Calculating 3 phase AC motor HP

On Fri, 01 Aug 2008 16:13:15 -0700 VWWall wrote: | snipped-for-privacy@ipal.net wrote: |> On Fri, 01 Aug 2008 05:18:21 GMT Don Kelly 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:

| 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

(reminder: use a fixed space font such as Courier to view diagrams correctly)

Take a look at the manual, (in several formats):

It is CLI only, but that makes it easy to copy and paste the results you need.

----------------- 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.

Oh well, have fun:)

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.

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

On Sat, 02 Aug 2008 04:52:44 GMT Don Kelly wrote: |> 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:

|> 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. | 120104 120.0 103.9 120.00103.92 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:

Different configurations, and hence different arithmetic paths, yield very close, but formally different, numbers. You could round them to 213.2 and

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.

On Sat, 2 Aug 2008 11:28:10 -0400 daestrom wrote: | VWWall wrote: |> snipped-for-privacy@ipal.net wrote: |>> On Thu, 31 Jul 2008 22:51:48 -0700 VWWall |>> wrote: | | |>

|> 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. | | |>

|> 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.

I think that the challenge was physically turning the knobs to get the voltages and phase angles correct, not doing the mathematical calculations!

This sort of thing has long been used in suppling the high voltage DC for the output stages of AM transmitters. The unfiltered ripple shows up as modulation in the RF output.

It's common to use multi-phase dc-dc converters. Of course the "phases" are interleaved pulses used to control the switching power transistors. It's not common to go above four "phases" as circuit complexity overcomes filtering ease.

Here's a controller for 2, 3, or 4 phases.

On Sun, 3 Aug 2008 12:46:43 -0500 Ben Miller wrote: | 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?

Actually the first table entry doesn't make much sense. -particularly the last part where you have

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.

------------ Agreed -It is possible and is done- to go from n phases to m phases as long as n,m>=2 (and ruling out the Edison system in which the "2 phases" are 180 degrees apart) . This is done over and over in machine analysis. You can also represent unbalanced systems in terms of a set of balanced polyphase systems as in using symmetrical components for power system analysis.

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

|> 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. | | 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 =120 +6 +j10.4=126.4 @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:

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:

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.

On Mon, 4 Aug 2008 12:50:29 -0400 daestrom wrote:

|> Simple trignometry. Do they need a web based helper program to do it? |>

| | 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.

And that's probably the real issue ... the technology of the day. Today, a waveform can be precisely generated from a chip, in terms of some form of digital output (numerically coded, or pulse width, or diversity pulsed). Today, lots of stuff, even analog stuff, gets modeled in a computer, and comes out usually damned close to what was intended, if the model was correct.

One nice way to make an analog, or even multi-level digital, transmitter, is to have 2 separate constant level sine wave carriers that vary in phase. They can be amplified more cheaply with class C/D or other PA designs, filtered, and combined passively with the power difference lost being less than the loss of doing a class A or A/B design. I know this has been done for AM radio transmitters. For something like 8VSB digital, this only involves 8 discrete levels, so only 8 discrete phase angles are needed in 2 separate carriers. OTOH, I'd probably do a design with 7 or 8 PAs "fired" in a round robin that balances the work load on each PA (which individually would just be going on and off like fast CW). It would be a more complex combiner.

| Agreed -It is possible and is done- to go from n phases to m phases as long | as n,m>=2 (and ruling out the Edison system in which the "2 phases" are 180 | degrees apart) . This is done over and over in machine analysis. You can | also represent unbalanced systems in terms of a set of balanced polyphase | systems as in using symmetrical components for power system analysis.

As long as you have a 2-D vector space instead of a 1-D vector space, you are good to go.

----------- You still simply don't seem to get it. Case closed.

------------ And a one=D vector space is a line, so all you have is + or - along this line. Not what I would call a true vector space. Also note that when we use normal AC analysis, we are in a 2D space. After all, a rms voltage doesn't actually exist and a real voltage is time varying- hence the mathematical transform from a time varying sinusoid to a complex number representation. The actual voltage is in a 2 D space- one of which is time, while the rms voltage is in a 2D space neither of which is time.

| 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).