# NCEES Power #107



## mike123 (Mar 17, 2009)

The solution in the book is given as pu impedance = Zline/Zbase where Zbase = kVbase/kVAbase.

With Zline given as 50 ohms per phase. Is it not incorrect to determine pu impedance using Zline per phase against Zbase established from 3-phase kV and kVA as the solution seem to suggest. Shouldn't Zbase be established based on per phase value by dividing kV and kVA by srt3?


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## geofs_PE (Mar 17, 2009)

The problem statement specifically says to use the line-rated values for the base. Doing so, using the formula Z(pu)=Z(line)*V(base)^2/KVA(base) gives the correct answer, (B). In practice, the values chosen as the base values are arbitrary but are usually chosen so as to simplify the math. In this case, for a calculation involving the line voltage, one would use V(line)/V(base) = 1, same for S, the rated MVA.


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## mike123 (Mar 17, 2009)

Sorry for missing the ^2 on the equation in original post.

What I am confused about is the Z(line) of 50 ohms per phase in the question. The pu impedance seem to be calculated by dividing a phase value of 50 ohms against a line-line value derived from kV^2/kVA.


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## mudpuppy (Mar 17, 2009)

mike123 said:


> The solution in the book is given as pu impedance = Zline/Zbase where Zbase = kVbase/kVAbase.
> With Zline given as 50 ohms per phase. Is it not incorrect to determine pu impedance using Zline per phase against Zbase established from 3-phase kV and kVA as the solution seem to suggest. Shouldn't Zbase be established based on per phase value by dividing kV and kVA by srt3?


Mike, you are on the right track. Zbase can be established on a per phase basis by dividing Vbase by sqrt(3) and the kVA base (Sbase) by three (not sqrt(3)--because each phase carries 1/3 of the power, not 1/sqrt(3) times the power). Then if you remember Z=V^2/S, you have:

Zbase = (Vbase/sqrt(3))^2/(Sbase/3) = (Vbase^2/3)/(Sbase/3) = Vbase^2/Sbase.


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## mike123 (Mar 20, 2009)

Thanks Mudpuppy.

Now it make perfect sense with the expanded equation for Zbase.


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