# Graffeo Ex. 18 Per Unit



## MyBeardAndMe (Mar 5, 2015)

On Example 18 of Graffeo, how is the transformer base old value selected for the new per unit impedance conversion? For both transformers, the old base is 28kV. Both transformers are 28kV delta - 115kV wye. Why 28kV instead of 115kV?

Pg 36 &amp; 37 for anyone who has the Graffeo book.


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## dayrongarcia (Mar 5, 2015)

To find the base voltage for zone 3, he used the equation:

Vb3 = Vs2/Vp2 = 28kV/115kV x Vb2

Now, he could have used 135.54kV for Vb2 which is the Vbase obtained in zone 2, but he decided to replaced Vb2 with Vs1/Vp1 X Vb1, and thats probably why you are getting confused.

Does it make sense?


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## dayrongarcia (Mar 5, 2015)

dayrongarcia said:


> To find the base voltage for zone 3, he used the equation:
> 
> Vb3 = Vs2/Vp2 = 28kV/115kV x Vb2
> 
> ...




Vb3 = Vs2/Vp2 x Vb2

Vs2 = secondary of 2nd transformer (28kV)

Vp2 = primary of 2nd transformer (115kV)

Vb2 = new base of zone (135.54kV)


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## KatyLied P.E. (Mar 6, 2015)

I'll need to dig my notes out. However, if you're still unsure Graffeo is very good about responding to emails.


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## jgharris P.E. (Mar 6, 2015)

I believe I did this same problem and had the same confusion about 2 weeks ago. I believe I got the right answer though even though I used the 115kV base for the second transformer. I am at work and like I said it has been awhile but I do remember stopping and trying to understand why he did what he did there.


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## MyBeardAndMe (Mar 6, 2015)

Ohhh, it's because it is related to the base of the zone. Zone 3 has a base of 33kV, so the old base value would have to be on the 28kV side of the transformer. If the new base value was based on Zone 2, or 135.54kV, he would have to use 115kV for the old base.


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## StinkyTofu (Sep 22, 2015)

We only changed the base of each zone because it was specified in the problem correct? What is the advantage of doing this? Would it not be easier to simply use the transformer ratings as base values? For example, using T1 values as base, we would get, for the generator: x_pu = 0.14*(105/100)*(33/28)^2 = 0.204 = 20.4%, and V_generator, pu = 33/28 = 1.18?


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## bripgilb (Feb 5, 2018)

I’ve got a question about this example. I think I may be using a revised edition, since this post is a few years old now. 

But, my question is in regards to the base impedance that is calculated for zone 1&amp;3. 

The equation states 

Zbase=0.18(vbase^2/sbase3p) 

But, wouldn’t zone 1 be 0.14?




View attachment 10784


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## supra33202 (Feb 6, 2018)

Sorry to hi-jack your question.

I also have other questions now.

1) For transformer#2 new pu impedance ZT2, should the Vbase-old be "115KV" instead of "28KV"? So the equation should be ZT2= 0.09 (100MVA/105MVA)(115KV/28KV)^2.

2) The Zbase for the transmission line. Zbase=0.18(vbase^2/sbase3p) = (28 kV^2)/(100MVA). The equation doesn't make sense. Where did the "0.18" go?

2a) How do we get "0.18"? 2 * 0.09 = 0.18?

Thanks!


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## bripgilb (Feb 6, 2018)

No problem @supra33202!  Let's see if we can make each other figure this stuff out. haha

OK.... So...

1.)  When working with Transformer#2 you will be finding Zt2 in regards to the "Zone 3"  That stated you will be using the Secondary Voltage of T2 for Vbase-old. 

Can you back check me on that?  http://www.electricalpereview.com/per-unit-example-tips-tricks-watch-electrical-pe-exam/  &lt;&lt;&lt; This is my reference for why I said this.

2.) I think the "0.18" is a typo.  I do not think Zline will require a % reactance.  See Example 17.

Also back check me on that!  My reference is the link i posed and Graffeo Example 17.

Let me know what you think about my question.

Thanks,

Brip


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## supra33202 (Feb 7, 2018)

bripgilb said:


> No problem @supra33202!  Let's see if we can make each other figure this stuff out. haha
> 
> OK.... So...
> 
> ...


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## supra33202 (Feb 7, 2018)




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## bripgilb (Feb 7, 2018)

@supra33202 Thanks for the screen shot!  Good support for using Vsecondary for Zt2.

What were your contemplations on the % reactance for Zbase for the Transmission Line in Zone 1?

Do you think
 

- Zbase1 = 0.14(28kV^2/100MVA)  &amp; Zbase3=0.18(28kV^2/100MVA)  or are they equal?


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## bobbilly (Feb 10, 2018)

@supra33202@bripgilb Not sure what edition book you have, mine says October 2017 printing. But the % reactance isnt even part of the equation to find the base impedance so I am not quite sure as to why he shows it, this book is full of errors. Finding Zbase1,3 isnt even necessary for the impedance diagram. 

I dont know if you have this example or not but it shows how the Zpu is found for the Transmission line, pg 38, 39 

https://imgur.com/a/ed3W8


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## bripgilb (Feb 10, 2018)

@bobbilly  Thank you for jumping in here!

So looking at your example and then looking at the solution again.  You're right.  There were lots of white outs on this example.  I don't have the Example you posted in my book. (July 2016 Printing).

But, I do see that I don't have to do anything with %impedance for Zbase1,3.  So thanks!

Brip


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## Zach Stone P.E. (Feb 13, 2018)

supra33202 said:


> View attachment 10789


http://www.electricalpereview.com/per-unit-example-tips-tricks-watch-electrical-pe-exam/

Thanks for posting the article. 

I'm Author that published it, if you have any questions I'd be happy to answer you.


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