# Per Unit Impedance



## Gnana (Sep 9, 2010)

Power system analysis by grainger provides the formula (1.55)

P.U Impedance =[ (actual impedance, ohm) x (base KVA)] / [(base voltage, Kv)^2 * 1000]

If you do a derivation for PU Impdance = Zactual/Zbase where Zbase = (Vbase, KV)^2/ (Sbase, KVA) you get thesame result as shown above without the 1000 in the denominator.

Not sure if this makes sense but it helps if you write it out and take a look.

Will be glad if anyone can clarify the confusion.

Thanks


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## DK PE (Sep 10, 2010)

Gnana said:


> Power system analysis by grainger provides the formula (1.55)P.U Impedance =[ (actual impedance, ohm) x (base KVA)] / [(base voltage, Kv)^2 * 1000]
> 
> If you do a derivation for PU Impdance = Zactual/Zbase where Zbase = (Vbase, KV)^2/ (Sbase, KVA) you get thesame result as shown above without the 1000 in the denominator.
> 
> ...


If you take Pu Z = Zactual/Zbase as you did and then substitute equation 1.53 for Zbase you get equation 1.55. You just end up inverting equation 1.53 and multiplying by actual Z.

I think you slipped a bit as Zbase Not equal (Vbase, KV)^2/ (Sbase, KVA) IT SHOULD BE equation 1.54 Zbase = (Vbase, KV)^2/ (Sbase, MVA) which is where you lost a couple 000's.


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## Gnana (Sep 10, 2010)

I see what you are saying.

I was working some sample problems and i used the the grainger formula but my answers did not match any of the proposed answers. When i looked at the solution in the book, the answer used Zbase equal (Vbase, KV)^2/ (Sbase, KVA). Not sure why they did that. That's why i was trying to get a clarification to see which one is correct.


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## DK PE (Sep 10, 2010)

Gnana said:


> I see what you are saying. I was working some sample problems and i used the the grainger formula but my answers did not match any of the proposed answers. When i looked at the solution in the book, the answer used Zbase equal (Vbase, KV)^2/ (Sbase, KVA). Not sure why they did that. That's why i was trying to get a clarification to see which one is correct.


Remember there are a few sample problems floating around that have an error in their solution. Feel free to post the sample if you want and someone will likely stop by to help.


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