Transmission Line Voltage drop/rise equation
Transmission Line Voltage drop/rise equation
(OP)
Hello All,
I am having trouble rectifying an equation for voltage drop....
IEEE Red book states that voltage drop on a line can be calculated as
Vdrop = IRcos(phi) + IXsin(phi)
where R, X are the line impedance and phi represents the load angle. I is a magnitude.
I am using the short TLine model where
Vsending = Vreceiving + I(R+jX)
and it seems that I(R+jX) should be approximately equal to the Vdrop as suggested by the RedBook. However, I seem to notice quite a bit of difference between the two, especially as line reactance goes up.
Mathematically it makes sense that they are not equal as
I(R+jX) = IRcos(phi) + IXsin(phi) + j(IXcos(phi) - IRsin(phi)) where the vector I = Icos(phi) +jIsin(phi)
and it seems that IEEE is just taking the real portion of the result for their Voltage drop.
My Question is, when does the IEEE version stop being applicable and you are forced to use the Short Line Model? Or should you ever use the IEEE model? Or have I missed something and am merely having a "doh!" moment?
I am having trouble rectifying an equation for voltage drop....
IEEE Red book states that voltage drop on a line can be calculated as
Vdrop = IRcos(phi) + IXsin(phi)
where R, X are the line impedance and phi represents the load angle. I is a magnitude.
I am using the short TLine model where
Vsending = Vreceiving + I(R+jX)
and it seems that I(R+jX) should be approximately equal to the Vdrop as suggested by the RedBook. However, I seem to notice quite a bit of difference between the two, especially as line reactance goes up.
Mathematically it makes sense that they are not equal as
I(R+jX) = IRcos(phi) + IXsin(phi) + j(IXcos(phi) - IRsin(phi)) where the vector I = Icos(phi) +jIsin(phi)
and it seems that IEEE is just taking the real portion of the result for their Voltage drop.
My Question is, when does the IEEE version stop being applicable and you are forced to use the Short Line Model? Or should you ever use the IEEE model? Or have I missed something and am merely having a "doh!" moment?






RE: Transmission Line Voltage drop/rise equation
This is the same as saying tha voltage drop equals I*Z. This is a bad assumption.
I don't know if the attachment helps. I have a diagram that goes with it but I can't locate it. I believe it is also in the Red Book.
RE: Transmission Line Voltage drop/rise equation
If your power factor is not 1; you would then need to use Vdrop = IRcos(phi) + IXsin(phi) to account for the difference in power factor.
phi = arcos(pf).
To answer your question, the IEEE version stops being applicable whenever the power factor at hand is not 1. Some tables have already done the calculation for you and tell you what the effective Z, or R and X are for a given power factor. See table 9 of NEC for an example of this; this table can be found on CH9 at the end of the code book.
RE: Transmission Line Voltage drop/rise equation
RE: Transmission Line Voltage drop/rise equation
RE: Transmission Line Voltage drop/rise equation
RE: Transmission Line Voltage drop/rise equation
I kept working on the problem this afternoon and came up with the following......
My new assumption is this (or my new understanding of what IEEE assumption of Vdrop approximation is)....
IEEE is calling voltage drop something similar to Voltage Regulation....
(|Vs| - |Vr|) / |Vr|
and it seems to work pretty decently as long as you have a lagging PF and your X/R ratio is small.
I ran thru some examples and it seems to fall apart rather quickly once your PF is leading and the X/R > 2
The attached sheet is what I have been using to help me understand... (if you can decipher my terrible formatting)
I am really just trying to make the IEEE model fit and recognize when their model is no longer sufficient.
RE: Transmission Line Voltage drop/rise equation
RE: Transmission Line Voltage drop/rise equation
Also note the Error on the diagram. This is the difference between the magnitude of Es and the real part of Es. The error gets larger as the phi approaches zero, or as X increases.
RE: Transmission Line Voltage drop/rise equation
The main problem may be that I am trying to use the equation outside of it's application as my lines are getting to be more than a mile long.
Thanks to everyone for their help.
RE: Transmission Line Voltage drop/rise equation
I believe the diagram does show the error increasing with X. If X is extended, Es will be longer and higher making the difference between its magnitude and real part greater.
Why is your pf leading? Both phasor diagrams show Ir lagging Vr or Er. If you want to look at leading pf, I would suggest redrawing the diagrams.
RE: Transmission Line Voltage drop/rise equation
I am really just trying to relate the Short Tline model (the top part of the sheet) with the IEEE equations (the bottom part of the sheet) for purposes of equivalency. It threw me for a loop when IEEE's exact equation did not match up with what I was seeing using the short Tline model.
Here is an updated version that has the exact IEEE calc included (as well as Magoo2's equation from the document he supplied). You can edit the highlighted cells to change the line variables. I put in a UG and an OH sample line for fun too.
RE: Transmission Line Voltage drop/rise equation
After playing some with your last spreadsheet, I believe the "exact" IEEE formula is not all that exact. I agree with your |Vs|-|Vr| column.
RE: Transmission Line Voltage drop/rise equation
RE: Transmission Line Voltage drop/rise equation
acos(pf) does not always = theta where pf =cos(theta).
Negative theta yields a positive acos. For some reason my results worsen when I substituted a signed angle, though.
The second term under the radical in your "exact" formula should be squared. Again the correction makes it further off.
Using Magoo2's formula for Er and then using the result in the next formula below makes no sense. Er (Vr) is a given in your question.
RE: Transmission Line Voltage drop/rise equation
Thanks for the tip on the calculation errors, I was bound to miss something with all that activity.
I had magoo's equation using the calculated voltage from the tline model and then back calculating, figured that it should work in reverse any way. The magnitude of that calculation should definitely be correct.
RE: Transmission Line Voltage drop/rise equation
Your latest spreadsheet has ABCD values that no longer short line. Now all bets are off, since IEEE only applies to short lines. Your Pi model will have an Is that differs from Ir.
I take back what I said earlier about the angles. IEEE's definition of phi indicates that acos(pf) is correct, and this is also consistent with the diagram.
RE: Transmission Line Voltage drop/rise equation
You can mix in Magoo's equation, because it references the angle of the sending end that mine calculates and performs the calculation in reverse. His result is very close to what IEEE is getting in all the samples that I have run. Now that I do not need it for a sanity check anymore, I will probably delete it as the IEEE form makes more sense to me.
Thanks again for the input.
RE: Transmission Line Voltage drop/rise equation
Where can I find the soft copy?
RE: Transmission Line Voltage drop/rise equation
RE: Transmission Line Voltage drop/rise equation
I'll definitely be getting myself a copy.