NCEES 2009 Power question 525

Question:

A single-phase transformer rated 50kVA, 2,300/120V is connected as an autotransformer as shown in the figure to boost the voltage of a 2,300V bus. What is the kVA rating of the autotransformer?

Any suggestions?

Bluekayak said:

Question:
A single-phase transformer rated 50kVA, 2,300/120V is connected as an autotransformer as shown in the figure to boost the voltage of a 2,300V bus. What is the kVA rating of the autotransformer?

Any suggestions?

Click to expand...

Here's the figure

Can you specify the trouble you're having with this one?

Flyer_PE said:

Can you specify the trouble you're having with this one?

Click to expand...

Not sure where to begin. The polarity dots in the solution look arbitrary:

VA=2300(21.74+416.7)=1008kVA

Please advise if you have a strategy for solving this one and more importantly for rationalizing these types of problems (e.g., autotransformer, transformer polarity schemes).

Bluekayak said:

Question:
A single-phase transformer rated 50kVA, 2,300/120V is connected as an autotransformer as shown in the figure to boost the voltage of a 2,300V bus. What is the kVA rating of the autotransformer?

Any suggestions?

Click to expand...

I figured it out; much easier than I thought. In fact this is a very basic problem.

Glad to hear it. It is one that I was having a hard time figuring out how to describe the solution to. I was going to just hand-write it out and scan it.

Flyer_PE said:

Glad to hear it. It is one that I was having a hard time figuring out how to describe the solution to. I was going to just hand-write it out and scan it.

Click to expand...

Switching to transmission line problems. What exactly is the difference between NCEES sample problems 132 (L-N voltage, 60kV/sqrt(3)) and 513 (L-L voltage, 12kV). Is it the transformer in 513, in contrast to #132 where there is no voltage transformation between stations?

The only real difference between the two is that you have to properly account for the transformer impedance in problem 513.

For problem 132 NCEES, why is the phase to ground voltage used for the system voltage for the 3 phase transmission system? I would of thought the line voltage is used when calculating the 3 phase fault current.

The standard practice is to do the math on a phase voltage basis. The same result can be determined using line voltage but you wind up adjusting the current by a factor of sqrt(3) rather than the voltage. It still works out the same but the math isn't nearly as simple.

Finally for problem 540, my solution seemed extremely fundamental:

T1Zpu,new=0.15(834/933)=0.134

Ssc,pu=VpuxIpu=1x(1/Zpu)=1x(1/(0.23+0.134))=2.75pu

Ssc,actual=Ssc,puxSsc,base=2.75x834=2291MVA

Do you agree with my methodology?

It seems as if all of the sample problems involve fundamental concepts, not real in-depth theory. The crux is indentifying the fundamental concept(s) upon which the problem is based.

Bluekayak said:

Finally for problem 540, my solution seemed extremely fundamental:
T1Zpu,new=0.15(834/933)=0.134

Ssc,pu=VpuxIpu=1x(1/Zpu)=1x(1/(0.23+0.134))=2.75pu

Ssc,actual=Ssc,puxSsc,base=2.75x834=2291MVA

Do you agree with my methodology?

Click to expand...

Yes. It appears to match that used in the NCEES solution. You'll also find that it works out regardless of what base MVA value you choose.

Bluekayak said:

It seems as if all of the sample problems involve fundamental concepts, not real in-depth theory. The crux is indentifying the fundamental concept(s) upon which the problem is based.

Click to expand...

To me, that is the key to passing the exam. You have to identify which fundamental concept or concepts are in play very quickly.