# Can this problem be solved with our reference handbook?



## Sparky Bill PE (Nov 8, 2020)

I have solved problems like this many times using Zach Stone's wonderful notes. I am going with the strategy that if it isn't in the book, and I don't know off memory. I haven't been solving problems (except protection because I think a large protection section will be added before the test SURELY).


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## speakeelsy PE (Nov 8, 2020)

Yup. Top of page 60 in the handbook - you'll have to rearrange the formulas a little bit.


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## Sparky Bill PE (Nov 8, 2020)

speakeelsy said:


> Yup. Top of page 60 in the handbook - you'll have to rearrange the formulas a little bit.


And that's why I asked, I seen that, but it was under "single phase xfmrs in parrallel" with all these stipulations. I guess those 5 stipulations and this formula aren't together? I didn't now if I assume they meet these conditions, or if these 2 things are unrelated to each other.


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## akyip (Nov 8, 2020)

I'm lucky enough to be able to more or less remember Zach Stone's method for limiting transformers (or generators) for 2 parallel transformers (or generators) after so much repetitive practice of such questions drilling them into my head.

I'm trying to remember stuff off the top of my head from repetitive practices of practice exam questions, since the NCEES reference handbook IMO is sorely lacking.

S1 = S1 rated x (Z2 pu / Z1 pu)

If S1 &gt; S1 rated, then transformer 1 is limiting

S2 = S2 rated x (Z1 pu / Z2 pu)

If S2 &gt; S2 rated, then transformer 2 is limiting

If transformer 1 is limiting, then:

S1 max = S1 rated

Smax = S1 rated + S2 rated (Z1 pu / Z2 pu)

If transformer 2 is limiting, then:

S2 max = S2 rated

Smax = S2 rated + S1 rated (Z2 pu / Z1 pu)


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## akyip (Nov 8, 2020)

SparkyBill said:


> And that's why I asked, I seen that, but it was under "single phase xfmrs in parrallel" with all these stipulations. I guess those 5 stipulations and this formula aren't together? I didn't now if I assume they meet these conditions, or if these 2 things are unrelated to each other.
> 
> View attachment 19332


Now that I think about it, I was re-reviewing my notes of Zach Stone's Electrical PE review (specifically on power flow). There are 2 equations from his Power Flow section that you can derive from this page of the handbook.

S1 = S1 rated x (S2 / S2 rated) x (Z2 pu / Z1 pu)

S2 = S2 rated x (S1 / S1 rated) x (Z1 pu / Z2 pu)

I might be a little off, feel free to correct me if I'm wrong.


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## speakeelsy PE (Nov 8, 2020)

SparkyBill said:


> And that's why I asked, I seen that, but it was under "single phase xfmrs in parrallel" with all these stipulations. I guess those 5 stipulations and this formula aren't together? I didn't now if I assume they meet these conditions, or if these 2 things are unrelated to each other.
> 
> View attachment 19332


@SparkyBill Sorry I didn't elaborate earlier, I was headed out of the house.

The restrictions go with the formulas. but they will also work for 3 phase too. I don't know why they've restricted it to 1 phase transformers. Granted your problem up there doesn't specify what kind of transformer. 

With the handbook formulas, you can also make the ones like this:

SL1 = SL2* ((ZT2%)*ST1) / (ZT1%)*ST2)

SL2 = SL1* ((ZT1%)*ST2) / (ZT2%)*ST1)

First solve for SL1 using SL2 = ST2... because you know you'll be maxing out 1 transformer, but you need to figure out which one you'll be maxing out.

Then solve for SL2 using SL1 = ST1.

one of your answers for SL1 or SL2 from your math above is going to be larger than the ST1 or ST2 value. That transformer will be overloaded in that situation, therefore it is the limiting transformer.

After that you know you'll be fully loaded on your limiting transformer, and then loading your other transformer to the SL1 or SL2 value you calculated above for the other transformer.

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For the problem you've given above, I'd solve like this

SL1 = 8MVA * ((2%*6MVA) / (3%*8MVA)) = 4MVA

SL2 = 6MVA * ((3%*8MVA) / (2%*6MVA)) = 12MVA

12MVA is larger than the 8 MVA transformer, therefore the 8MVA transformer is your limiting transformer because it can only load up to 8MVA.

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Zach's Power Flow section has a lot of the derivations if you want to review that, I find his notation to be a tad confusing though.

Another white paper that you might find helpful is this one from schneider electric: https://www.se.com/us/en/download/document/7400DB0701/


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## N-ABC (Nov 9, 2020)

speakeelsy said:


> @SparkyBill Sorry I didn't elaborate earlier, I was headed out of the house.
> 
> The restrictions go with the formulas. but they will also work for 3 phase too. I don't know why they've restricted it to 1 phase transformers. Granted your problem up there doesn't specify what kind of transformer.
> 
> ...


Thanks for detail explanation, I am also confuse using this formula.


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## Sparky Bill PE (Nov 9, 2020)

speakeelsy said:


> @SparkyBill Sorry I didn't elaborate earlier, I was headed out of the house.
> 
> The restrictions go with the formulas. but they will also work for 3 phase too. I don't know why they've restricted it to 1 phase transformers. Granted your problem up there doesn't specify what kind of transformer.
> 
> ...


There was another question like this in spin-up, and I used your analysis. The only difference is my 2 XFMRS were 3 MVA and 4 MVA with difference impedances. The final answer ended up not being WHICH transformer was overloaded, it was HOW MUCH is the overloaded transformer OVERLOADED by. Answer was 6 MVA. 

Not only do I see this being a question that will probably be on PE, but it will be a big divider question. If people (myself included) don't REALLY KNOW exactly what the question is asking or how to derive different formulas its going to be hard to get right.


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## speakeelsy PE (Nov 9, 2020)

SparkyBill said:


> There was another question like this in spin-up, and I used your analysis. The only difference is my 2 XFMRS were 3 MVA and 4 MVA with difference impedances. The final answer ended up not being WHICH transformer was overloaded, it was HOW MUCH is the overloaded transformer OVERLOADED by. Answer was 6 MVA.
> 
> Not only do I see this being a question that will probably be on PE, but it will be a big divider question. If people (myself included) don't REALLY KNOW exactly what the question is asking or how to derive different formulas its going to be hard to get right.


@SparkyBill  This stuff does take a bit of headscratching to figure out, I spent a while translating between Zach's notes, the handbook, and that whitepaper, until it finally clicked! 

Interpreting what the questions are asking is going to be up to you, but I've written a bit more of a plain words explanation below for you that will hopefully help with these types of problems!

Here's a little more of an explanation of what you are figuring with the two equations above.

So with my analysis above, what you're doing is maxing out the load on one transformer, and finding the load on the other transformer.

Both of these situations *cannot* happen at the same time, but you do need to solve both so that you can find which transformer is overloaded in which situation.

In this equation: SL1 = SL2* ((ZT2%)*ST1) / (ZT1%)*ST2), you are maxing out the load on transformer #2 (SL2 = ST2), and finding the load on transformer #1 (solving for SL1).

In this equation: SL2 = SL1* ((ZT1%)*ST2) / (ZT2%)*ST1), you are maxing out the load on transformer #1 (SL1 = ST1), and finding the load on transformer #2 (solving for SL2).

ST1 and ST2 will be the power ratings for your transformers. SL1 and SL2 are the loads on your transformers.
 

In one of these situations, the calculated SL1 or SL2 value will be more than the respective ST1 or ST2 value. That is the limiting transformer, and will be overloaded in that situation.

For example: you calculate SL2 = 6MVA, but the ST2 = 2MVA. Your Transformer #2 will be overloaded by 4MVA when Transformer #1 is fully loaded (SL1 = ST1)

The situation where the calculated SL1 or SL2 value is less than the respective ST1 or ST2 value is the situation that you want.

For example: you calculate SL2 = 2MVA, but ST2 = 4MVA. Transformer #2 will be under loaded by 2MVA when Transformer #1 is fully loaded (SL1 = ST1). So both transformers are operating within their specifications!


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