Calculating 3 phase AC motor HP

------- It is the grounded line.

We are trying to figure out what "this setup" is!

That is the grounded line. It will measure zero volts to ground, since it is connected to ground. See the fourth diagram down at

Except that Steve's description:

"If I understand correctly, the voltage was measured across two wires at a time. Two wires had 550V, another two had 550V, and the remaining two had nearly 0V."

made it sound like they measured between each possible pair of wires. A

550V delta (corner grounded or not) should measure 550 volts for each pair of wires.

If each measurement was from each of the 3 conductors to ground, and not to each other, then it is consistent with a corner grounded delta.

Also this has nothing to do with a "bastard leg" configuration. AFAIK, that configuration (delta with a grounded center tap) exists only in the

120V/240V form. Has that configuration ever been used for other voltages?

I agree. If they measured it that way then it makes no sense that there would be readings near zero between any two.

That is what leads me to believe that he may have gotten confusing information from the electrician about the measurements.

I agree. My experience is that the terms "bastard leg"/ "high leg"/ "wild leg" etc.refer to the center-tap delta. I have never heard them used for a corner ground, although the electricians on the group may prove me wrong.

Not that I know of. However, a 550 volt center-tapped delta would give 277 to ground (okay, 275.00000 to make Phil happy!) on two phases, which is usable for lighting the same as a 480 wye. It would have 480 to ground on the high leg. This would be a "bastard leg" system, but as you pointed out, it should measure 550 between all three pairs of phase conductors with no measurements at or near zero. This does not agree with what he reported. There must be some other information we don't have yet.

I agree with Ben that we don't have all the facts.

Another possibility is that the 3rd wire isn't the 3rd phase. Either it's not connected to the same system or it's connected to one of the other phases and the OP has only a single phase of the supposed 3 phase system. Since it gave 550V to one other leg, I'd think that the second situation is a possibility.

Fred Lotte wrote in news: snipped-for-privacy@sn-ip.vsrv-sjc.supernews.net:

I believe I've given every piece of information explained to me.

If the system is a 'corner ground', how does the third phase come into play?

Thanks for the help so far.

Steve Have you looked at the diagrams on my web page? If you connect loads line to line on a corner grounded system, they don't know the difference. Each load sees the L-L voltage (550) between all three pairs of wires, and it is happy. You could, in theory, disconnect the ground (ungrounded delta), connect it to a different corner, or center tap it to one winding (center-tap grounded delta) and there is no difference as far as a three-phase three-wire load is concerned. Any one point on a system can be grounded. The location of the ground affects the voltage to ground from various points, but it does not affect the voltage line to line.

On Tue, 29 Jul 2008 11:20:20 -0700 VWWall 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.

Just because there are only 2 transformers does not mean you have to limit your view of the system as being 2 phase.

| 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.

|> Given that, the steps *I* use to figure this out is to convert the electrical |> system to its wye/star equivalent, which in this case is 230/133. I multiply |> the voltage of each leg relative to a (virtual) neutral (e.g. 133) times the |> current (20) times the phases (3) times efficiency in units (0.895) times the |> typical power factor (0.8), and _divide_ by 746 and get 7.66 HP. |> |> Electrical power engineers generally do the arithmetic a little differently, |> multiplying just the delta or line-to-line voltage by the square root of 3 |> (1.732). They skip multiplying by number of phases because by multiplying |> by the square root of 3, that automatically includes all three phases. It's |> still effectively the same thing. I just worked out my steps from the science |> of three phase power as I learned it before I ever encountered the practiced |> formula (I did not study this in formal education). Engineers like shortcuts |> and their method is slightly shorter (less work, unless remembering the square |> root of 3 is considered work, which I have found is not the case) than mine. |> |> The current ratings given for a motor is not an indication of power used, but |> rather of current drawn in the course of motor operation. Since the motor is |> partially inductive, it will store some energy in the field and "generate" it |> back towards the supply during part of the next voltage half-cycle. This is |> seen in the fact that the current phase is shifted relative to the voltage |> phase. The power factor is the ratio of the volts applied times current drawn |> divided by power used and wasted. The power factor on _this_ motor may be a |> tad bit lower than 0.8, or the actual current drawn may be a tad bit lower |> than 20A. And the usual utilization voltage listed for motors is 230/460V |> even though standard electrical supply in North America is 240/480V. Except |> in extreme cases, the accuracy of these numbers is good enough for engineering |> practice. It's good enough to select the proper motor and correctly rate the |> circuit needed to power it. |> |> BTW, I sometimes use extreme precision of arithmetic when exploring scientific |> or mathematical theory related to electrical systems (or anything else I am |> studying). It drives the engineers nuts :-) | | You need to learn how to use a slide rule for engineering calculations! | That was all that was allowed when I took the Professional Engineer | exam. It also prevents you from giving many-place answers derived from | two-place accuracy inputs.

I know how to use a slide rule. It has no means to reduce the precision. It just has a precision limit built in.

The higher precision is used in a mathematical theory sense. It is NOT used with low precision measured values. If I measured the voltage as 122 volts L-N then I could say the volts are 244 L-L on single phase or 211 L-L on three phase. Maybe you should watch when and where and how I use higher precision and thus see how I actually apply it. Note that one way I will sometimes apply it is in humorous anecdotes. But the usual way it is applied is when mathematical comparisons are involved. I do math with high precision on all intermediate steps. That translates whatever precision and accuracy I have in the input directly to the output undistorted. One thing do not let happen is the effort of the choice of number base system influence rounding.

| I believe I've given every piece of information explained to me.

You might not have been given the information in the correct context. Sometimes an electrician trying to simplify things for non-electricians changes the perspective in a way that loses or distorts information.

| If the system is a 'corner ground', how does the third phase come into | play?

In a typical (North American) home single phase wiring, there are 4 wires. One is the grounding wire that does not carry current normally. The other three consist of a grounded conductor that is also the neutral conductor and two phase wires at 180 degree phase angles. If you measure between the neutral and the grounding wire, you should get 0 volts or very near to that.

A delta system can ungrounded, or grounded two ways. One way of grounding is to tap the center of one winding (between 2 phases) and ground there. The third phase that was not part of that tapped winding then has a higher voltage relative to the ground, compared to the other two. That phase is termed the high leg, or wild leg, or bastard leg. I've only heard of it used for 240 volt delta because it provides a means to get 120 volts for lights and stuff. The bastard leg in that case is 208 volts. The other way of grounding a delta system is to ground one regular phase. That gives you full voltage relative to ground on each of the other phases. But on the grounded phase, relative to ground, of course you get 0 volts.

You can also get the effect of a delta system from transformers wired in a WYE configuration, by simply ignoring the neutral, even though the system would typically be grounded at the neutral. For example a motor designed to be run on a 240 volt delta system could be run on a 240Y/139 volt WYE system (just don't connect the neutral to the motor).

The scenario you describe just doesn't match up exactly to anything known. If two wires have ZERO volts between them, then they are at the same potential. Then the third wire, which has voltage between it and either of the other two, would have to have these voltages in the SAME phase angle. Then you don't have three phase at all.

One small change in the information, changing how the voltages measurements are taken, so each wire is measured relative to ground (the 4th safety wire), easily makes this fit a corner-grounded (one of the phases is a corner of a delta) scenario. Note that such a system only needs two pole breakers, not three pole breakers, provided the breakers are rated per pole at the full system voltage.

---------------- 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 :)

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!)

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.

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?

| 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.

On Thu, 31 Jul 2008 22:51:48 -0700 VWWall wrote: | snipped-for-privacy@ipal.net wrote: |> On Tue, 29 Jul 2008 11:20:20 -0700 VWWall 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.

On Fri, 1 Aug 2008 11:22:24 -0500 Ben Miller wrote: | 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).

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

From:

"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:

"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!

I assume you meant "Phil is *not* talking about..."

See my reply to Phil just before this.

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:

It uses arbitrary precision and can work in almost any number base. The built-in math library, in addition to the normal trig functions has bessel functions and logs:

I haven't used the Windows version, but bc in Linux is excellent if somewhat specialized.