# Calculating the real and reactive power of a transmission line

I have a single machine connected to an infinite bus with the following parameters:

• Sending end power = 3.75MW
• RL=5.18 ohms
• XL=130 ohms
• VS (Generator bus)=161kV
• VR (Infinite bus)=161kV
• Sending end voltage angle (delta) = 0.01877 (Angle which allows 3.75MW to be transferred)

Using these I want to calculate the amount of reactive power sent by the sending end as well.

I calculated it first without factoring in the line resistance (RL=0) Then got the result for Q as : 35.24kVAR

Next I calculated it with the line resistance factored in Then got the result for Q as: -114.77kVAR

When the line resistance is factored in, the answers for reactive power vary immensely. And when the resistance is factored in, the sign of Q is negative indicating the generator bus is absorbing VARS which doesn't seem to make sense.

Why are they so different? What am I doing wrong?

The equations I used are here

I derived these equations using Matlab to do the algebra, so it hopefully should be correct :)

• perhaps your assumptions are wrong. You must conjugate match the impedance by phase shift but also add voltage for line R loss. try adding V²/W voltage to Vs and adjust phase lead to 0.538 degrees (using power per phase not total) – Tony Stewart Sunnyskyguy EE75 Jun 22 '17 at 2:49
• Thanks for the response Tony. I didn't get what you meant by "conjugate match the impedance by phase shift"? and how did you calculate 0.538rads and why do i need to adjust it by this much? – CKCK Jun 22 '17 at 3:46
• www.ece.rutgers.edu/~orfanidi/ewa/ch13.pdf I said degrees – Tony Stewart Sunnyskyguy EE75 Jun 22 '17 at 3:52
• Apologies i misread. Ill have a look at that link. Thanks – CKCK Jun 22 '17 at 4:01
• did u not understand the voltage loss part? Conjugates use easy vector match with opposite reactance which is your phase with R +jX – Tony Stewart Sunnyskyguy EE75 Jun 22 '17 at 4:05