# autotransformers- NCEES #525 and #535



## ElecPwrPEOct11 (Oct 17, 2011)

Sorry for the NCEES blast, it has been a busy day.

Before taking the practice test I hadn't looked much at autotransformers. Now I'm trying to figure out these 2 problems and realize that my resources don't spend much time with autotransformer equations and have no examples.

I thought I understood #525 and the solution until I got to #535. The solution to 535 seems opposite what was done for 525. My understanding of 525 was that under a 'normal' transformer setup, the upper and lower coil both have the rating of 50kVA, as stated in the problem description. From this you can easily find the currents in each coil and then by KCL the current in the 2300V autotransformer leg. (of course the simple solution is Sauto = Srated * (a+1)). But the solution for 535 begins by saying both W1 and the I2 leg transfers 60MVA. I don't know why, is this somehow clear from the problem statement? These two problems seem to be the reciprocal of each other, but the solutions are very different. Can anyone help? Thanks a ton!


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## vdubEE (Oct 19, 2011)

ElecPwrPEOct11,

I understand your pain and confusion on this one. The first couple of times running through the NCEES practice exam, I never researched why the difference in the solution methods. Since test time is getting close, I am going back through the calculation-based problems adding notes and pointers on how each problem is solved to make sure I understand everything. That is when I started digging around through all my old college textbooks and found the figures that answer our question. The textbook is Electricmachines by Cathey.

In problem #525, the non-boosted voltage is on the left-side of the autotransformer and matches this figure.







In problem #535, the non-boosted voltage is on the right-side of the autotransformer and matches this figure.






Using the arrows from the figures, it is simple KCL as shown in the solution. Hopefully, this clarifies the issue you were seeing too!!


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## vdubEE (Oct 19, 2011)

I think this answers the part on how they say that each side of the autotransformer can transfer 60MVA in #535.


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## R2KBA (Oct 20, 2011)

This bugged me for a while. What is happening here is NCEES is trying to trick you on 535. 525 is a straightforward autoXFMR problem where a single transformer is connected as an autoXFMR. The voltages are given and you can simply solve either using the proportional equations or by using circuit analysis.

535 tries to trick you two ways: First, it is WYE connected. They did not show the actual voltage between the terminals as they did in 525 because they want you to figure out that you have to convert from the given VLL to VLN. Second, they state in the problem that there is a 3-phase autoXFMR that can transfer 180MVA, however only one phase has been shown, and they want your answer for only one phase. The trap would be to use the 180MVA which would be 3x too high since you are only dealing with 1 phase. Once you realize those two things, the problem is then the opposite of 525.

I have learned to pay close attention to problem statements involinve 1phase vs. 3 phase, grounded vs. ungrounded, delta vs wye connections, etc.


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## ElecPwrPEOct11 (Oct 20, 2011)

Thanks for the pics vdubEE. I realized I was drawing the current arrow in the lower coil in the wrong direction. This was throwing off my answers (esp in 525) as I was adding currents when I should have been subtracting, or vice versa.

What is really helping me conceptually think about autotransformers is Pout = Pin. (also an EQ you show above) So Vh * Ih = Vx * Ix. From this basic equation you can find the currents in the output and input. Then using KCL you can find the current in the lower leg. If you use any of the EQs shown above, you can always use Pout = Pin to check that your answers work and make sense. That was my breakthrough today.

And yes, you need to be very aware of issues with sqrt 3, total power vs phase power, etc. Thanks to both for your help.


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## EEVA PE (Oct 20, 2011)

R2KBA said:


> This bugged me for a while. What is happening here is NCEES is trying to trick you on 535. 525 is a straightforward autoXFMR problem where a single transformer is connected as an autoXFMR. The voltages are given and you can simply solve either using the proportional equations or by using circuit analysis.
> 
> 535 tries to trick you two ways: First, it is WYE connected. They did not show the actual voltage between the terminals as they did in 525 because they want you to figure out that you have to convert from the given VLL to VLN. Second, they state in the problem that there is a 3-phase autoXFMR that can transfer 180MVA, however only one phase has been shown, and they want your answer for only one phase. The trap would be to use the 180MVA which would be 3x too high since you are only dealing with 1 phase. Once you realize those two things, the problem is then the opposite of 525.
> 
> I have learned to pay close attention to problem statements involinve 1phase vs. 3 phase, grounded vs. ungrounded, delta vs wye connections, etc.



I understand to watch for 1phase vs 3 phase, and delta vs wye. But for grounded vs ungrounded, when does this become a factor in terms of calculating something? I know of the effects of grounding a transformer (both delta and wye) at its phases, but where else should we be watching out for ground or unground that may influence our calculations?


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## R2KBA (Oct 20, 2011)

I'm not exactly sure, but I just decided to look for it since NCEES mentioned it on that one problem.


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## ElecPwrPEOct11 (Oct 21, 2011)

I don't see how grounding an autotransformer would affect anything. Also you normally can't separately ground an autotransformer because it is does not provide electrical separation like a 3 phase transformer (not a "separately derived system" in NEC-speak).


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## snerts50 (Oct 22, 2011)

i think. i now have this down. it's all making sense. i found some good power systems lecture slides that helped a ton. what was posted here covers it but let me know if people want some screen shots from what i found


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## ElecPwrPEOct11 (Oct 23, 2011)

snerts50 said:


> i think. i now have this down. it's all making sense. i found some good power systems lecture slides that helped a ton. what was posted here covers it but let me know if people want some screen shots from what i found


If you've found some good resources I'm always keen to learn more. I think uploading is pretty easy. Thanks!


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## snerts50 (Oct 24, 2011)

ElecPwrPEOct11 said:


> snerts50 said:
> 
> 
> > i think. i now have this down. it's all making sense. i found some good power systems lecture slides that helped a ton. what was posted here covers it but let me know if people want some screen shots from what i found
> ...


I started here first, http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-061-introduction-to-electric-power-systems-spring-2011/index.htm

MIT has a great open course catalog. This is intro to power systems, there is also power electronics and electric machines in there as well.

I actaully apologize for not sharing this earlier.

There are lecture notes and homeworks/quizzes. This wont help with the NEC stuff but helps with everything else.


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## ElecPwrPEOct11 (Oct 24, 2011)

Wow, I didn't know about this resource at all. Very cool that it's all online. Thanks for the link, wish I had more time to read up.


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## kris7o2 (Jul 9, 2021)

Hi all,

Would there ever be a situation where we do not divide the voltages (138 kV, and 57.7 kV) by sqrt(3). I.e. is there ever a time that this would be a delta connection? Otherwise, do we always assume a wye connection for an autotransformer, and thus we should always divide the voltages by sqrt(3)?


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