# EERM #53



## Rei (Mar 27, 2010)

A section of a wye-connected 3-phase transmission line has a phase voltage rating of 15kV and a power rating of 30kVA. The per-phase line impedance is 75 ohm. What is the per-unit impedance?

solution: Zbase=(15k)^2/30kVA

Does the question imply that 30kVA is the phase load or you just always don't need to divide it by 3 to get the phase value? The way I read this question is 30kVA load is the 3-phase load.


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## Flyer_PE (Mar 27, 2010)

Unless it is spelled out otherwise, when given a power rating for a three phase system, it's the three phase value.


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## Rei (Mar 29, 2010)

Flyer_PE said:


> Unless it is spelled out otherwise, when given a power rating for a three phase system, it's the three phase value.


Then is it not right that he Zbase used the 3-phase power and not divided by 3? I think we had this similar question in the NCEES sample exam.


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## Flyer_PE (Mar 29, 2010)

No. You don't divide by 3.

By definition: ZBase = VLine2/SBase. For a 3-phase system, S is the 3-phase apparent power.


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## Art (Mar 29, 2010)

or if you do use the per phase power 30/3 = 10, you better use the line (not phase-phase) voltage = V/sqrt3

so Zbase = (V/sqrt3)^2 / 10 = (V^2 / 3) / 10 = V^2 / 30

same as V^2 / 30

can't mix phase to phase with phase to line


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## DK PE (Mar 30, 2010)

Art said:


> or if you do use the per phase power 30/3 = 10, you better use the line (not phase-phase) voltage = V/sqrt3
> so Zbase = (V/sqrt3)^2 / 10 = (V^2 / 3) / 10 = V^2 / 30
> 
> same as V^2 / 30
> ...


I still think the orginal poster had a valid point. I hope we all agree that

Zbase = (V L-L2)/S3phase or equivalently Zbase = (V L-n2)/Sbase 1ph

where S base 1phase is the per phase apparent power = S base 3phase /3

So the original poster stated *"phase" voltage, not line *voltage and since phase voltage is defined as line to neutral voltage (Hayt and Kemmerly, among others)(not line-line), then the solution to me appears to be Zbase = 15 kv2 / 10KVA

Art, I think I'm confused with your terminology above... did you mean to state ..you better use the phase (line to neutral) voltage, rather than the line (line-line) voltage?

I would agree if the problem statement stated line voltage, the solution is (15)kv2/30


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## Art (Mar 30, 2010)

DK PE said:


> Art said:
> 
> 
> > or if you do use the per phase power 30/3 = 10, you better use the line (not phase-phase) voltage = V/sqrt3
> ...



I call phase-phase the phase V, and phase to n, the line voltage

I was just pointing out you could work the problem on a 3 phase basis or a single line equivilent...

Zbase = V3^2/S3 = VL^2/S = 15kv ^2 / 30 = (15kv/sqrt 3)^2 / 30/3 (3's cancel so = 15kv^2 / 30, the same)

where S = S3/3 and VL = V3/(sqrt 3)


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## DK PE (Mar 31, 2010)

Art, I'm in agreement with your math but used to using the term "line voltage" to refer to the line-line voltage and "phase voltage" to refer to the line-neutral voltage. I thought that was a the standard convention terminology with VL = sqrt(3) Vp. Thanks for your explanation.


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## Jonneyo (Apr 2, 2010)

So to complete this problem, I get:

Zpu = Zactual / Zbase = 75/7500 = .01

Is that correct?

Then, for all three phases, what is the total Zpu and Zactual? Are Zpu and Zactual multiplied by 3?


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## DK PE (Apr 3, 2010)

I still believe that the problem is either mis-stated, or deliberately trying to get you to recognize that:

they provided a phase voltage = line to neutral voltage and to use this formula you need line voltage.

Zbase = V line2 / S base 3 phase

And since they didn't state phase-phase voltage I assume they are providing line-neutral voltage, in fact my EERM states "The line-to-neutral voltages are usually referred to as the phase voltages"

Zbase = (15kv *sqrt(3))^2 / 30kVA = 22500

And you don't have to worry about all three phases... it works out in the end if you work everything three phase.

If the solution in EERM is as you have posted above I believe it is wrong and would challenge it...


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