Per Unit Analysis Confusion

[Xtrem]

I have this problem I'm trying to figure out, doing the problem normally versus using per unit gives me different answers!

So I have a three-phase motor that is rated for 20MVA at 13.8kV and it is connected to a bus at 1<0 degrees pu. The system base Sb=100MVA and Vb=13.8kV.

To find the PU current:

I = S / (sqrt(3)*V) = (20MVA/100MVA) / (sqrt(3)*(13.8kV/13.8kV)) = 0.1155 pu

Another way of doing it is to find the actual current:

I = S / (sqrt(3)*V) = 20MVA /(sqrt(3)*13.8kV) = 836.739 A
The base current = S / (sqrt(3)*V) = 100MVA / (sqrt(3)*13.8kV) = 4183.7 A
The PU current using this approach is 0.2 pu

Comparing the two answers (0.1155 pu) and (0.2 pu, there is a factor of sqrt(3) somewhere...

Can anyone tell me which is right and why the two different approaches yield different answers? Was my assumptions wrong?

Thank you

 

[johndaniel]

your first answer is correct 0.1155 pu. In second problem while calculating the base current is simply base Mva/base voltage. you dont have to divide this factor with sqrt(3).

 

[Xtrem]

Why is that so? Isn't the standard formula for base current in a three phase system Ib=Sb/(sqrt(3)*Vb)?

 

[johndaniel]

No base current is directly base MVa/ base voltage.

 

[dpc]

Johndaniel: For a three-phase system, the root 3 is used to compute base current from base MVA and base V.

http://en.wikipedia.org/wiki/Per-unit_system

 

[Xtrem]

Thank you, I crosschecked many books as well. So, what seems to be the solution to this conundrum?

 

[dpc]

Calculate the base current. Then calculate the motor full load amps. Then calculate the per unit current from the those two quantities. You'll figure out if you keep it simple.

 

[Xtrem]

I have done that in the second part of my first post, it does not match the first approach!

 

[johndaniel]

I made few mistakes in my last post. So you should have calculated this thing as follows:

I base= Sbase/(sqrt3* Vbase)

So your second solution is correct.

your first solution I = S / (sqrt(3)*V) = (20MVA/100MVA) / (sqrt(3)*(13.8kV/13.8kV)) = 0.1155 pu is wrong as it involves direct conversion of values in per unit. Hence, you left the factor of sqrt3.
you should apply following rule to solve P.U problms: For given Sbase and Vbase find Ibase as Sbase/(sqrt3* Vbase)
and from main circuit find current I.
Therefore, I(p.u) is I/Ibase.

Hope this helps

 

[Xtrem]

"it involves direct conversion of values in per unit"

Can you explain a bit what you mean here? Maybe in terms of my problem?

 

[odlanor]

in 3-phase balanced system Ipu= Iline-to-line.
in symmetrical components Ipu=Iline-to-neutral= Iline-to-line/V3

 

[jghrist]

The simple solution is to recognize that if the rated voltage of the motor equals the base voltage, then the Ipu = Spu. Spu = 20/100 =0.2