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Per Unit Analysis Confusion

Per Unit Analysis Confusion

Per Unit Analysis Confusion

(OP)
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

RE: Per Unit Analysis Confusion

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).

RE: Per Unit Analysis Confusion

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

RE: Per Unit Analysis Confusion

No base current is directly base MVa/ base voltage.

RE: Per Unit Analysis Confusion

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

RE: Per Unit Analysis Confusion

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.

RE: Per Unit Analysis Confusion

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

RE: Per Unit Analysis Confusion

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 :)

RE: Per Unit Analysis Confusion

(OP)
"it involves direct conversion of values in per unit"

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

RE: Per Unit Analysis Confusion

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

RE: Per Unit Analysis Confusion

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

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