Calculating 3 phase AC motor HP

| snipped-for-privacy@ipal.net wrote:
|> |> | You can use high precision in the intermediate steps but if you start with
a |> | lower precision, after the intermediate steps, in the final answer, you |> | should round off to the original precision. We all do that as long as it |> | doesn't need re-entry of multi-digit numbers. If you want to emphasise a |> | higher precision mathematically then maybe you should start with |> | 120.0000000/207.8460970 and come up with an answer to the same number of |> | digits (less a few in multiple calculations). If you do this to bug |> | engineers, fine- as they aren't the ones having to do the extraneous and |> | meaningless typing. |> | |> | We have been here before and likely neither of us will change :) |> |> Not that I see. I do things both ways, but I think some people just cannot |> see the distinction between when I do high precision, and when I do reduced |> precision (to match the input) and ... a third way: when I use labels that |> happen to be numbers. I often say "347 volts" when what I mean is a system |> found mostly in Canada based on 600 volts. Dividing 600 by sqrt(3) gives me |> 346.41016151377545870548926830117447338856105076207612561116139589038660338176 |> which when rounded gives me 346, not 347. So 346 is the rounded result and |> 347 is the label. Fortunately in most cases things are the same. But a lot |> of people still use the label "220" while I use 240 as the label, as well as |> the rounded result of a defined standard. |> |> FYI, I did not type that high precision result in. I used copy-and-paste. | | You might be interested in a calculator called "bc", if you have not | already discovered it. It was developed for Unix and has been available | in Linux for some time. It has recently been made available for | Windows, for those that prefer that operating system:
I've used it. But when I need to do more like programming something that needs the extra precision, I write it in Pike or use libgmp with C.
Not all calculations need the extreme precision. What comes in C in double or long double is usually adequate to tell what calculation method was used in the results. For example ...
this program: http://phil.ipal.org/usenet/aee/2008-08-01/buckboost.c outputs this: http://phil.ipal.org/usenet/aee/2008-08-01/buckboost.out
which is a list of different voltages readily available from using common buck boost transformers on a given three phase wye/star system. As you can see there are more digits there than a slide rule normally gives you, but it is not more than type double supports.
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wrote:

----------------- I see the extra and meaningless digits. In these cases, single precision is more than enough and rounding off to significant figures is satisfactory. starting from 120.000 even if that number was known to that precision and getting 103.92305 is simply wrong-more sig figs in the answer than in the input data. It is fine to carry extra figures in your calculations to eliminate computer roundoff but it simply has no purpose other than that. 120<>104 120.0<> 103.9 120.00<>103.92 is about as good as it gets. Double precision is only needed in specific cases and these are not all that common. One such is the case of ill conditioned matrices - but for calculating transformer ratios???
Oh well, have fun:)
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|> reduced |> |> precision (to match the input) and ... a third way: when I use labels |> that |> |> happen to be numbers. I often say "347 volts" when what I mean is a |> system |> |> found mostly in Canada based on 600 volts. Dividing 600 by sqrt(3) |> gives me |> |> |> 346.41016151377545870548926830117447338856105076207612561116139589038660338176 |> |> which when rounded gives me 346, not 347. So 346 is the rounded result |> and |> |> 347 is the label. Fortunately in most cases things are the same. But |> a lot |> |> of people still use the label "220" while I use 240 as the label, as |> well as |> |> the rounded result of a defined standard. |> |> |> |> FYI, I did not type that high precision result in. I used |> copy-and-paste. |> | |> | You might be interested in a calculator called "bc", if you have not |> | already discovered it. It was developed for Unix and has been available |> | in Linux for some time. It has recently been made available for |> | Windows, for those that prefer that operating system: |> |> I've used it. But when I need to do more like programming something that |> needs the extra precision, I write it in Pike or use libgmp with C. |> |> Not all calculations need the extreme precision. What comes in C in |> double |> or long double is usually adequate to tell what calculation method was |> used |> in the results. For example ... |> |> this program: http://phil.ipal.org/usenet/aee/2008-08-01/buckboost.c |> outputs this: http://phil.ipal.org/usenet/aee/2008-08-01/buckboost.out |> |> which is a list of different voltages readily available from using common |> buck boost transformers on a given three phase wye/star system. As you |> can |> see there are more digits there than a slide rule normally gives you, but |> it is not more than type double supports. | ----------------- | I see the extra and meaningless digits. In these cases, single precision is | more than enough and rounding off to significant figures is satisfactory. | starting from 120.000 even if that number was known to that precision and | getting 103.92305 is simply wrong-more sig figs in the answer than in the | input data. It is fine to carry extra figures in your calculations to | eliminate computer roundoff but it simply has no purpose other than that. | 120<>104 120.0<> 103.9 120.00<>103.92 is about as good as it gets. Double | precision is only needed in specific cases and these are not all that | common. One such is the case of ill conditioned matrices - but for | calculating transformer ratios???
I didn't calculate transformer ratios in the above code. I merely used them as provided in terms of knowing the voltages in and out of common ones. These common voltages are readily about to be implemented with exact ratios. For example, for the 240 volt to 24 volt transformer, it is clear that the exact ratio is 10:1. This isn't about a precision of measurement because there is no measurement to be imprecise with.
I generated the table with some degree of precision remaining in the values for many reasons. One is that these numbers may then be used in other calculations. But, again, there are no measurements of finite precision involved. Rounding is left up to the reader ... to determine if his usage of these numbers needs them or not.
The use of double precision in C is a common practice. In many cases double precision is the default and single precision (float) is converted to double. While single precision could be used, I don't ever bother with C programs. The only real value of using single precision is when you have very massive arrays or matrices and are hitting space or swapping limits. I cannot recall ever having that in any of my math/science programs.
Consider these 2 entries in the table:
213.232268 Y / 123.109707 : 120.000 + 6.000 @ 60 (120.000 via 240 -> 12) 213.316666 Y / 123.158435 : 120.000 + 27.713 @ 90 (207.846 via 240 -> 32)
Different configurations, and hence different arithmetic paths, yield very close, but formally different, numbers. You could round them to 213.2 and 213.3 and maintain some of the difference. But you'd have a difference of 0.1 when subtracting the rounded numbers. Subtract the full numbers and you get a difference of 0.084398. That's much more of a change when rounding before the difference.
Had I rounded these numbers, I might not have detected that these two vectors really do not formally hit the same spot (whereas some other combinations do). So I know that _mathematically_ these are different vector sums. Depending on the scale, it would be possible to miss this even with 4 digits precision of the printed results. It just depends on where the digits "land" when this close.
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If you are using a 6V signal from 120/6V then the 123.1 value that you give is fine. If you start with n sig figs and have a perfect transformer ratio (which is not necessarily true- the transformer ratio may be actually 120/12.1) then you have n sig figs that have meaning. The remaining figures are meaningless- even for further calculation. Considering real life- they definitely are meaningless.
Mathematically different- but only in exceptional circumstances will the difference actually be meaningful and only in those cases will it matter a damn. Actually when you have massive arrays -that is where you need double precision simply because of the number of sequential operations involved. An example is a power system load flow study. For most calculations (such as the above) it isn't needed but some languages do use double precision as a default. I have no problem with that. I do have a problem with reporting numbers to a ridiculous "precision" which doesn't exist.
I don't know where you got your physics exposure as the physicists are just as adamant about significant figures as the engineers are.
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|> 12)
|> 32) |> |> Different configurations, and hence different arithmetic paths, yield very |> close, but formally different, numbers. You could round them to 213.2 and |> 213.3 and maintain some of the difference. But you'd have a difference of |> 0.1 when subtracting the rounded numbers. Subtract the full numbers and |> you |> get a difference of 0.084398. That's much more of a change when rounding |> before the difference. |> |> Had I rounded these numbers, I might not have detected that these two |> vectors |> really do not formally hit the same spot (whereas some other combinations |> do). |> So I know that _mathematically_ these are different vector sums. |> Depending |> on the scale, it would be possible to miss this even with 4 digits |> precision |> of the printed results. It just depends on where the digits "land" when |> this |> close. | | Actually the first table entry doesn't make much sense. -particularly the | last part where you have | 120.000 + 6.000 @ 60 (120.000 via 240 -> 12) | if this is what I think it means it implies adding a 12V signal at 60 | degrees to the 120 volt source | I get 120 +12 @60 0 +6 +j10.46.4 @4.7degrees | If you are using a 6V signal from 120/6V then the 123.1 value that you give | is fine.
The program just tries all combinations of transformers and voltages that have unique ratios. In the case of this example, it's a 240->12 transformer so the ratio is 20:1. But it is fed with 120 volts, so the output is 6 volts at 60 degrees. I coded it to allow undervoltage on transformer configurations.
The part after "via" tells what transformer configuration is used, and the part before "via" tells what voltage is applied to that transformer.
| If you start with n sig figs and have a perfect transformer ratio (which is | not necessarily true- the transformer ratio may be actually 120/12.1) then | you have n sig figs that have meaning. The remaining figures are | meaningless- even for further calculation. Considering real life- they | definitely are meaningless.
The figures are for theory. This is not a reflection of real life, but rather, is a guide to theoretical possibilities. The precision is that of the theory itself. Apply "YMMV" to consider it in practice, and round the numbers you get. I anyone would limit their choice of configuration over a 1 volt difference. But they might limit their choice based on what they have on hand in their transformer inventory. Then the theory shows them how far off they might be as a starting point. They can then take it even further by figuring in inconsistencies in transformer manufacture, and the actual supply voltage.
| Mathematically different- but only in exceptional circumstances will the | difference actually be meaningful and only in those cases will it matter a | damn.
But this table is not one that can consider actual circumstances. You have to consider this yourself.
Think of logaritm tables. I've seen those in a variety of precisions.
| Actually when you have massive arrays -that is where you need double | precision simply because of the number of sequential operations involved.
That depends on the formula involved. If the array is of millions of values just individually calculated, then maybe float is good enough for storage. The calculations after picking out values from the masssive array can still be done in double or greater precision as needed.
| An example is a power system load flow study. For most calculations (such as | the above) it isn't needed but some languages do use double precision as a | default. I have no problem with that. I do have a problem with reporting | numbers to a ridiculous "precision" which doesn't exist. | | I don't know where you got your physics exposure as the physicists are just | as adamant about significant figures as the engineers are.
Again and again and again, this is about theory vs. actually measured errors. I do it both ways. When calculating things for a theoretical study, I use as much precision as I have. Long ago I was doing some calculations on some theoretical stuff and found something where the difference was 7 digits in. Backtracking and working on that I found that these two numbers were just coincidentally close. They were indeed different formulas.
When comparing floating point numbers by computer program, it is appropriate to do a fuzzy comparison. That is, subtract, take absolute value of difference, and see if that is greater than a small threshold. The question is just how much of a threshold to use. What I use is something just above the "noise" level I expect out of the floating point calculations. And that can still be over 10 digits of precision.
In some cases in the past I have seen that numbers were different by exactly one. All the fractional part was the same. The more digits of precision led to a greater confidence there was a difference in how the formula affected these numbers such that a "true one" was the result. Without the extra digits I would not have seen that.
Again, more digits helps. And it does NOT hurt _me_ because I don't have any trouble seeing the practical low precision values when looking at high precision number expressions. I've worked with high precision calculations for decades, at least since 1974, and I'm quite familar with using them and have no trouble seeing a low precision value in the high precision expression.
I would be quite happy boosting 208Y/120 with one of the following:
235.558910 Y / 136.000000 : 120.000 + 16.000 @ 0 (120.000 via 120 -> 16) 249.415316 Y / 144.000000 : 120.000 + 24.000 @ 0 (120.000 via 120 -> 24)
and thus avoiding any angular changes in current.
Looking through the table, I do see a couple cases where the L-L voltage has all zeros in its fractional part:
168.000000 Y / 96.994845 : 120.000 + 27.713 @ 150 (207.846 via 240 -> 32) 180.000000 Y / 103.923048 : 120.000 + 60.000 @ 120 (120.000 via 240 -> 120)
I would consider these to be theoretically "interesting" cases.
And remember, I can round _when_ I need to. Since I have not wired up any such buck-boost configuration, that need has not yet come.
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----------- You still simply don't seem to get it. Case closed.
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| You still simply don't seem to get it.
Everyone that tries to explain to me something about it keeps explaining a case that I understand to be different than what I am doing where I use the higher precision values (except the cases where I use it to poke fun, such as how many digits I memorize).
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snipped-for-privacy@ipal.net wrote:

A Scott-Tee is used to provide two phase (ninety degree) power from three phase input. It was once commonly used to drive two-phase motors. There is no center tapped transformer, although a tap at 86%, (slide rule accuracy), is required.

I view a two phase system as one that has two phases at 90 degrees, one from the other. This is not a count of the number of transformers!
Three phase system have phases at 120 degrees apart. The common 120/240 system is sometimes called two phase, with the "phases" being 180 degrees apart.

You can indeed get them in very small boxes since they are not used to supply power, but only to convert the three phase synchro output to the two phase resolver signals when these are used in a servo feedback loop.
An exercise for the reader: Figure out why the 86% tap is needed. Calculate it to ten places! (A vector diagram helps!)
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Phil is talking about the 90 degree 2 phase system. It is possible to convert 3 phase to 3 phase using a Scott-T like transformer configuration.

It is possible to transform 3 phase to 3 phase using a Scott-T like transformer configuration. That's what Phil was talking about.
Look at the diagram of a Scott-T configuration. One side (primary or secondary, depending on whether you're going from 3 phase to 2 phase or vice versa) is configured for 3 phase, the other side is 2 phase. Now, take that same diagram and wire _both_ sides with the 3 phase diagram, and voila! You have a 3 phase to 3 phase configuration using only 2 transformers. If the load is balanced, the transformer loads (VA) are the same as well. Look at the secondary of what Phil wrote. One transformer is 240V CT, the other is 208V (86.6% of 240V) with one lead going to the center tap. Look familiar?
A little trivia: The Scott-T configuration is generic. You can go from any number of phases (except single phase) to any number of phases using just 2 transformers, although they may have many windings and many oddball (at sqrt(whatever)) taps. Scott-T is the 3 phase to 2 phase version, and the Scott-T like system is the 3 phase to 3 phase version. Exercise: Show a diagram to convert from 5 phases to 7 phases using 2 transformer cores. :-) Yes, it can be done, and if done correctly, the 5 phases will be loaded evenly if the 7 phase load is balanced.
There is a way to "cheat" with a Scott-T configuration if the neutral is available on the primary. Connect one transformer line-line as before, but connect the other from the third phase to the neutral (not the CT of the first transformer). This has the advantage of not needing a CT in one transformer and only one MV bushing in the other, but has the disadvantage of a nonzero neutral current and a low PF in two phases, even if the load is balanced. Not a problem for small configurations. Phil mentions this configuration.

I've heard that some of the pad mount transformers are really 2 core Scott-T like internally.
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Michael Moroney wrote:

I have never actually worked with a Scott-T connected as you describe. What happens with unbalanced loads? Is the voltage regulation as good as a full delta, or is it more like an open delta?
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| Michael Moroney wrote: |> |> Look at the diagram of a Scott-T configuration. One side (primary or |> secondary, depending on whether you're going from 3 phase to 2 phase |> or vice versa) is configured for 3 phase, the other side is 2 phase. |> Now, take that same diagram and wire _both_ sides with the 3 phase |> diagram, and voila! You have a 3 phase to 3 phase configuration using |> only 2 transformers. If the load is balanced, the transformer loads |> (VA) are |> the same as well. Look at the secondary of what Phil wrote. One |> transformer is 240V CT, the other is 208V (86.6% of 240V) with one |> lead going to the center tap. Look familiar? |> | I have never actually worked with a Scott-T connected as you describe. What | happens with unbalanced loads? Is the voltage regulation as good as a full | delta, or is it more like an open delta?
I would suspect it has characteristic difficulties in ways similar to, but not identical to, an open delta. In a way it is a pair of open deltas sharing one leg in commn, with different voltages (208 on the shared one and 120 on the non-shared one). Of course you'd get funny current phases on the windings and you will need to derate.
Because a T-T connects one transformer A-C and the other B-N on the primary, it will result in funny current phase angles on the distribution lines. Back past a D-Y transformer feeding the distribution, the currents should be in their normal configuration. But you wouldn't want to put a lot of 3-phase load on there with these T-T's. Contrast that with a D-Y between distribution and service drop. The D-Y won't put any current on the neutral (it doesn't even connect to it), whereas the T-T will (because one transformer connects between neutral and one of the phases).
If you have a big single phase 2-bushing transformer connected L-L input for 120/240 volt service, and the customer needs a little bit of three phase to spice it up, you can add on a small 2-bushing transformer connected L-L to the different phase and one of the existing phases, with 240 out for open delta, or you can add on a small 1-bushing transformer connected L-N to the different phase, with 208 out for Scott-T. Which of the latter two is better I cannot say. But in either case this would be for a small amount of 3-phase.
Now days I'd prefer wye/star everywhere. If I have a motor that needs 240 volts and can't run on 208 (or runs too hot), then I'd just boost those 120 volt legs up to around 138.5 volts or so to give it a 240Y/138.5 system on the motor circuit. I wonder how many 277 volt transformers can be split in half internally much like the 120/240 volt transformers can be split to make a pure 120 volt transformer at double the current (e.g. 138.5/277).
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Michael Moroney wrote:

I assume you meant "Phil is *not* talking about..."
See my reply to Phil just before this.
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| snipped-for-privacy@ipal.net wrote:
|> |> |> Yes. It's 240V delta, or a Scott-T derived equivalent. One could also make |> |> a system equivalent enough for the purpose of this motor with 230/133 wye/star, |> |> but such systems are generally non-existant. It's definitely NOT a 400/230 or |> |> 416/240 wye/star system. That was what my question was trying to figure out. |> | |> | See Ben Miller's answer for the real circuit. It has nothing to do with |> | a Scott-Tee, which is a way to get two phase power from a three phase input. |> |> A Scott-Tee can give you the same three phase system as you can get with a |> delta where one side is center tapped. But unliked closed delta, it nedes |> only 2 transformers. One is the same (a 120/240V center tapped secondary) |> with the primary wired to one phase (A-N) and the other is different (208V) |> with the primary wired L-L to the other phases (B-C). The secondary of the |> 208V transformer is wired directly to neutral and provides the high leg. |> There is some current rating limitation on a Scott-T. | | A Scott-Tee is used to provide two phase (ninety degree) power from | three phase input. It was once commonly used to drive two-phase motors. | There is no center tapped transformer, although a tap at 86%, (slide | rule accuracy), is required.
It sounds like you are talking about a whole different kind of transformer configuration than I have heard of that somehow shares the same name.
The one I know about has secondary connections labeled A,B,C,N that have exactly the same voltages AND phase angles as a center tapped delta.
|> Just because there are only 2 transformers does not mean you have to limit |> your view of the system as being 2 phase. | | I view a two phase system as one that has two phases at 90 degrees, one | from the other. This is not a count of the number of transformers! | | Three phase system have phases at 120 degrees apart. The common 120/240 | system is sometimes called two phase, with the "phases" being 180 | degrees apart.
Take the Scott-Tee I'm referring to (not the one you are referring to) and connect voltage and phase measurements to each of the various secondary terminals (or wires as configured with a pair of transformers) and you will get something that is indistinguishable from a center tapped delta.
|> | This is not used much anymore for power, but the equivalent is often |> | used in servo circuits to convert "synchro" feedback into "resolver". |> |> You can even get Scott-T in a dry-type transformer in a 3R box. | | You can indeed get them in very small boxes since they are not used to | supply power, but only to convert the three phase synchro output to the | two phase resolver signals when these are used in a servo feedback loop.
You can get that in power transformers, too.
| An exercise for the reader: Figure out why the 86% tap is needed. | Calculate it to ten places! (A vector diagram helps!)
Engineers can't do ten places with their slide rules!
I assume you mean at 86% away from the neutral on the stinger leg. You want ten places, so here you go: 180.0000000000
What 86% (as a common label) really refers to is sqrt(3)/2*100, which is 86.602540378% in extra precision. The stinger leg, in extra precision is 207.846096908 volts. Multiplying just that many digits gets 179.999999998. When I crank the digits way up I get 180 on the nose.
Even when using the already rounded numbers I get 208*0.86 = 178.88. I see no need for the 86% tap. What uses 180 volts?
You need a fixed spaced font, such as Courier, to view this diagram:
B | T | | | A---N---C
These voltages can be measured (with extra precision only to show which means of calculation I used):
A-N: 120 B-N: 207.8460969 C-N: 120 A-B: 240 B-C: 240 C-A: 240
Now with your 86% tap where I think you meant it:
T-N: 180 A-T: 216.3330765 B-T: 27.8460969 C-T: 216.3330765
If you meant it to be somewhere else, please explain.
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snipped-for-privacy@ipal.net wrote:

It does use one center tapped transformer and my slide rule read 0.87. :-)

From: http://en.wikipedia.org/wiki/Scott-T_transformer
"A Scott-T Transformer (also called a Scott Connection) is a type of circuit used to derive two-phase (2-?) current from a three-phase (3-?) source or vice-versa. The Scott connection evenly distributes a balanced load between the phases of the source. Standard Scott Connection
Nikola Tesla's original polyphase power system was based on simple to build two-phase components. However, as transmission distances increased, the more transmission line efficient three-phase system became more prominent. Both 2-? and 3-? components coexisted for a number of years and the Scott-T transformer connection allowed them to be interconnected.
Assuming the desired voltage is the same on the two and three phase sides, the Scott-T transformer connection (shown below) consists of a center-tapped 1:1 ratio Main transformer T1 and an 86.6% (0.5?3) ratio Teaser transformer T2. The center-tapped side of T1 is connected between two of the phases on the three-phase side. Its center tap then connects to one end of the lower turn count side of T2, the other end connects to the remaining phase. The other side of the transformers then connect directly to the two pairs of a two-phase four-wire system."
This may be what you are are thinking of:
"The Scott-T Transformer connection may be also be used in a back to back T to T arrangement for a three-phase to 3 phase connection. This is a cost saving in the smaller kVA transformers due to the 2 coil T connected to a secondary 2 coil T in-lieu of the traditional three-coil primary to 3 coil secondary transformer. In this arrangement the X0 Neutral tap is part way up on the secondary Teaser transformer see below. The voltage stability of this T to T arrangement as compared to the traditional 3 coil primary to three-coil secondary transformer is questioned."
It's possible to go from n phases to m phases:
http://en.wikipedia.org/wiki/Three-phase
"Provided two voltage waveforms have at least some relative displacement on the time axis, other than a multiple of a half-cycle, any other polyphase set of voltages can be obtained by an array of passive transformers. Such arrays will evenly balance the polyphase load between the phases of the source system. For example, balanced two-phase power can be obtained from a three-phase network by using two specially constructed transformers, with taps at 50% and 86.6% of the primary voltage. This Scott T connection produces a true two-phase system with 90 time difference between the phases. Another example is the generation of higher-phase-order systems for large rectifier systems, to produce a smoother DC output and to reduce the harmonic currents in the supply."
I ran across the Scott-Tee three phase to two phase configuration in the exam for Registered Professional Engineer in California in 1951. As an electronics rather than power engineer, I've never forgotten it!
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| This may be what you are are thinking of: | | "The Scott-T Transformer connection may be also be used in a back to | back T to T arrangement for a three-phase to 3 phase connection. This is | a cost saving in the smaller kVA transformers due to the 2 coil T | connected to a secondary 2 coil T in-lieu of the traditional three-coil | primary to 3 coil secondary transformer. In this arrangement the X0 | Neutral tap is part way up on the secondary Teaser transformer see | below. The voltage stability of this T to T arrangement as compared to | the traditional 3 coil primary to three-coil secondary transformer is | questioned."
Close. I'm thinking of one where the teaser has no tap, and is just a 208 volt secondary. But since an 86.6% tap on a 240 volt winding gives you 208 and 32 volts, maybe that is the 86.6% tap being referred to as in:
(reminder: use a fixed space font such as Courier to view diagrams correctly)
B <-- 240 volts from X, 208 volts from N | | | | | A---N---C <-- 120/240 | X <-- 32 volts from N (unconnected)
The first Scott-T that I saw was the above WITHOUT the -X extension. If one is designing a Scott-T integrated transformer, no need to include the -X part.
OTOH, one could build a Scott-T using a 104/208 volt center tapped winding, plus a 180 volt teaster winding, with a tap at 60 volts above the common connection connected to ground serving as neutral, and emulate 208Y/120.
B <-- 180 volts from X | | | N <-- 60 volts from X | A---X---C <-- 104/208
This would give 120 volts for A-N or B-N or C-N and 208 volts for A-B or B-C or C-B
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VWWall wrote:

<snip>
I ran across a transformer setup that converted three phase to nine phase to feed into a rectifier bank. The purpose was to reduce some of the harmonics that would normally be found in rectifying three phase.
<snip>

First place I ran across Scott-Tee was for generating 400 Hz 3-phase to supply some navigation equipment. Used a single-phase inverter to produce a precise 400 Hz into the 'main' leg and then a slave inverter that was synced to the first one with a 90-degree phase shift. That second inverter fed the other transformer and the three-phase was taken from the output of the two transformers connected Scott-Tee.
Regulating the output of the main inverter controlled the voltage of phase A-B. Increasing/decreasing the output of the second inverter raised/lowered phase A-C and B-C together. Adjusting the exact time-delay (phase-angle of second phase) of the slave inverter would increase A-C while decreasing B-C or vice-versa. PITA to adjust.
daestrom
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wrote: | VWWall wrote:
|>> wrote: | | <snip> |> |> It's possible to go from n phases to m phases: |> | | I ran across a transformer setup that converted three phase to nine phase to | feed into a rectifier bank. The purpose was to reduce some of the harmonics | that would normally be found in rectifying three phase. | | <snip> |> |> I ran across the Scott-Tee three phase to two phase configuration in |> the exam for Registered Professional Engineer in California in 1951. As an |> electronics rather than power engineer, I've never forgotten it! | | First place I ran across Scott-Tee was for generating 400 Hz 3-phase to | supply some navigation equipment. Used a single-phase inverter to produce a | precise 400 Hz into the 'main' leg and then a slave inverter that was synced | to the first one with a 90-degree phase shift. That second inverter fed the | other transformer and the three-phase was taken from the output of the two | transformers connected Scott-Tee. | | Regulating the output of the main inverter controlled the voltage of phase | A-B. Increasing/decreasing the output of the second inverter raised/lowered | phase A-C and B-C together. Adjusting the exact time-delay (phase-angle of | second phase) of the slave inverter would increase A-C while decreasing B-C | or vice-versa. PITA to adjust.
Once you have 2 different phases, you can cross connect anywhere in a 2-D space if you extend things far enough, and pick the correct ratio, even if the 2 phases are not 90 degrees. And all our polyphase systems can be represented in a 2-D space, so a 2-phase system can be made to get any of the other phases.
I always liked this one for deriving the missing phase-C when supplied with only phase-A and phase-B (as in those "single" phase 208/120 services):
A X \ / \ N C / B
Use two 120:120 volt isolation transformers, deriving N-X from B-N, and deriving X-C from A-N. Then wire them as shown as autotransformers.
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snipped-for-privacy@ipal.net wrote:

I think that the challenge was physically turning the knobs to get the voltages and phase angles correct, not doing the mathematical calculations!
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| snipped-for-privacy@ipal.net wrote: |>>> |>> First place I ran across Scott-Tee was for generating 400 Hz 3-phase |>> to supply some navigation equipment. Used a single-phase inverter |>> to produce a precise 400 Hz into the 'main' leg and then a slave |>> inverter that was synced to the first one with a 90-degree phase |>> shift. That second inverter fed the other transformer and the |>> three-phase was taken from the output of the two transformers |>> connected Scott-Tee. |>> |>> Regulating the output of the main inverter controlled the voltage of |>> phase A-B. Increasing/decreasing the output of the second inverter |>> raised/lowered phase A-C and B-C together. Adjusting the exact |>> time-delay (phase-angle of second phase) of the slave inverter would |>> increase A-C while decreasing B-C or vice-versa. PITA to adjust. |> |> Once you have 2 different phases, you can cross connect anywhere in a |> 2-D |> space if you extend things far enough, and pick the correct ratio, |> even if |> the 2 phases are not 90 degrees. And all our polyphase systems can be |> represented in a 2-D space, so a 2-phase system can be made to get |> any of |> the other phases. |> | | I think that the challenge was physically turning the knobs to get the | voltages and phase angles correct, not doing the mathematical calculations!
Simple trignometry. Do they need a web based helper program to do it?
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snipped-for-privacy@ipal.net wrote:

You missed the point.
The design was two inverters, a master and a slave feeding into a fixed transformer configuration.
Sure the *math* is easy. But you have to get the inverters to *actually* perform the way the 'math' expects. That is, you have to get the slave inverter to be delayed behind the master by exactly 1/4 cycle. In order to get the output to be exactly 120 VAC 400 Hz and all three phases be 120 degrees and 120V, you have to control the master and slave inverters to a high degree of precision and know exactly how to adjust them when you aren't getting the output you want.
If you didn't understand the whole setup, you could spend all day going back and forth tweaking 'R-17' or 'R-22' or 'R-33' to get one voltage in spec only to find that another phase was now out of spec.
But understanding how the voltage output of the primary inverter fed line A-B directly, and how the voltage output of the secondary inverter added to both A-C and B-C at the same time, while the phase delay added to B-C and subtracted from A-C made it easy. You measured all three phases L-L and tuned A-B to exact spec. Then you tuned the phase delay to get B-C and A-C to be exactly equal. Finally, you adjusted secondary inverter to raise/lower B-C and A-C at the same time until they were both in spec (since they are now equal after step two).
Considering this stuff was early 1960's, all before ARPANET, much less the WWW, no 'web-based helper program' was involved.
daestrom

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