Question for experienced rewinders
Question for experienced rewinders
(OP)
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





RE: Question for experienced rewinders
As for HP, need the machine size.
Purpose - Any purpose, I guess.
Muthu
www.edison.co.in
RE: Question for experienced rewinders
Hi, Edison,
Thank you for your quick response. But just one thing:
I think that it is impossible to make a symmetrical (balanced), three-phase winding for 6 and 12 poles and 96 slots. Am I right?
Regards.
Zlatkodo
RE: Question for experienced rewinders
Muthu
www.edison.co.in
RE: Question for experienced rewinders
Do you have an example diagram for a symmetrical, balanced coil with 6 or 12 poles, 96 slots?
I think that windings for 6 or 12 poles and 96 slots are asymmetric windings. Therefore, they must be unbalanced. The only question is: what we can do to reduce imbalances? There are not many cases where the imbalance can be effectively reduced. But even in these cases, these windings are still unbalanced and should be avoided.
Zlatkodo.
RE: Question for experienced rewinders
Muthu
www.edison.co.in
RE: Question for experienced rewinders
1/ it's possible to balanced winding for 6 & 12 poles with 96 slots. The only requirement for 3 phase balanced winding is that the no. of slots be divisible by 3.
2/- No, it is not an asymmetric winding. You have 32 slots per phase.
I disagree with that. It is NOT only requirement for 3 phase balanced winding is that the no. of slots be divisible by 3.
There are other very important conditions that must be met.
Here we are talking about the three-phase windings with fractional number of slots per phase and per pole , such as: q = 1⅓ or q = 2⅜ etc .
This fractional number we can write in this form: q = A b/c
If q is an integer then the winding is always symmetrical. But if q is fractional number then symmetrical three-phase winding MUST meet two additional requirements:
1/ - Number of poles must be divisible with "c" and
2/ - Number "c" should not be divisible by 3 .
In our case (for 6 and 12 poles and 96 slots) is q = 5 1/3 and q = 2 2/3.
Obviously this is asymmetrical winding.
In all such cases it is necessary to make additional calculations of asymmetry-size . Then we must decide whether such a winding corresponds to a certain motor regarding type ( squirrel-cage or wound-rotor), power and purpose. Asymmetry has a bad impact on the motor: increase of vibration, noise, current, winding-heating ,serious loss of torque ...
I think it was shown that balanced windings are not possible with certain numbers of slots, notably for 6 and 12-pole windings.
If we decide to use such a winding arrangement , previously we must done additional calculations.
Regards
Zlatkodo
RE: Question for experienced rewinders
Edison (Muthu) is right.
For a 6 pole motor the number of slots per pole and phase is 5 1/3. For phase A you have 5 slots for the first pole, 5 slots for the second pole and 6 slots for the third pole. This you repeat once with this phase for poles 4, 5 and 6 and you've filled 32 slots total for phase A. Phase starts with 5 slots, next 6 slots, last 5 slots. With repetition you again filled 32 slots. Phase C starts with 6 slots, next 5 slots, last 5 slots. As you can see, each phase has 32 slots in series and all phases are symmetrical winding-wise.
Regards
Wolf
www.hydropower-consult.com
RE: Question for experienced rewinders
I do not doubt that such a winding we can cram in stator, but I say that it is asymmetrical, unbalanced winding. The fact that it has the same number of coils in each phase, means nothing.
Winding is not symmetrical only because it visually looks symmetrical. There are also symmetrical, balanced windings, which in general do not look visually balanced.
It is asymmetric, unbalanced winding with all the bad qualities that such windings have.
If we decide to use such a winding arrangement , previously we must done additional calculations.
Zlatkodo
RE: Question for experienced rewinders
96 slot, 6/12 pole is known as fractional slot winding and thousands of motors are running with such a winding.
I will simplify futher
96/6 - 4x5 and 2x6 coil groups per phase
96/12 - 8x3 and 4x2 coil groups per phase
Now it is just a question of arranging these coil groups around the periphery to get a "symmetrical, balanced" winding.
Muthu
www.edison.co.in
RE: Question for experienced rewinders
zlatkodo:
Phase A: 2 x (5 + 5 + 6) = 32 slots
Phase B: 2 x (5 + 6 + 5) = 32 slots
Phase C: 2 x (6 + 5 + 5) = 32 slots
Total 96 slots
Each of the 6 poles has a slot number of 16.
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.
Regards
Wolf
www.hydropower-consult.com
RE: Question for experienced rewinders
Your question:
"zlatkodo - Can you please define asymmetrical unabalanced winding ?"
If you carefully read my previous posts, you can find there a precise definition of three-phase unbalanced windings.
But I'd like to read your definition, because you say:
"The only requirement for 3 phase balanced winding is that the no. of slots is divisible by 3."
Does this mean in practice that unbalanced thee-phase windings do not exist at all?
Regards.
zlatkodo
RE: Question for experienced rewinders
Yes. The only requirement of 3 phase balanced winding is that the no. of slots be divisible by 3.
I am out.
Muthu
www.edison.co.in
RE: Question for experienced rewinders
Muthu:
I may add that the number of slots per phase and the number of turns per phase is equal.
Regards
Wolf
www.hydropower-consult.com
RE: Question for experienced rewinders
Guess you don't like things unsaid.
Muthu
www.edison.co.in
RE: Question for experienced rewinders
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RE: Question for experienced rewinders
ht
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RE: Question for experienced rewinders
Q = 96
p=12
m=3
q = 96/36
we have z/n is q expressed as lowest fraction 8/3
z = 8
n = 3
Look at table 2.6 conditions of symmetry, last item (three phase m=2).
It requires that n/m is not a whole number
we have n/m = 3/3 =1 is a whole number
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RE: Question for experienced rewinders
http://b
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RE: Question for experienced rewinders
http://www.reliance.com/mtr/pcrss.htm
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RE: Question for experienced rewinders
For Q = 96, 2.84 implies Q0 must be 6, 12, 18 etc
For Q = 96, 2.86 implies Q0 must be 3, 9, 15 etc
There is no Q0 that satisfies both 2.84 and 2.86 when Q=96. I conclude there is no way to create a symmetric 96 slot machine even by leaving slots empty. But that's just going by what I read at that link (and assuming I didn't make any mistakes). I guess doing a full vector diagram provides better insight as to what is the degree of imbalance, and apparently must be small if 96 is used by Reliance.
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RE: Question for experienced rewinders
(Should've have said no way to create symmetric 96 slot machine for 6 or 12 pole.)
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RE: Question for experienced rewinders
Muthu
www.edison.co.in
RE: Question for experienced rewinders
Noise/vibration is also a consideration. The same reference I linked above suggests n=2 is required for fractional slot winding to avoid subharmonic noise/vibration. The 12/6 has n=3. How much a problem it is I don't know - it is somewhat mysterious to me.
We have two sets of large fractional slot machines at our site: one is 800 hp 900 rpm. The other is 3500 hp 324 rpm. During uncoupled run in the repair shop, you can stand right next to them and can't tell theyr're running. When under load, they SCREAM. And I have to put scream in capital letters because there is no other way to describe the noise. The 324 rpm 3500 hp are about a mile from the parking lot, and I can tell whether they're running when I get out of the car in the parking lot each morning. I don't know how much this is related specifically to fractional slot design features of these motors... it is just something I have always associated with fractional slot windings in general based on these two.
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RE: Question for experienced rewinders
I can assure you, there are some windings that look completely odd ball, but it takes effort and time to analyze it to determine whether or not it affects operation. In general if you speak with the winding engineers regarding some odd configurations, I've always had a good technical answer.
Even if it's unbalanced, you can likely still run. Which is the case ones you start bypassing stator coils.
RE: Question for experienced rewinders
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RE: Question for experienced rewinders
Hi, Electricpete,
Thanks for useful link (Reliance).
You wrote:
I guess doing a full vector diagram provides better insight as to what is the degree of imbalance.
That's true. Right way to know what is the degree of imbalance is doing a vector diagram to see
how much the angle of mmf -vectors deviate from the ideal direction and what is the percentage difference in the size of these vectors.
If these differences are in the allowed limits (for a particular purpose, power and motor-type), then the winding can be used... Otherwise, this test should be repeated but with a different coil-order . It should be noted that the minimum imbalance is often achieved with the order in which is no repetition (repetition is not necessary). Of course, it is suitable for small power motors, because in that case we can not do parallel circuits.
Regards.
Zlatkodo
RE: Question for experienced rewinders
Fractional slot windings are perfectly balanced windings electrically if all phases have the same no. of coils and same total no. of turns. But the magnetic balance spatially around the periphery has to be obtained by proper placing of the coil groups around the machine so that there is no uneven magnetic pull.
Your scream problem seems interesting. It is normally due to improper stator/rotor slot design. IIRM, excessive skewing of slots creates a noise. Have you talked to the OEM about that issue ?
Muthu
www.edison.co.in
RE: Question for experienced rewinders
I have a hard time believing that one. If we looked at voltage induced in the coils by the main flux wave, each coil has a different phasor voltage induced by virtue of different position relative to main flux wave. So looking at number of coils can't guarantee anything. If conditions are not met, then it's never going to be exact. There are lots of tricks you guys mentioned to get it close, but it can't be perfect.
The scream problem - both motors are 25 years old - 2 different OEM's, one out of business and one not particularly responsive. The fact that it occurs on 2 for 2 of our families of large fractional slot motors (and nothing like it on about 20 families of higher speed motors) makes me think it is relatively commomn among fractional slot motors. If not all fractional slot motors, then there is something to do with the design... maybe some obscure rule related to slot selection.
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RE: Question for experienced rewinders
To answer the OP's question: For 96 slots; 2, 4, 8, and 16 poles results in an even group (integral slot) winding. This means that the number of coils per pole group is the same for all pole groups. This is the easiest winding to perform. In a general case, you will usually find integral slot windings on standard design motors. The manufacturer uses different stators to acheive integral slot windings for different pole combinations. For this reason, integral slot motors are more common than fractional slot motors.
If you are limited to a fixed number of stator slots, in this case 96 slots, you can still design a symmetrical winding at different speeds using an odd group (fractional slot) winding. For 96 slots; 6, 10, 12, 14, 18, 20, and 24 poles results in odd groups.
electrcipete's link gives conditions of symmetry. If we agree that there is no problem when n/m is not = 3/3 then we have agreed that for 96 slots the 10, 14, 18, and 20 pole windings would be symmetrical.
The question comes up when n/m = 3/3 such as the case for 6, 12, and 24 poles. The link suggests that this results in a non-symmetrical winding and to a certain degree, this is true. The reason is that mathematically this results in an odd grouping where the number of groups in a section is equal to the number of phases. For a 96 slot six pole, this results in a grouping of 556. When you repeat this through the phases (a,b,c) you get 556,556,556. Obviously C phase has too many coils.
The solution that is not addressed by the link is that in this case the section grouping must be varied for three sections to result in a symmetrical winding. So, the proper grouping would be 556, 565, 655. Wolf39 correctly demonstrated this when he wrote:
Phase A: 2 x (5 + 5 + 6) = 32 slots
Phase B: 2 x (5 + 6 + 5) = 32 slots
Phase C: 2 x (6 + 5 + 5) = 32 slots
Total 96 slots
Each of the 6 poles has a slot number of 16.
If you constructed this winding, it would be electrically and magnetically symmetrical. However, as suggested by electricpete and zlatkodo, I suspect that this arrangement may not result in a perfectly sinusiodal mmf wave in the air gap. But, the imperfection will be symmetrical.
RE: Question for experienced rewinders
I agree perfect isn't necessary.
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RE: Question for experienced rewinders
On page 239 he defines
Ng = N1 / (p q) = A / B
Ng is slots per group, plays the role of previous q
N1 is total slots plays the role of previous Q
p is poles
q is phases, plays the role of previous m (3)
B plays the role of previous n. It is the number upon which both of the cited symmetry conditions apply.
Page 243 begins an example. 150 slots, 12 pole. It has B=6 (similar to n=6 in previous) which does not meet the symmtery. He shows at the bottom of page 239 that coils are judiciously regrouped to optimize resulting in same number of coils per phase.
But it is not a perfect balance. I assume it is a similar regrouping that you guys are talking about.
I am not a winder, and I could be wrong. But I think you guys are talking about getting close but not perfect just like the example in the link above.
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RE: Question for experienced rewinders
should have been
" He shows at the bottom of page 243 that coils are judiciously regrouped to optimize resulting in same number of coils per phase."
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RE: Question for experienced rewinders
Here is my previous attempt:
556 565 655 556 565 655
This particular one doens't seem symmetric to me because the 6-coil B groups have another phase 6-coil group 2 groups away on both sides. While the 6 coils a and c groups have distance 4 to the next 6-coil group on one side. So if I were looking just at the sequence, I can see there is something different about B phase than A phasel That doesn't seem symmetric to me. Would you call it symmetric?
I am open to the idea there is another way to insert the 5's and 6's to create symmetry, but I sure can't see it.... so if you can provide one, that would help.
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RE: Question for experienced rewinders
Balanced means the same voltage is induced in each phase (or circuit).
Symmetric to me means 3-phase symmetry. I can't tell A from B from C by looking at it. That symmetry also creates a pure rotating flux pattern (although it surely has spatial harmonics). I don't think we get a pure rotating flux pattern unless we have the three-phase symmetry.
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RE: Question for experienced rewinders
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I assume symmetry is a sufficient but not necessary condition for balance.
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RE: Question for experienced rewinders
1)determine # of groups = poles * phases = 12 poles * 3 phases = 36 pole groups
2)Determine # coils per group = slots/group = A B/C = 96/36 = 2 2/3 If A B/C is a whole number, the grouping is even and you can stop with this portion of the design and skip to step 8 (design the connection, # turns, etc.) If the result is a fractional number, the result A B/C tells you this; some groups will have A coils, some will have A+1 coils, C is the number of pole groups in each section with a section being the number of poles to until the pattern repeats.
3) Determine # of repeatable patterns = poles/C = RP = 4 This is the number repeatable pattern in the winding and the maximum number of parallel circuits.
3) Determine # groups with 'A' coils = 3 * RP * (C-B) = X = 12
4) Determine # group with 'A + 1' coils = 3 * RP * B = Y = 24
5) Determine # groups per section with 'A' coils = C * X/groups = 36/36 = 1
6) Determine # group per section with 'A + 1' coils = C * Y/groups = 72/36 = 2
7) If C does not equal 3 or a (multiple), you have determined the section grouping. According to the reference you have also made a symmetrical fractional slot winding. To demonstrate what happens in this case, if you went through the steps for 10 pole 96 slot, C = 5 and at this point you would know that the section grouping is 33343 and the number of repeatable patterns in the winding is 2. You divide the section into three phases and repeat the section three times to finish one repeatable pattern. Then you repeat once more (RP=2). You get:
333,433,334,333,343/,/333,433,334,333,343 = 96 slots 10 pole // separates the two repeatable patterns
In the 12 poles 96 slot example we are looking at, C = 3, the section grouping is 233 (or 232 or 332), and the repeatable patterns is 4. The section grouping is problematic since it would result in a winding that is 233,233,233...where there is obvious unbalance. In this case you vary the section grouping for three sections to form a repeatable pattern. Specifically, instead of repeating the same section three times to get a repeatable pattern you vary the section three different ways to get a repeatable pattern. Then you repeat that pattern 4 times (RP=4). You get:
233,323,332/,/233,323,332/,/233,323,332/,/233,323,332 = 96 slots 12 poles // separates the 4 repeatable patterns.
8) The final step is to design the connection, the number of parallel circuits, and the number of turns.
Now, if you at the difference in 'symmetry' between the 10 pole/C=5 and the 12 pole/C=3, there does not appear to be a difference. It makes me wonder why the first reference that you brought said that C=3 cannot result in symmetry.
Anyway, I have some thoughts on how symmetrical this really is in the vector sense that you are thinking about and what things to consider when looking at this. However, I am out of time for now so I'll come back later.
Pete...I hope this helps and I hope I didn't make any mistakes. Let me know what you think.
RE: Question for experienced rewinders
I have to admit that definition throws me a little. Is it the same as my definition? Or is it the same as my definition of balance? How do you define symmetry?
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RE: Question for experienced rewinders
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RE: Question for experienced rewinders
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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RE: Question for experienced rewinders
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?
RE: Question for experienced rewinders
RE: Question for experienced rewinders
Happy Holidays.
Muthu
www.edison.co.in
RE: Question for experienced rewinders
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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RE: Question for experienced rewinders
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RE: Question for experienced rewinders
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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RE: Question for experienced rewinders
RE: Question for experienced rewinders
RE: Question for experienced rewinders
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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RE: Question for experienced rewinders
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).
RE: Question for experienced rewinders
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.
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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RE: Question for experienced rewinders
"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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RE: Question for experienced rewinders
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
RE: Question for experienced rewinders
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
www.hydropower-consult.com
RE: Question for experienced rewinders
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
www.hydropower-consult.com
RE: Question for experienced rewinders
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
www.hydropower-consult.com
RE: Question for experienced rewinders
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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RE: Question for experienced rewinders
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RE: Question for experienced rewinders
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RE: Question for experienced rewinders
"For such units there is a design prerequisite that fractional slot windings with a denominator (devider) devisible by 3 must be avoided."
When you say denominator, do you mean no. of poles like 6, 12, 18 etc. (even multiples of 3) ?
Hi pete - I have downloaded your spreadsheet. Thanks. Let me see if I'm capable of learning something from it. :)
Muthu
www.edison.co.in
RE: Question for experienced rewinders
q = Q/(m*p) = A + B/C
Q = Slots
m = phases
p = poles
q = slots per pole phase group
B/C is the fractional part of q expressed as a lowest fraction.
The quoted references suggest C=3 is to be avoided to preserve balance. Although the degree of unbalance can be quite small as in Wolf's 6-pole 96 slot example.
======================
The spreadsheet requires the analysis tookpak. I think the calculation is pretty simple, but my explanation and spreadsheet made it look more complicated than it really is. It can all be summarized in one equation:
Vk = exp(I*k*[p/2]*2*pi/Q)
where
Vk is voltage in kth coil
I=sqrt(-1) is used to give complex representation of the vector in the complex plane based on Euler's identity (exp(I*x) = cos(x) + I*sin(x))
After that you just add up the vectors of voltages of coils in each series leg and compare them.
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RE: Question for experienced rewinders
Muthu
www.edison.co.in
RE: Question for experienced rewinders
When n is equal to 3, we cannot create a fractional slot winding that has geometric symmetry and therefore we can expect some degree of unbalance. Ray's 12 pole 96 slot example and Wolf's 6 pole 42-slot and 6-pole 96 slot are exmples of this.
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RE: Question for experienced rewinders
I am attaching excerpts out of WINDING ALTERNATING-CURRENT MACHINES (A Book for Winders, Repairmen, and Designers of Electric Machines) By Michael Liwschitz-Garik & Assisted By Celso Gentilini, I hope that they will help the discussion and verify some of the exceptional work that appears on this thread. This book is by far my favorite as a re-winder, the fact that it is dated helps out when I come across some old 2 phase water turbine generators. It has all of the charts, tables and formulas for most of what is being discussed here (although most is over my head).
Thank You
RE: Question for experienced rewinders
RE: Question for experienced rewinders
The case where the denominator (C or n) equals the number of phases seems to be problematic. The problem appears to be that since the section pattern is equal to the number of phases that this results in unbalance. I agree at this point that this (C=3 for 3 phase or C-2 for two phase, etc.) is a 'special case'. However, I am not convinced of the reason why this is imbalanced.
Since you appear to be posting based on 'google book' references, perhaps you can show us the reference that explains your ideas and that derives the equations:
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)
Are you sure that this equation applies to the general case (any number of poels) and not specifically to a two pole winding ( 2 * PI)?
Also, your reference to the EASA Technical Manual is interesting since you said that; "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." Are you implying that the 'Easa Technical Manual' is wrong or are you saying that the Easa Tech. Manual correctly contradicts your point?
RE: Question for experienced rewinders
The excerpt quoted is correct as written but I think the shifting of p into the definition of alpha (alpha is electrical angle here) could be misleading:
where in this case p was defined as pole pairs
We can deduce from the statement "k*p*2*pi/Q = k*alpha" that alpha = p*2*pi/Q. So the angle of the kth slot voltage vector is the same as the slot electrical angle.... k*p*2*pi/Q. If p=1 (2-pole motor), then the angle is 2*pi/Q = 360deg/Q.... same as mechanical angle... as expected for 2-pole. For more poles pairs, the factor of p included in electrical angle alpha increases electrical angle for the same mechanical angle.
What is tricky is that in the spreadsheet alpha was strictly the mechanical angle... no p included there.... but I multiplied alpha by p before I plugged it into the argument so it still works. Same results, sloppy notation. Sorry.
Also in some places I used p = poles and some places (like this message) p = pole pairs. I try to define it each time.
The method of the spreadsheet is based on the same principle that is used for developing distribution factor (see Fitzgerald or other books). Again, once you have an expression for voltage in a coil like exp(I*k*p*2*pi/Q) , just add up the voltages. Starkopete had a reference... but we can't see it. (Did you click the "insert link" button?)
EASA isn't specific, but the fact they include it with no warning I interpret to mean the results will definitely not be catastrophic and probably be "acceptable". But there will be an unbalance and I suspect an OEM would not design one this way.
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RE: Question for experienced rewinders
Muthu:
Pete explained your denominator question perfectly well. Every fractional slot winding with a denominator devisible by 3 is unsymmetrical.
q = A + B/C
The lower the A number the higher the imbalance.
The higher the C number (still devisible by 3) the lower the imbalance.
Also, for a 60 pole 420 slot winding it may be possible to minimize voltage imbalances by re-grouping stator coils or stator bars.
Regards
Wolf
www.hydropower-consult.com
RE: Question for experienced rewinders
Pete:
Yes, I was wrong to say that adding 5 + 5 + 6 or 5 + 6 + 5 or 6 + 5 + 5 voltage vectors lead to identical phase voltages. This I found out when further investigating on this topic (see my post dated 3 Jan 10 7:06). I'm sorry to have shaken you by shifting gear from forward to reverse. But what you mean by saying
"It leaves me wondering exactly where the heck you are coming from".
This remark somehow tells me that I irritated you with my views. This was not my intention, I assure you. As a generator designer I'm familiar with stator windings but must admit that I'm not a winding specialist.
Regards
Wolf
www.hydropower-consult.com
RE: Question for experienced rewinders
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RE: Question for experienced rewinders
RE: Question for experienced rewinders
Pete:
You've quoted a definition of a symmetrical winding from a publication as follows:
"A winding is said to be symmetrical if when fed from symmetrical supply it creates a rotating field".
I'm also sceptical about this statement. We all agree now that the 96 slot 6 pole winding is unsymmetrical. Nevertheless a symmetrical supply obviously creates a rotating field in this unsymmetrical stator winding and the motor works as expected.
An internet source confirmed my suspicion that the inversely rotating magnetic field causes a negative (breaking) torque, thus reducing the motor output. The motor bearings may suffer mechanical damage because of the induced torque components at double system frequency and the rotor is heated up which may lead to faster thermal ageing. We therefore agree with each other that no competent OEM would choose fractional slot windings with a denominator devisible by 3. Instead of a 96 slot winding for a 6 pole motor it would be advisable to select 5 1/2 slots per pole and phase to obtain a symmetrical 99 slot winding. An additional way to fine-tune a multiple-turn coil winding would be to modify the number of turns per coil.
When I previously mentioned that the 96 slots 6 pole winding is physically balanced (symmetrical) I had in mind the winding appearance. Looking from the non-connection side you couldn't tell which coil numbers (slot numbers) belong to a group of 2 or 3. And there are no empty slots.
I may have been wrong to treat as equivalent the terms "balanced" and "symmetrical". The term "balanced" can be expressed as
reasonably balanced
nearly/almost balanced
balanced
well balanced
perfectly balanced
whereas the term "symmetrical" to me implies that something is perfect. But I may be wrong here. English is not my native language.
In this context I found in the internet a definition as follows:
"A three-phase power system is called balanced if the three-phase voltages and currents have the same amplitude and are phase shifted by 120 degrees with respect to each other. It is assumed that the waveforms are sinusoidal". This definition may satisfy all of us.
It is possible to quantify an imbalance in voltage or current of a three-phase system. European standard EN 50160 gives limits for the unbalance ratio of less than 2% for LV and MV systems and less than 1% for HV systems, measured as 10-minutes values, with an instantaneous maximum of 4%. As we can see certain standards even specify an allowance for the term "balanced". The only problem I see is this one: A phase voltage related imbalance of 1% may be permissible by the EN 50160 standard. With an inverse reactance of X2 = 0.20 p.u. this leads to a current imbalance of 5% which doesn't seem to be acceptable standard-wise nor may this be acceptable loss-wise for stator and rotor.
Regards
Wolf
www.hydropower-consult.com
RE: Question for experienced rewinders
The book Winding Alternating-Current Machines (Liwschitz-Garik) refers to balanced & unbalanced fractional-slot windings. From the book:
"Conditions of Balance. It has been mentioned that in this chapter only the balanced fractional-slot windings will be considered. These are the windings for which
No.of poles/d = an integer
d/No. of phases = fractional number
When these 2 conditions are satisfied, the winding is balanced, i.e., the voltages generated in the phases have the same magnitude and are displaced from each other by the same angle."
Thanks
RE: Question for experienced rewinders
If you read my earlier post from 21. Dec. 09. 3:46:
"But if q is fractional number then symmetrical THREE-PHASE winding MUST meet two
additional requirements:
1/ - Number of poles must be divisible with "c" and
2/ - Number "c" should not be divisible by 3 ."
then you can see, this is the same thing.
Zlatkodo
RE: Question for experienced rewinders
You are correct, they are the exactly the same thing.
Thanks
RE: Question for experienced rewinders
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