2*X

The Attempt at a Solution

I'm trying to solve this system of equations which has two unknows (d & E2) but I don't think that's the right approach... Any ideas?

 

[KataKoniK]

Thank you for your question. To determine the receiving end line voltage, we can use the following steps:

1. Calculate the total impedance of the line using the given resistance and reactance values:
Z = √(R² + X²) = √(5² + 8²) = 9.433 Ohms

2. Calculate the sending end line current using the given power and power factor values:
I1 = P/S√(1-p.f.²) = 3600/(33kV*√(1-0.85²)) = 60.72 A

3. Use the power triangle to find the sending end line voltage:
S = √(P² + Q²) = 3600/(0.85) = 4235.29 kVA
E1 = S/I1 = 4235.29/60.72 = 69.74 kV

4. Use the power equations to determine the receiving end line voltage:
P2 = E1*E2*sin(z+d)/Z - (E2/Z)^2*R
Q2 = E1*E2*cos(z+d)/Z - (E2/Z)^2*X

We can rearrange these equations to solve for E2 and d. Once we have these values, we can plug them into the equations to find the receiving end line voltage. I hope this helps. Let me know if you have any further questions.