Per Unit Values from a short circuit example

[Grouch]

Gents,
I attached a one-line diagram that I'm looking at. It's from GE's white paper on short circuit calculations.

The 2nd attachment shows how they derive the per unit X and R values at each piece of equipment (transformers, motors, the cables, and the utility). The base power value throughout is 15000 kVA.

My questions are how they derived the X and R values where I highlighted in blue in the 2nd attachment.

For the utility (top blue rectangle): the equation to solve for the per unit impedance (Z)... shouldn't it be actual power / base power? The equation that they are using seems to be base power / actual power. The utility power is 1500 MVA. Base power as I mentioned above is 15000 KVA.

For Motor M1 (the bottom blue rectangle): what equation are they using to solve for the motor impedance X? The equation includes an X"d of 15% (sub-transient reactance) and a horsepower of 4000. I'm not familiar with the equation though. What equation is this?

Thanks!

 

[D. Castor]

The utility X/R is a given or an assumption. The motor X calculation is putting the X value in per unit. X/R is given in the one-line. I think they are using the hp to approximate the kVA by the 0.8 in the divisor.

 

[Elect117]

For the motor, they are getting current from horse power and then using the subtransient reactance% of 15/100.

For motors, to covert it to per unit, it is :

M_PU = (HP / S_base) * PF

They probably substituted that in.


X = X"_d * (1 / M_pu )

X = X"_d * ( S_base / (HP * PF) )

 

[Elect117]

I think they chose the base as 15,000 but I couldn't tell you why. You can try to calculate it with your own base and see if you get the same results.

 

[Grouch]

X = X"_d * (1 / M_pu )

X = X"_d * ( S_base / (HP * PF) )

Thanks for the equation. Sorry for my delayed response.

Regarding my question on the utility calculation, here is a similar example, see the attached image.

They are calculating per unit power as (base power / actual power). Isn't this backwards though? Shouldn't it be actual power / base power? Any time you calculate a per unit value, you divide by the base value. To me, Xpu = 500,000 / 10,000.

 

[dkarst]

Maybe this will make sense, maybe not but when you calculate your actual power/base power you get PU power, not impedance. You stated "they are calculating per unit power as (base power / actual power)" when they are actually calculating PU reactance or impedance.

If you think of the original utility in this example and it is a powerful utility with a capability of supplying 1500 MVA... compare it to a weak utility capable of supplying only 15MVA. The IMPEDANCE of the more powerful utility would be less to enable the larger power flow. Hope it helps.

 

[Grouch]

Maybe this will make sense, maybe not but when you calculate your actual power/base power you get PU power, not impedance. You stated "they are calculating per unit power as (base power / actual power)" when they are actually calculating PU reactance or impedance.

Thanks! I follow. I had it all backwards. It makes sense now... I was thinking of power instead of impedance. So I had the wrong value in my mind together with the wrong equation.