Question for experienced rewinders 5

[zlatkodo]

I would like to know how often exist in practice (on the U.S. market and in other areas outside Europe), three-phase low voltage induction motors with 96 slots and for which number of poles , power and purpose ?
Thanks in advance.
Zlatkodo

 

[electricpete]

Thanks Ray. I will study that for awhile.

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[electricpete]

Ray - First thanks very much for a detailed explanation. That is helpful. I vote you a star for your patience.

Now let's compare your 10-pole layout to your 12-pole layout

10 pole
333,433,334,333,343/,/333,433,334,333,343
or in a disguised version to hide the phase definitions:
333433334333343333433334333343

Is it symmetric (three identical windings,just shifted)?

We can tell by inspection the pattern is symmetric with a mental experiment. If I show you the pattern to begin with including a label of A B C labeled and a starting point... THEN take away the labels and the starting point and show you the same patter... you have no way of telling which phase is A, B or C. They are identical except for their relation to some arbitrary staritng point in the pattern which is arbitrary. In other words they are identical and perfectly symetrical.

Now look at 12 pole arrangement
233,323,332/,/233,323,332/,/233,323,332/,/233,323,332
or in a disguised version to hide the phase definitions:
233323332233323332233323332233323332

Do the same experiment. Look at the pattern knowing the starting point and the A, B, C references. Now take away the starting reference and the phase labels and figure out which one is phase B. Easy answer. It is the one whose 2-coil groups are never adjacent to any other 2-coil group (A and C each have 2-coil groups which appear adjacent to each other) in the sequence.

That is the way I am understanding symmetry (open to discussion of the definition of symmetry). Your 10pole layout meets this definition but your 12 pole layout does not.

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[rhatcher]

Pete,

Nice observation (*). I wasn't expecting that an assymetrical relationship of any kind could be found. The answer that I offer is that I don't think (and also don't know!) that the relationship that you are pointing to matters with respect to symmetry in the way that I am defining symmetry (major qualifier).

This is based on my understanding of symmetry. I have yet to determine whether my definition of symmetry fully matches the conditions set out by your references. The problem in determing this is successfully translating the variables and equations used in that reference to the variables and equations that I am accustomed to. I only have the 'google books' version that you linked so I am missing some vital pages. Since you would appear to have the complete reference (book), perhaps you can translate the variables and equations that I present to see if they are equivalent to those in your reference and to see if the reference definition of symmetry is the same as mine.

When looking for symmetry, I am considering the combined flux of the three phases distributed across the circumference of the air gap to create a single mmf wave. The conditions of symmetry I look for are:
- I want the mmf to be balanced around the circumference of the air gap such that the combined forces create only circumferential (rotational) force and not axial force. This means that no mechanical vibrations will be created.
- I want the mmf to be constant in time such that the combined rotational force that is created does not vary from one moment to the next. This means that there will be no electrical vibrations created (torque pulsations).
- I want to accomplish this in such a way that the resulting electrical circuit(s) are balanced. I do not want to generate circulating currents between parallel circuits or to create current unbalances between the phases. This third requirement may, by defintion, be true if the first two requirements are met. (??)

So, I want single rotating mmf that is balanced in space (circumferentially/mechanically) and in time (electrically). I believe that the procedure that I have outlined accomplishes this. As an aside, I also want a woman that is mentally balanced in space and time, but I have not found a procedure to accomplish this goal. Of course, this is the wrong forum to seek that answer (haha). Anyway...

The 10 pole winding is symmetrical when comparing one half to the other. This winding could be connected for one or two circuits and still one half equals the other. If you connected this winding for five or ten circuits then you would be in trouble; the parallel circuits would not balance mechanically or electrically. Of course, according to the procedure I outlined, RP = the maximum # of circuits which equals 2. If you follow the procedure, five or ten circuits connections are avoided.

The 12 pole winding is symmetrical for one, two, or four circuits (RP=4). For three, six, or twelve circuits there is trouble as defined above.

For any other combination of slots/poles, this procedure results in symmetry 'by my definition'....

What do you think?

 

[rhatcher]

By the way...Merry Christmas and a happy New Year to all!

 

[edison123]

Well done Ray. You explained it all much better than I ever could.

Happy Holidays.

Muthu

http://www.edison.co.in

 

[electricpete]

Thanks Ray. By the way I saved your earlier post for future reference.

I think I understand the google book's definition of symmetry better now (yes I have a copy but I don't understand the darned thing!). The pitch and distribution factors work forwards and backwards - you can either apply a rotating sinusoidal flux and look at induced voltage in the winding, or you can apply a sinusoidal current and look at the resulting mmf. If we have a winding where the voltages induced in each of the three phases are not equal and 120 degrees apart...then when you turn it around and apply current the fundamental flux it will not be pure circular rotating vector of constant magnitude. We ONLY get that if the three vectors we add are exactly equal magnitude and 120 degrees apart. So it is closely related to balance. The symmetry I defined above (a identical to b except for a shift) would be seem to be a sufficient but not necessary condition to establish the book definition of symmetry.

Attached I have tried to analyse the 10-pole winding and the 12-pole winding configurations that you described above.

The 10 pole has an exactly balanced distribution factor on all three phases (0.955) and the three phases are exactly 120 degrees apart.

The 12 pole has an exactly balanced distribution factor on all three phases (0.852) BUT the three phases are not exactly 120 degrees apart. (I have to admit I didn't see that one coming).

That would not meet the google book definition of symmetry It is also in some manner an imbalance, although I'm not sure what the practical implication would be. (interested in comments).

If we don't correspond again before the Holiday's, have a good one.

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[electricpete]

Whoops. Just found an error in that 12-pole. Stand by for an updated version.

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[electricpete]

Attached I have corrected errors in the 12 pole analysis. It still shows a phase unbalance on the 12 pole and now a slight magnitude unbalance also (0.953 distribution factors for A and C phase, but 0.943 for B phase).

I don't rule out the fact there may be some remaining error in there - either typo or logical error. But B phase was after all the one that looked different than the others.

If you are bored, you are welcome to inspect the logic for yourself. I used excel's complex algebra (requires analysis tookpak add-in). The phasor voltage for slot k was assumed given by Vk = exp(j*k*[p/2]*2*pi/Q).
I just added up all the vector voltages for each phase. If you see any logical or typo error let me know.

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[rhatcher]

Pete, let it go until after Christmas and spend this time enjoying your family and your life, The questions that we are looking at have existed since the first AC motors were designed and they will stll be here waiting for us to ponder and decifer after December 26. Spend the next few days using your brain for fun, not work.

 

[rhatcher]

BTW, I do plan to continue to examine this question further...after having christmas fun first!

 

[electricpete]

After sleeping on it last night (my thoughts did turn to winding factors and symmetric windings ...in between presents, elves, and pecan pie), I am pretty sure the spreadsheet is correct. The 10-pole calc was intended as a validation of the method, I just made some errors when I edited that to convert it to the 12 pole problem which are now corrected. Also it seems confirmed thru the identical nature of A and C phase voltage magnitude and phases (phases are subtle, but if you look carefully A phase and C phase have equal/opposite phase relationship to B phase)... no logical reason to think I made some error on B that didn't apply to A and C... it is the same formula copied.

The book definition of symmetric (simplified/summarized based on my 23 Dec 09 22:16 discussion) is that the voltages induces in the windings by a sinusoidal flux wave would be a balanced 3-phase set.

Considering the vector problem, for a fractional slot design it would seem to be quite a challenge to ever create an EXACTLY symmetric winding any way other than a "geometrically symmetrical" winding (one where B phase is a 120 degree shifted version of A phase etc). Even if we started with a geometrically symmetrical winding, and then tried to exchange coils between phases, I don't think there can be any exact swaps possible.

The computed difference 1% distribution factor definitely means it is not exactly symmetrical. How close is good enough?... I leave it to you guys to comment (I don't know).

I would also like to revisit at some time my comment 23 Dec 09 0:51 – whether deviating from n=2 (C=2 for Ray and slotkodo) in a fractional slot winding should be expected to create noise and vibration problems.

Now that I have written that all down, I am going to take your advice and focus on more important things. Where's that egg nog?

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[rhatcher]

Pete,

It took me a while to be able to view your spreadsheets with the toolkit addon. I am not familiar with the formula that you are using but it does have elements that I recognize. I'd be interesting in knowing how it is derived. That being said, the results are pretty interesting.

The 12 pole case is almost symmetrical. It is close enough that you might say that it is 'practically' symmetrical. This is true for grouping of 233,323,332 or 332,323,233. However, for the cases where the 323 section is the first or last section (ie. 323,233,332 or 332,233,323, etc) it becomes definitely unsymmetrical. Obviously, the order of the grouping is important here to maintain the 'appearance' of symmetry and obviously the case where n=3 (C=3) may not be truly symmetrical (in any grouping). These results from your speadsheet are interesting.

Of course, when you look at the 10 pole case, there is no mistaking the exact symmetry. In fact, when you vary the grouping the result is the same. 33343 gives the same result as 33433, 43333, etc...all exactly symmetrical. In my opinion, these results from your speadsheet are pretty impressive.

So, without fully understanding how you derived these results, I'd have to say that the results do speak for themselves.

About the question from your last post: "whether deviating from n=2 (C=2 for Ray and slotkodo) in a fractional slot winding should be expected to create noise and vibration problems?"

I'm not sure about the premise of the question since it seems to imply that n=2 is the only symmetrical case. The symmetrical 10 pole 96 slot winding we are examining has n=5. We also know that n=1 results in even groups which are symmetrical. As far as I know, the only case where symmetry may be an issue is when n=3. More specifically, according to a reference you cited earlier symmetry is a problem if n is equal to the number of phases (n=2 for two phase or n=3 for three phase).

 

[electricpete]

I'd be interesting in knowing how it is derived

You are probably already familiar with this, but here is an explanation of the spreadsheet / approach.

The spreadsheet is derived from the same principles that are used to derive pitch and distribution factors. The pitch factor for all coils is the same, so it can be ignored for purposes of a phase comparison.

For a 2-pole motor with Q slots, the voltage in each slot can be represented as a vector. All vectors have the same magnitude, but they have a different angle. The angle between vectors is alpha = 2*Pi/Q. The Q equally spaced vectors go from angle alpha to angle 2*Pi (or could have also said from angle 0 to angle [2*pi-alpha]... same thing). The locus of the tips of the vectors forms a circle, traversed once going from slot 1 to slot Q.

Let p be the number of pole pairs.

For a (2*p)-pole motor with Q slots, the voltage in each slot can again be represented as a vector.... The vectors are again the same magnitude but the angle between vectors is now p*2*Pi/Q. The locus of tips of the vectors forms a circle which is traversed p times going from slot 1 to slot Q.

A unit vector at angle theta from a reference axis is represented in the spreadsheet as exp(I*theta), taking advantage of Euler’s identity to take care of all the vector arithmetic details.

The kth slot is at mechanical angle k*2*pi/Q.
The kth slot electrical angle is k*p*2*pi/Q = k*alpha
The kth slot voltage vector is therefore represented as exp(I*k*alpha)

The voltage which would be induced in any phase by a sinusoidal flux is given by the vector sum of voltages induced in all the slots within the phase.

For each phase, compute the distribution factor as follows:
Kd = (Vector sum of voltages) / (sum of voltage magnitudes)
where the sums are carried out over all slots in the phase.

About the question from your last post: "whether deviating from n=2 (C=2 for Ray and slotkodo) in a fractional slot winding should be expected to create noise and vibration problems?"

I'm not sure about the premise of the question since...

I'll see if I can dig up a direct quote to make sure I have not misrepresented what the author said.


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[electricpete]

Addition in bold:
"The vectors are again the same magnitude but the angle between vectors is now alpha=p*2*Pi/Q"

i.e. when p is more than 1, I redefined alpha as shown above

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[zlatkodo]

Hi, Electricpete,
Thank you for your very useful analysis of the unbalanced windings .
I wonder whether there is a publication with specific calculations about which order is best used in unbalansed three-phase windings, for example: for 6 poles (24, 30, 42, 48, 60 and more slots), 12 poles (48 and more slots)?
This publication for all unbalanced windings up to 96 slots (for example) would be very useful for all rewinders worldwide.
Maybe someone gets the idea that deals with this theme (but not only in general but in specific cases).
Zlatkodo

 

[wolf39]

Zlatko:

Your question was whether three-phase low voltage induction motors with 96 slots exist in practice for certain number of poles. Muthu confirmed this, mentioning practical pole numbers of between 6 and 18. I mentioned in my post dated 21 Dec 09 4:10 that 96 slots for a 6 pole motor results in a fractional slot winding with 5 1/3 slots per pole and phase. My experience is in the hydro generator field where wye connected stator windings are common. For such units there is a design prerequisite that fractional slot windings with a denominator (devider) devisible by 3 must be avoided. In the induction motor business, however, delta connected stator windings are utilized quite often. I therefore have to leave this question primarily to the motor specialists but will comment on generator related problems shortly.

Regards

Wolf

http://www.hydropower-consult.com

 

[wolf39]

Zlatko:

A stator winding for a 6 pole motor with 96 slots is physically balanced (symmetrical). However, electrically and mathematically this winding is unbalanced to a certain extent. The number of slots per pole and phase is 5 1/3 and the coil distribution over the stator circumference is asssumed as follows:

Phase A: 5 + 5 + 6 + 5 + 5 + 6 = 32 slots

Phase B: 5 + 6 + 5 + 5 + 6 + 5 = 32 slots

Phase C: 6 + 5 + 5 + 6 + 5 + 5 = 32 slots

With the help of a collegue of mine I was able to determine the following data:

Phase A: Phase voltage 1.000 p.u.
Phase angle 0 degrees

Phase B: Phase voltage 1.000 p.u.
Phase angle 119.58 degrees

Phase C: Phase voltage 0.99809 p.u.
Phase angle 239.79 degrees

If you draw this up on a piece of paper you will find that there is very little imbalance present compared with the ideal case of 3 phase voltages of 1.000 p.u. each, separared by 120 degrees each. However, for a synchronous hydro generator the above unsymmetry would lead to an inverse system phase voltage of 0.00142 p.u. and a zero system phase voltage (if the star point is grounded) of 0.00275 p.u. Assuming an inverse reactance of X2 = 0.20 p.u. and a zero reactance X0 = 0.10 p.u. the resulting phase currents are I2 = 0.007 p.u. (0.7%) and I0 = 0.0275 p.u. (2.75%). In other words, the winding imbalance would not lead to substantial additional losses.

To be continued.

Regards

Wolf

http://www.hydropower-consult.com

 

[wolf39]

Zlatko:

For a 6 pole stator winding with 2 1/3 slots per pole and phase the coil distribution over the stator circumference is assumed as follows:

Phase A: 2 + 2 + 3 + 2 + 2 + 3 = 14 slots

Phase B: 2 + 3 + 2 + 2 + 3 + 2 = 14 slots

Phase C: 3 + 2 + 2 + 3 + 2 + 2 = 14 slots

The resulting phase voltages and phase angles are:

Phase A: Phase voltage 1.000 p.u.
Phase angle 0 degrees

Phase B: Phase voltage 1.000 p.u.
Phase angle 117.83 degrees

Phase C: Phase voltage 0.99148 p.u.
Phase angle 238.92 degrees

The resulting inverse system phase voltage is 0.0082 p.u. and the zero system phase voltage (if the star point is grounded) is 0.0137 p.u. With X2 = 0.20 p.u. and X0 = 0.10 p.u. we get phase currents of I2 = 0.041 p.u. (4.1%) and I0 = 0.137 p.u. (13.7%). Equalizing currents of this magnitude are unacceptable, especially for hydro generators where loss evaluation figures of US$ 10,000 per kilowatt (and even above) were occasionally specified.

Note: A 60 pole hydro generator with 420 slots also has a fractional slot winding with 2 1/3 slots per pole and phase.

The smaller the integer portion of the fractional slot number is the greater the undesirable equalizing currents will be.

Usually there is no need to select a fractional slot number with a denominator devisable by 3. For a 6 pole unit a denominator of 2 would be possible and for a 12 pole unit a denominator of 2 or 4 can be selected. Most critical are 18 pole and 54 pole generators for which only integer numbers or fractional slot numbers with a denominator of 2 are feasible.

Regards

Wolf

http://www.hydropower-consult.com

 

[electricpete]

A stator winding for a 6 pole motor with 96 slots is physically balanced (symmetrical).

As I have previously stated, the definition of symmetrical winding per "Design of Rotating Electrical Machines" is "A winding is said to be symmetrical if when fed from symmetrical supply it creates a rotating field"

My interepretation is that this textbook definition of symmeric winding is the same as balanced winding. Here is my logic: A rotating field implies that the locus of the instantaneous voltage vector (not a phasor) lies on a constant-radius circle and rotates with uniform speed... this occurs only when the induced phase voltages (from a sinusoidal airgap mmf) are balanced. If you take any other set and add together the 3 phase voltages you will get something other than a circle rotating at constant speed.

By your own vector analysis (** see further comments later), this winding does not meet this textbook definition of symmetry.

Now let's look at geometric symmetry (is A phase a shifted version of B phase etc).

If I characterize your 6 pole 42 slot machine sing Ray's terminology, A + B/C = 2 + 1/3
C=3 is the number of pole groups in a repeating pattern
poles/C = 6/3 = 2 = number of repeating patterns.

The repeating pattern that you have described, I would write as:
AB'C A'BC' A'BC' = 223 232 322
(we have to repeat it twice to form the entire 6 pole winding or 20 times to form the 60 pole).

From inspection of the above repeating pattern, we can already see the lack of geometric symmetry: B-phase has a 3-coil group which is never adjacent to two consecutive 2-coil groups. The same statement cannot be made about A and C phases. B phase is not simply a shifted version of A phase. B phase has a different pattern than A and C phases.

The winding does not have geometric symmetry.

Based on above discussion, the 6 pole 42 slot (or 60 pole 420 slot) slot does not meet either definition that I can see. Do you have a different definition of symmetrical winding and a reference for your definition?

** About the vector analysis of the 6-pole 42 slot motor. A + B/C = 2 + 1/3

First of all, I assume that somewhere along the line you have reconsidered your earlier position? ("It doesn't matter whether the phase winding is the result of adding 5 + 5 + 6 voltage vectors or 5 + 6 + 5 or 6 + 5 + 5 voltage vectors. The resulting phase voltage is always the same.") If that were true, there would be no need for any vector analysis... just count the slots, coils, turns per phase or per circuit and your done! I'm not trying to be a stickler, but it was the only controversial subject in this thread and the one we spent the most time on. I'm not used to someone shifting the engine from forward to reverse at 65 mph without even mentioning a gear shift. It leaves me wondering exactly where the heck you are coming from.

Second, attached I have added a tab "6-poleWolf" to my previous spreadsheet to analyse the machine you described. I used the sequence of coils per group:
AB'C A'BC' A'BC' AB'C A'BC' A'BC' = 223 232 322 223 232 322
which I believe corresponds to your
A: 2 2 3 2 2 3, B: 2 3 2 2 3 2, C: 3 2 2 3 2 2
(If it is not correct, let me know).

My calculated distribution factors for this machine are
A, B, C = 0.95152 0.94341 0.95152
The magnitude balance is on the order of 0.0085 = 0.85% = much larger than your magnitude unbalance.

As a curiosity, in the 6-poleAlt tab, I used the EASA Tech Manual table ("Coil Grouping For 3phase Windings) configuration where the repeating pattern is: 322 232 223. The resulting phase vector magnitudes and angle differences are suprisingly EXACTLY the same as Wolf's 223 232 322 (0.85% unbalance), even though the winding looks significantly differerent as you can see at a glance looking at column I.

I assume that one of us has made an error, and I would be interested to pursue resolution of the contradiction in results to find out where the error is. You are welcome to inspect my spreadsheet and ask questions. Alternatively, if you can provide any of your calculation details, I'd be interested.

I agree that for rewinding an existing motor it is common practice that a 96 slot motor might be rewound as 12 or 6 pole during a speed change. That would be supported by the comments of many rewinders here. Also the 6 and 12 pole 96 slot options are shown in the EASA Technical Manual section 3 "Coil Groupings for 3-phase Windings" without any precautions/warnings.

But for a speed change of existing motor, there are constraints that limit our choices to some that an OEM would not choose when designing from scratch. I doubt that an OEM would ever design a new motor this way (C=3). We can see from my Reliance link that 96 stator slots is used for their 8 pole, but not for their 6 pole. I have a feeling that for an OEM designing a new motor from the ground up this type of assymetry (C=3) would be avoided. It is the same sentiment expressed by Wolf: "Usually there is no need to select a fractional slot number with a denominator devisable by 3...." If there are counter-examples of OEM original design configuration with C=3 out there, I'd be interested to hear them.

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[electricpete]

The magnitude balance is on the order of 0.0085 = 0.85% = much larger than your [Wolf's] magnitude unbalance.

Correction, your magnitude unbalance is (1-0.99148)/1 = 0.0085 = 0.85%. Your magnitude unbalance agrees very well with my magnitude unbalance. My apologies on this point.

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