Solve AC Circuit Analysis: Calculate Current, Real & Reactive Power

[bd411]

Homework Statement

Two nodes in a network are connected by a line with an impedance of 0.5 + 1.2j Ω. The voltage at the sending end is 33KV and at the receiving end is 32.5 KV with a lag of 1.5° compared to the sending end..

Calculate the current in the line and the real and reactive power consumed by the line itself.

Homework Equations

Standard AC circuit analysis equations.

The Attempt at a Solution

I think I've got this just want to make sure that I'm not doing anything silly with the angles etc:

I_SR = V_S - V_R / 0.5 + j1.2 = (33) - (32.5 ∠ -1.5°) / 0.5 + j1.2

= 763.45 ∠ -8.38°

Real Power consumed = I²*Re(Z) = (763.45)^2 * 1/2 = 291.5 KW
Reactive = I²Im(Z) = (763.45)^2 * 1.2 = 700KVAr

Have I done anything silly? I feel to ask because it seems unusual to me that the reactive power is larger than the real power consumed by the line.

Many thanks !

 

[gneill]

Looks okay.

 

[bd411]

Great, thanks a lot !