Per Unit calculation problem

[lyrath]

I have a problem when I did Per-Unit calculation. Under the same condition, I got two different P.U. results for the load current by using two methods, which doesn't make sense to me.

Condition: Terminal voltage is 10 kV, load power is 100 MVA, solidly ground Y system

Method 1: Let base voltage is 10kV and Base complex power is 100 MVA,
then Base line current is 100/(sqrt3*10) = 5.77 kA
in this case, the p.u. load current magnitude is 1 p.u

Method 2: By setting the same base voltage and base MVA as in Method 1,
load current magnitude p.u = complex power_p.u./(sqrt3 * line voltage_p.u.) = 1/(sqrt3 * 1) = 1/ (sqrt3) p.u.

My expertise is telling me Method 1 is right, but I just can't figure out what is wrong with Method 2.

 

[7anoter4]

If we shall translate the Method 2 in usual symbols it seems to me this could be :
Ipu=Spu/sqrt(3)/Upu
By definition Spu=S/Sbase; Upu=U/Ubase. Then:
Ipu=S/Sbase/sqrt(3)/[U/Ubase]=[S/U/sqrt(3)]/[Sbase/Ubase]
Actually Ipu=Iactual/Ibase
Iactual=S/U/sqrt(3) indeed, but Ibase=Sbase/Ubase/sqrt(3) [it is not only Sbase/Ubase].
So, as you can see Method 2 gets not Ipu [load current magnitude p.u]. Actually, in your case is Ipu= 1 as in Method 1.

 

[waross]

Method 2: By setting the same base voltage and base MVA as in Method 1,
load current magnitude p.u = complex power_p.u./(sqrt3 * line voltage_p.u.) = 1/(sqrt3 * 1) = 1/ (sqrt3) p.u.
As I read your formula:
Complex power_p.u = 1
line voltage_p.u. = 1
You have gone to a lot of work to calculate the reciprocal of √3.
Compare:
100000000(complex power)/(sqrt3* 10 (line voltage)) Method 1
complex power_p.u./(sqrt3 * line voltage_p.u.) Method 2
Complex power/line voltage = 100,000,000/10 = 10,000,000
You have used the same formula but you have used p.u. values when it is inappropriate.
I expect your answer to be off by a ratio of 10,000.

What would be appropriate is if you use the p.u. values to calculate a change in one or more values.
As in:
Let
100 MVA = p.u.1
10,000 V = p.u.1
5.77 kA = p.u.1
When MVA increases 10%. What is the resulting kA?
or
The current drops to 5.5 kA. What is the resulting MVA

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[lyrath]

Right, that is where I got confused. I am using the same formula separately in per unit domain and actual domain but they gave me different answers.

Method 1: calculate actual current first and convert it to per unit
Method 2: calculate per unit power and voltage first, then directly calculate the current in per unit domain

They shall agree to each other in terms of per unit current, but they don't.

 

[waross]

p.u.current = 1_p.u.
actual current = 5.77 kA


Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[xnuke]

Method 1 is correct. In Method 2, you should not be dividing by the square root of 3, just divide the per unit power by the per unit voltage to find per unit curretn. Once both power and voltage variables are in per unit, there is no need to include the square root of 3. The square root of 3 only needs to be reapplied if you convert back to actual value of S.

xnuke
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