# Change of Base



## kulalv (Oct 27, 2010)

All problems related to short ckt calcs in the NCEES book I used the P.U. method using this formula:

[SIZE=10pt]Znew,pu = Zold,pu*(Sb,new/Sb,old)[/SIZE]

(like NCEES #540, where I chose Sb=933MVA [T1], and needed to convert Zold=0.23 [G1] to a new)

When do we use the following, which i just found in one of my power books????

Znew,pu = Zold,pu*(Sb,new/Sb,old)[SIZE=10pt](Vbase,old/Vbase,new)^2[/SIZE]

Why don't I have to put in the (Vbase)^2 factor in my original calculations???


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## cableguy (Oct 27, 2010)

For example, when you are setting your base to the high side of a transformer (example, 138kV), and the transformer is a 138:13.8 transformer, but the generator on the low side of the transformer is a 9kV generator. To make the base of the generator match the base of the transformer, you'll have to include the voltages as in your formula when you calculate your generator Zpu.

You include the voltages when you have equipment at slightly different voltages. If it were a 13.8kV transformer and a 13.8kV generator, you don't need to include the voltage step.


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## kulalv (Oct 27, 2010)

Referring to NCEES #540

G1=22kV and T1 on secondary=230kV. Not sure why we don't need include the voltages, since the voltages don't match. I realize that in other cases Vbase,new = Vbase,old so obviously the factor is 1.

Too close to test time to be stressing!!


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## cableguy (Oct 27, 2010)

kulalv said:


> Referring to NCEES #540
> G1=22kV and T1 on secondary=230kV. Not sure why we don't need include the voltages, since the voltages don't match. I realize that in other cases Vbase,new = Vbase,old so obviously the factor is 1.
> 
> Too close to test time to be stressing!!


No, I'm talking about the situation where G1 is a 22kV generator, and T1 would be a 24kV low side, {whatever} high side. See how G1 (in my example) is 22, T1 is 24? That's the kind of mismatch I'm talking about.

I don't see any in the NCEES sample exam that need this, but there are numerous examples elsewhere (like Kaplan, Testmasters, I'm sure Camara had some in his stuff too).


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## nmh0408 (Oct 27, 2010)

kulalv said:


> All problems related to short ckt calcs in the NCEES book I used the P.U. method using this formula:
> [SIZE=10pt]Znew,pu = Zold,pu*(Sb,new/Sb,old)[/SIZE]
> 
> (like NCEES #540, where I chose Sb=933MVA [T1], and needed to convert Zold=0.23 [G1] to a new)
> ...


Znew,pu = Zold,pu*(Sb,new/Sb,old)(Vbase,old/Vbase,new)^2------When Sbase changes

Why don't I have to put in the (Vbase)^2 factor in my original calculations??--------When Sbase and V base change


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## Flyer_PE (Oct 27, 2010)

Another way to look at it is that the equation for converting an impedance from one base to another is always:

Zpu-new=Zpu-old*(SBase-new/SBase-old)*(Vbase-old/Vbase-new)2

When either the MVA or voltage bases don't change, the applicable term winds up being "1".


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## vinnius (Oct 28, 2010)

Flyer_PE said:


> Another way to look at it is that the equation for converting an impedance from one base to another is always:
> Zpu-new=Zpu-old*(SBase-new/SBase-old)*(Vbase-old/Vbase-new)2
> 
> When either the MVA or voltage bases don't change, the applicable term winds up being "1".



i think its only because when you reference impedance, S covers the Vbase as well since S = VI. Bases are always arbitrary. one could use 1MVA or another use 1kVA, but it reflects the changes accomodated for Vbase as well. if the question called for base of whatever, then you'd probably need to pay attention to the Vbase and I base and apply this equation FlyerPE used. If it only asks for the actual, then as long as you keep your equations straight and not change bases midway, you'll arrive at the same answer. Gotta love per units!


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